what if?

Could I cool down the Earth by capturing a comet and dropping it in the ocean, like an ice cube in a glass of water?Daniel BeckerNo. In fact, it's honestly sort of impressive to find a solution that would actively make the problem worse in so many different ways.Dropping a comet into the ocean to cool the planet, famously suggested by the 2002 Futurama episode None Like It Hot,[1] wouldn't work for a few reasons.One is that dropping things from space creates heat. When water-or anything else-falls, it gains kinetic energy. When it stops falling, that energy has to go somewhere. Generally, it turns into heat. Water that goes over Niagara Falls, for example, gains enough kinetic energy during the 50-meter plunge to warm it up by about 0.1C by the time it reaches the bottom. (This added heat is minor compared to the cooling effects of evaporation on the way down, so the actual temperature at the bottom is likely colder.)Outer space is a lot higher up than Niagara Falls, so the plunge down into the atmosphere at the bottom of Earth's gravity well adds a lot more than 0.1 degrees worth of heat. A chunk of ice from space that falls to Earth gains enough energy to warm the ice up, melt it, boil it into vapor, and then heat the vapor to thousands of degrees. If you built an icy waterfall from space, the water would arrive at the bottom as a river of superheated steam.Small chunks of ice falling from space disintegrate and boil away before they reach the ground, warming the upper atmosphere. Large comets can reach the ground intact and be vaporized on impact as their kinetic energy is converted to heat all at once. This heat energy would be about 100 times greater than the energy needed to bring even a very cold comet up to room temperature, so a comet falling from space would heat the Earth 100 times more than it cooled it.But let's suppose you figure out a way to lower the comet slowly, using some kind of magical crane,[2] and gently set the comet in the ocean.Comets are more dust than ice, but they're not particularly dense. A tiny piece of a comet would float for a short time until it became waterlogged, melted, and broke apart. A full-size comet wouldn't be strong enough to support its own weight, and would collapse like a drying sand sculpture.If the comet were placed in the ocean,[3] the added ice would cool the water down by only about a millionth of a degree. If you set the comet on land, it would soak up heat from the atmosphere-which contains much less stored heat than the oceans-briefly cooling the air by an average of one or two thousandths of a degree.Okay, so we just need thousands of comets, right? Each one will cool the air a little bit. With a large enough supply of comets, we can keep the Earth nice and cool, as long as we make sure they're lowered slowly.Unfortunately, comets would affect the Earth's temperature in another way. In addition to dust and water, they contain a small amount of CO, which would be released into the atmosphere as the comet melted. This CO[4] would change Earth's radiation balance, trapping heat near the surface and raising the planet's temperature. After a few years, the comet's greenhouse effect would have trapped more heat than the ice absorbed, and over the decades to follow, the extra heat would keep piling up.The CO released from the comet would raise the temperature of the Earth for centuries. It wouldn't just cancel out the cooling effect of the ice-over time, the comet's greenhouse effect would deliver as much heat as if you'd just let it slam into the planet and vaporize.[5]It's okay. Despite all this, your scenario could fix global warming.Remember that hypothetical crane that lets you lower comets to the surface? Well, if you hooked it up to a generator, you could use the slowly-descending comet to produce electricity.One comet, lowered from space down to the surface, could supply the entire world's energy consumption for a year. Sure, it would release a little CO, but it would be nothing compared to the pollution from our current sources of energy. A comet crane generator could cut our energy-related greenhouse gas emissions to almost zero. The comet isn't the important part, the crane is.Sadly, we don't have the technology to build comet-lowering cranes-certainly not in time to help mitigate climate change. But harvesting orbital energy like this is a neat idea! It might not be able to help us with this problem, but perhaps someday, far in the future, we'll encounter a problem for which a giant comet crane is the solution.[1] I'm used to stuff making me feel old, but the fact that this episode aired 20 years ago is distressing in multiple ways.[2] Magical storks deliver babies, magical cranes deliver comets.[3] It actually wouldn't have much effect on global sea level, but the influx of cold water on the surface-and the dust released into the air-could definitely mess with the atmosphere.[4] Along with carbon monoxide, which indirectly affects the climate in a similar way-see pg. 718-719 of the IPCC WG1 AR5 report for more.[5] Although letting a comet slowly decay on the surface would definitely be preferable to a high-speed impact, as any dinosaur from the end of the Cretaceous can tell you.

If every country's airspace extended up forever, which country would own the largest percentage of the galaxy at any given time?Reuven LazarusToday's question is adapted from What If 2: Additional Serious Scientific Answers to Absurd Hypothetical Questions, which contains many more What If answers and is available now!Congratulations to Australia, new rulers of the galaxy.The Australian flag has a number of symbols on it, including five stars that represent the stars of the Southern Cross.[1] Based on the answer to this question, maybe their flag designers should think bigger.Countries in the southern hemisphere have an advantage when it comes to star ownership. Earth's axis is tilted relative to the Milky Way; our North Pole points generally away from the galaxy's center.If each country's airspace extended upward forever, the core of the galaxy would stay under the control of countries in the southern hemisphere, changing hands over the course of each day as the Earth rotates.At its peak, Australia would control more stars than any other country. The supermassive black hole at the core of the galaxy would enter Australian airspace every day south of Brisbane, near the small town of Broadwater.After about an hour, almost the entire galactic core-along with a substantial chunk of the disk-would be within Australian jurisdiction.At various times throughout the day, the galactic core would pass through the domain of South Africa, Lesotho, Brazil, Argentina, and Chile. The United States, Europe, and most of Asia would have to be content with outer sections of the galactic disk.The northern hemisphere isn't left with the dregs, though. The outer galactic disk has some cool things in it-like Cygnus X-1, a black hole currently devouring a supergiant star.[2] Each day, as the core of the galaxy crossed the Pacific, Cygnus X-1 would enter the United States's airspace over North Carolina.While owning a black hole would be cool, the United States would also have millions of planetary systems constantly moving in and out of its territory-which might cause some problems.The star 47 Ursae Majoris has at least three planets and probably more. If any of those planets have life on them, then once a day all that life passes through the United States. That means that there's a period of a few minutes each day where any murders on those planets technically happen in New Jersey.Luckily for the New Jersey court system, altitudes above about 12 miles are generally considered "high seas." According to the American Bar Association's Winter 2012 issue of the Admiralty and Maritime Law Committee Newsletter, this means that deaths above these altitudes-even deaths in space-are arguably covered by the 1920 Death on the High Seas Act, or DOHSA.But if any aliens on 47 Ursae Majoris are considering bringing a lawsuit in a US court under DOHSA, they're going to be disappointed. DOHSA has a statute of limitations of 3 years, but 47 Ursae Majoris is more than 40 light-years away......which means it's physically impossible for them to file charges in time.[1] Epsilon Crucis has five points, while the others have seven, implying that the view of Epsilon is from a telescope with different lens geometry from the others. Minor symbolic/graphic design choice? Or clue to a secret multiversal alliance between parallel universe Australias? No way to know for sure![2] Cygnus X-1 was the subject of a famous bet between astrophysicists Stephen Hawking and Kip Thorne over whether it was a black hole or not. Hawking, who had spent much of his career studying black holes, bet that it wasn't. He figured that if black holes turned out not to exist, at least he would win the bet as a consolation prize. In the end, luckily for his legacy, he lost.

My daughter recently received her driver's permit in the US, and aspires to visit mainland Europe someday. She has learned enough about the rules of the road to know never to drive into the ocean; however, she jokingly suggested that given a sufficient quantity of rental cars, she could eventually get to Europe by driving east repeatedly. The question is, how many vehicles would it take to build a car-bridge across the Atlantic?Eric MunsonAfter extensive research, I can conclusively state that this would be a violation of your rental car agreement.Also, you would disrupt ocean circulation in the North Atlantic, potentially seriously altering the climate in the northern hemisphere. That's very bad, although not necessarily a violation of your rental car agreement.If you try to drive from the US to Europe, your car will stop working pretty quickly, since according to Google Maps there's a large hole between them and it's full of water. Once your car gets stuck, you'll have to leave it there and go get another one.Driving your second car onto the roof of the sunken first one could get you a little closer to Europe. If we assume you're starting in Boston and heading toward Lisbon, using a car as a bridge would get you about a millionth of the way there, since Boston and Lisbon are about a million car-lengths apart. If the Atlantic Ocean were two feet deep, you could make a bridge out of a million cars placed end to end. Unfortunately, a quick rewatch of Titanic (1997) suggests that the Atlantic Ocean is more than two feet deep. You'll quickly have to start piling up cars in multiple layers.At first, when the bridge would be just one or two cars high, you could stack them in a single vertical column. But as the water gets deeper, you'll need to create a wider base to keep the wall of cars from tipping over.[1] The North Atlantic current would push against the car causeway, but the tipping force from the water motion would be relatively minor compared to the pile's tendency to topple under its own weight.[2]As you built your bridge out into the deep ocean, the cars on the bottom of the stack would be crushed. The pressure crushing them wouldn't be the water pressure. Once the windows broke and the interior of the car flooded, the pressure would equalize and the cars would hold their shape, relatively unaffected by the weight of the ocean above them. Instead, what would crush the cars would be the weight of the other cars sitting on top of them.Even when they're underwater, cars weigh a lot. About 50% of the weight of modern cars is steel and iron, which is much denser than water,[3] so submerged cars are still quite heavy-about 60% to 70% of their surface weight, depending on their exact composition. The cars on the bottom of a mile-high stack would be subjected to extreme pressures, even greater than what they experience in hydraulic car crushers. Those crushers[4] are capable of flattening a car into a pancake a foot or two thick, and the same thing would happen to the cars on the bottom of our stack.The first part of your bridge to Europe would be over the continental shelf, where the water is relatively shallow-just a few hundred crushed cars deep.You'd still need a lot of cars to form this shallow-water portion of the bridge; getting out to the edge of the continental shelf would take about a billion of them, which is probably close to the total number of cars in the world. Parking lots hold about 1 car per 30 square meters, so a billion cars would cover a large portion of eastern Massachusetts.[5]After the continental shelf, the water gets a lot deeper. The deep-ocean portion of your bridge would require a lot more cars-likely about a trillion of them. This is far more cars than exist in the world; a parking lot big enough to hold them would take up most of the Earth's land area.So you can't rent anywhere close to a billion or a trillion cars-Enterprise, for example, only has about half a million cars in its fleet. But if you tried, you'd run into other problems, too. I got a copy of a recent Enterprise rental car agreement, and I have some bad news:

My 4 year old son and I were wondering about soccer ball sized hail today. How much damage would a hail storm with size 5 soccer ball sized hail do?Michael GrillWhen you think about it, it's honestly kind of weird that hailstones haven't killed all of us already. I mean, they're chunks of ice that plunge from the sky!Hailstones fall from really high up. There's a popular myth that a penny dropped from the Empire State Building can kill you. The myth isn't true,[1] but for anyone who believes it, hailstones should be terrifying-after all, they often fall from the height of ten Empire State Buildings.Luckily, the same thing that saves us from falling pennies also generally protects us from hailstones: Air resistance. As they fall, both pennies and hailstones quickly reach terminal velocity, the speed at which drag balances out gravity and prevents them from speeding up any more. For a small hailstone the size of a pea or a marble, terminal velocity might be only 10 or 20 miles per hour, the speed of an object tossed across a room. Getting hit by them isn't comfortable, but it's not likely to cause serious injury.[2]Large hailstones travel much faster than small ones and can be a lot more dangerous. The terminal velocity of a golf-ball-sized hailstone is about 60 miles per hour,[3] which could easily cause serious injury. Large hailstorms often cause extreme damage to cars, and the largest hailstones can be deadly. A storm in China in 2002 dropped egg-sized and baseball-sized hailstones that killed several dozen people and hospitalized many others.Luckily, deaths from hail aren't very common, for two main reasons: First, because hailstones big enough to be deadly are rare, and second, because when there's a thunderstorm severe enough to produce such large hail, people generally try to take shelter.A hailstone the size and shape of a regulation soccer ball would be more than twice the weight of the heaviest hailstones on record. It would have a terminal velocity of roughly 140 miles per hour, which is really fast. If one of them hit your car, it wouldn't just dent the body or crack the windshield, it could punch right through the roof. Sheltering indoors might not be enough to protect you, unless you had a particularly sturdy roof or possibly several floors above you.When a hailstorm is nearby, it's good to take shelter even if you're not right below the storm. As a hailstone forms in a thunderstorm updraft, it bounces around like popcorn in a popcorn machine. Usually, it falls out of the bottom of the storm, but sometimes it's ejected out of the top or sides, then carried by wind to fall some distance from the storm. Aircraft flying near thunderstorms have been hit by hail when they have nothing but blue sky above them.Real hailstones, especially large ones, aren't round like a soccer ball. As they tumble around in a thunderstorm, they grow via water freezing onto their sides. If they have a lump on one side, the protrusion can collect more water and grow faster than the areas around it, forming a blobby appendage. Liquid water can also run out to the edges of a rotating hailstone and freeze, forming icicle-like features.The weird shapes of large hailstones are good news for us ground-dwellers with breakable bones, because these protrusions tend to increase their drag and lower their terminal velocity.But the weird shapes of hailstones also raises an interesting possibility. If a hailstone had just the right combination of lobes, it's possible-if unlikely-that it might happen to form a lifting body. This strange category of aircraft-which includes the Space Shuttle, the M2-F1, and the Dream Chaser-can be unexpectedly aerodynamic despite their compact shapes, capable of gliding or even swoops.It's unlikely that any gliding hail has ever been observed, but in the 4 billion years that Earth has had water and thunderstorms, there have probably been some pretty strange hailstones. Not only has there likely been one the size of a soccer ball ...... there might even have been one able to score a goal.[1] Mythbusters tried it in Season 1 Episode 7 and found that the penny would really sting and make you go "ow!!"[2] While dropping a penny on someone from the height of the Empire State Building wouldn't kill them, dropping the Empire State Building on a them from the height of a penny would, as demonstrated by the tragic demise of Jebediah Mythbuster in the pilot episode of the show eventually named in his memory.[3] A little slower than an actual golf ball, thanks to the golf ball's greater weight and those weird drag-reducing dimples.

I heard that bananas are radioactive. If they are radioactive, then they radiate energy. How many bananas would you need to power a house?Kang JIBananas are radioactive. But don't worry, it's fine.Bananas are radioactive because they contain potassium, some of which is the radioactive isotope potassium-40. The factoid about banana radioactivity was popularized by nuclear engineers trying to reassure people[1] that small doses of radiation are normal and not necessarily dangerous. Of course, this kind of thing can backfire.Thanks to their use as a radiation dose comparison, bananas now have a reputation as an especially radioactive food, but they're really not. The CRC Handbook of Radiation Measurement and Protection, the source of the original data behind the banana factoid, lists lots of other foods with more potassium-40 than bananas, including coconuts, peanuts, and sweet potatoes. A large cheese pizza might be three times more radioactive than a banana,[2] and your own body emits a lot more radiation than either.Potassium-40 decays slowly, with individual atoms sitting around for millions or billions of years before quantum randomness finally triggers their decay. Imagine you're an atom of potassium; every second you roll 21 dice. If they all come up 6s, you decay.There are gazillions[3] of atoms of potassium-40 in a banana. In any given second, 10 or 15 of them make that all-sixes roll, spit out a high-energy particle, and become stable calcium or argon.That high-energy particle released by the expiring potassium atom[4] will promptly bonk[5] into other atoms, leaving everything vibrating with extra heat energy. In theory, you could use this heat energy to do work-that's how the Mars rovers Curiosity and Perseverance are powered.The Mars rovers use plutonium, which decays millions of times per second, releasing a lot of power. By comparison, the 15 decays per second from one banana work out to a couple of picowatts of power, roughly the power consumption of a single human cell. Even if you captured that decay energy with perfect efficiency, powering a house would require about 300 quadrillion[6] bananas, which would form a heap large enough to bury most of the skyscrapers in the NYC metro area.[7]The potassium-40 in bananas is a terrible source of energy. But that's okay, because you know what's a great energy source? The banana itself! A banana contains about 100 calories of food energy, and if you incinerate whole bananas as fuel, it would only take about 10 bunches per day to keep your house running.Unfortunately for New York City, which we buried in bananas a moment ago while trying to make the radiation idea work (sorry!), radioactivity vs chemical energy isn't an either/or thing. If you piled up a lot of bananas, they would start to release that chemical energy, one way or another. The sun-baked banana pile would start to rot. The heat from the bananas decomposing in the atmosphere would immediately swamp the heat from radioactivity. The sun-dried bananas would dry, crack, and eventually burn.Decomposition by anaerobic bacteria deep in the pile would produce various gases, including highly flammable methane. As they bubbled up to the surface of the burning banana swamp, they could ignite; gas buildup from food waste is a major industrial explosion hazard.So don't worry about the radioactivity in bananas. It's the rest of the banana that's the real threat. But if you're willing to risk the danger, you could power a lot more than just your house. With just a modest weekly supply of bananas-enough to cover Liberty Island in NYC......you could power the entire city.[1] After nuclear engineering, this is the main pastime of nuclear engineers.[2] Google has a handy tool for looking up the amount of potassium in foods, which even lets you select specific pizza brands. But for some reason, if you select Pizza Hut Pepperoni Pizza, your only serving size options are either "1 slice" or "40 pizzas." Nothing in between.[3] There are about 800,000,000,000,000,000 of them, which is probably quadrillions or quintillions or something, but life is too short to sit around counting zeros and then looking up the Latin prefixes for big numbers.[4] RIP[5] The technical term is THUNK.[6] Fine, I looked it up this time.[7] It's 300 quadrillion bananas, Michael-what can it cost, 3 quintillion dollars?

My son (5y) asked me today: If there were a kind of a fireman's pole from the Moon down to the Earth, how long would it take to slide all the way from the Moon to the Earth?Ramon Schönborn, GermanyFirst, let's get a few things out of the way:In real life, we can't put a metal pole between the Earth and the Moon.[1] The end of the pole near the Moon would be pulled toward the Moon by the Moon's gravity, and the rest of it would be pulled back down to the Earth by the Earth's gravity. The pole would be torn in half.Another problem with this plan. The Earth's surface spins faster than the Moon goes around, so the end that dangled down to the Earth would break off if you tried to connect it to the ground:There's one more problem:[2] The Moon doesn't always stay the same distance from Earth. Its orbit takes it closer and farther away. It's not a big difference,[3] but it's enough that the bottom 50,000 km of your fire station pole would be squished against the Earth once a month.But let's ignore those problems! What if we had a magical pole that dangled from the Moon down to just above the Earth's surface, expanding and contracting so it never quite touched the ground? How long would it take to slide down from the Moon?If you stood next to the end of the pole on the Moon, a problem would become clear right away: You have to slide up the pole, and that's not how sliding works.Instead of sliding, you'll have to climb.People can climb poles pretty fast. World-record pole climbers[4] can climb at over a meter per second in championship competition.[5] On the Moon, gravity is much weaker, so it will probably be easier to climb. On the other hand, you'll have to wear a spacesuit, so that will probably slow you down a little.If you climb up the pole far enough, Earth's gravity will take over and start pulling you down. When you're hanging onto the pole, there are three forces pulling on you: The Earth's gravity pulling you toward Earth, the Moon's gravity pulling you away from Earth, and centrifugal force[6] from the swinging pole pulling you away from Earth.[7] At first, the combination of the Moon's gravity and centrifugal force are stronger, pulling you toward the Moon, but as you get closer to the Earth, Earth's gravity takes over. The Earth is pretty big, so you reach this point—which is known as the L1 Lagrange point—while you're still pretty close to the Moon.Unfortunately for you, space is big, so "pretty close" is still a long way. Even if you climb at better-than-world-record speed, it will still take you several years to get to the L1 crossover point.As you approach the L1 point, you'll start to be able to switch from climbing to pushing-and-gliding: You can push once and then coast a long distance up the pole. You don't have to wait to stop, either—you can grab the pole again and give yourself a push to move even faster, like a skateboarder kicking several times to speed up.Eventually, as you reach the vicinity of the L1 point and are no longer fighting gravity, the only limit on your speed will be how quickly you can grab the pole and "throw" it past you. The best baseball pitchers can move their hands at about 100 mph while flinging objects past them, so you probably can't expect to move much faster than that.Note: While you're flinging yourself along, be careful not to drift out of reach of the pole. Hopefully you brought some kind of safety line so you can recover if that happens.After another few weeks of gliding along the pole, you'll start to feel gravity take over, speeding you up faster than you can go by pushing yourself. When this happens, be careful—soon, you'll need to start worrying about going too fast.As you approach the Earth and the pull of its gravity increases, you'll start to speed up quite a bit. If you don't stop yourself, you'll reach the top of the atmosphere at roughly escape velocity—11 km/s[8]—and the impact with the air will produce so much heat that you risk burning up. Spacecraft deal with this problem by including heat shields, which are capable of absorbing and dissipating this heat without burning up the spacecraft behind it.[9] Since you have this handy metal pole, you can control your descent by clamping onto it and controlling your rate of descent through friction.Make sure to keep your speed low during the whole approach and descent—and, if necessary, pausing to let your hands or brakepads cool down—rather than waiting until the end to try to slow down. If you get up to escape velocity, then at the last minute remember that you need to slow down, you'll be in for an unpleasant surprise as you try to grab on to the pole. At best, you'll be flung away and plummet to your death. At worst, your hands and the surface of the pole will both be converted into exciting new forms of matter, and then you'll be flung away and plummet to your death.Assuming you descend slowly and enter the atmosphere in a controlled manner, you'll soon encounter your next problem: Your pole isn't moving at the same speed as the Earth. Not even close. The land and atmosphere below you are moving very fast relative to you. You're about to drop into some extremely strong winds.The Moon orbits around the Earth at a speed of roughly one kilometer per second, making a wide circle[10] every 29 days or so. That's how fast the top end of our hypothetical fire pole will be traveling. The bottom end of the pole makes a much smaller circle in the same amount of time, moving at an average speed of only about 35 mph relative to the center of the Moon's orbit:35 miles per hour doesn't sound bad. Unfortunately for you, the Earth is also spinning,[11] and its surface moves a lot faster than 35 mph; at the Equator, it can reach over 1,000 miles per hour.[12]​[13]Even though the end of the pole is moving slowly relative to the Earth as a whole, it's moving very fast relative to the surface.Asking how fast the pole is moving relative to the surface is effectively the same as asking what the "ground speed" of the Moon is. This is tricky to calculate, because the Moon's ground speed varies over time in a complicated way. Luckily for us, it doesn't vary that much—it's usually somewhere between 390 and 450 m/s, or a little over Mach 1—so figuring out the precise value isn't necessary.Let's buy a little time by trying to figure it out anyway.The Moon's ground speed varies pretty regularly, making a kind of sine wave. It peaks twice every month as it passes over the fast-moving equator, then reaches a minimum when it's over the slower-moving tropics. Its orbital speed also changes depending on whether it's at the close or far point in its orbit. This leads to a roughly sine-wave shaped ground speed:Well, ready to jump?Ok, fine. There's one other cycle we can take into account to really nail down the Moon's ground speed. The Moon's orbit is tilted by about 5° relative to the Earth-Sun plane, while the Earth's axis is tilted by 23.5°. This means that the Moon's latitude changes the way the Sun's does, moving from the northern tropics to the southern tropics twice a year.However, the Moon's orbit is also tilted, and this tilt rotates on an 18.9-year cycle. When the Moon's tilt is in the same direction as the Earth's, it stays 5° closer to the Equator than the Sun, and when it's in the opposite direction, it reaches more extreme latitudes. When the Moon is over a point farther from the equator, it has a lower "ground speed," so the lower end of the sine wave goes lower. Here's the plot of the Moon's "ground speed" over the next few decades:The Moon's top speed stays pretty constant, but the lowest speed rises and falls with an 18.9-year cycle. The lowest speed of the next cycle will be on May 1st, 2025, so if you want to wait until 2025 to slide down, you can hit the atmosphere when the pole is moving at only 390 m/s relative to the Earth's surface.When you do finally enter the atmosphere, you'll be coming down near the edge of the tropics. Try to avoid the tropical jet stream, an upper-level air current which blows in the same direction the Earth rotates. If your pole happens to go through it, it could add another 50-100 m/s to the wind speed.Regardless of where you come down, you'll need to contend with supersonic winds, so you should wear lots of protective gear.[15] Make sure you're tightly attached to the pole, since the wind and various shockwaves will be violently battering and jolting you around. People often say, "It's not the fall that kills you, it's the sudden stop at the end." Unfortunately, in this case, it's probably going to be both.[17]At some point, to reach the ground, you're going to have to let go of the pole. For obvious reasons, you don't want to jump directly onto the ground while moving at Mach 1. Instead, you should probably wait until you're somewhere near airline cruising altitude, where the air is still thin, so it's not pulling at you too hard—and let go of the pole. Then, as the air carries you away and you fall toward the Earth, you can open your parachute.Then, at last, you can drift safely to the ground, having traveled from the Moon to the Earth completely under your own muscle power.(When you're done, remember to remove the fire pole. That thing is definitely a safety hazard.)[1] For one, someone at NASA would probably yell at us.[2] Ok, that's a lie—there are, like, hundreds more problems.[3] You may occasionally see people get excited about the "supermoon," a full Moon that appears slightly larger because it happens at the time of the month when the Moon is closest to Earth. But really, the full Moon always looks surprisingly large and pretty when it's near the horizon, thanks to the Moon illusion. In my opinion, it's worth going outside and looking at the Moon whenever it's full, regardless of whether it's super or not.[4] Of course there's a world record for pole climbing.[5] Of course there are championship competitions.[6] As usual, anyone arguing about "centrifugal" versus "centripetal" force will be put in a centrifuge.[7] At the distance of the Moon's orbit and the speed it's traveling, centrifugal force pushing away is exactly balanced by the Earth's gravity—which is why the Moon orbits there.[8] This is why anything that falls into the Earth hits the atmosphere fast enough to burn up. Even if an object is moving slowly when it's drifting through space, when it gets close to the Earth it gets accelerated up to at least escape velocity by that final segment of the trip down into the Earth's gravity well.[9] People often ask why we don't use rockets to slow down, to avoid the need for a heat shield. You can read this article for an explanation, but the bottom line is that changing your speed by 11 km/s takes either a tank of fuel the size of a building or a tiny heat shield, and the tiny heat shield is a lot easier to carry. Thanks to heat shields, slowing down is much easier than speeding up—which requires the aforementioned giant fuel tank. (For more on this, see this What If question).

I used to work on a fisheries crew where we would use an electro-fisher backpack to momentarily stun small fish (30 - 100 mm length) so we could scoop them up with nets to identify and measure them. The larger fish tended to be stunned for slightly longer because of their larger surface area but I don't imagine this relationship would be maintained for very large animals. Could you electrofish for a blue whale? At what voltage would you have have to set the e-fisher?—Madeline CooperSo you want to give endangered whales powerful electric shocks. Great! I'm happy to help. This is definitely a very normal thing to want to do.There are various electrofishing setups, but they all operate on the same general principle: An electric current flows through the water, and also through any fish that happen to be in the water. The electric current, through a few different physical effects, draws the fish toward one of the electrodes and/or stuns them.For a long time, people didn't really notice that electrofishing injured fish at all. For the most part, stunned fish seemed to be fine after a few minutes. However, they frequently suffer from internal damage which isn't obvious from the outside. The electric current causes involuntary muscle spasms, which can fracture the fish's vertebrae. As this paper shows, these kinds of spinal injuries are more common and severe in larger fish.As you mention, for a given electrofishing setup, larger fish are usually more affected than smaller ones.[1] Why? Well, we don't know. In their comprehensive 2003 study Immobilization Thresholds of Electrofishing Relative to Fish Size, biologists Chad Dolan and Steve Miranda modeled the way electric currents stun fish of different sizes, but caution that "no adequate conceptual system exists to explain the effects of size on electroshock thresholds from the perspective of electric fields."None of these studies dealt with animals anywhere near the size of whales. The largest fish in Dolan and Miranda's study were still quite small. This experiment tested larger fish up to 80cm long,[2] but nothing whale-sized.[3] Since we don't know exactly why larger fish respond differently, it's hard to confidently extrapolate.Fish are typically[4] stunned by equipment delivering about 100 µW of power per cm of body volume, so for a whale, that would be about 20 megawatts.But there's a catch: Most electrofishing is done in fresh water. Unfortunately, blue whales live in the ocean,[5] where the salt water conducts electricity much more easily. That might seem like good news for our electrofishing plans, but it turns out to make it much more challenging.Electrofishing works best when the water and the target animals are about equally conductive. In highly conductive saltwater, most of the current flows past the animals in the water rather than through them. This means that ocean electrofishing requires much more power. Using our simple extrapolation, instead of 20 megawatts, we might need a gigawatt. In other words, you'll need to bring a large nuclear generating station.Simple extrapolation is misleading here, since we know that large animals respond to electricity differently. How differently? Well, according to an electrofishing.net post by Jan Dean, a human who fell into the water in front of a typical electrofishing boat could easily die.[6] Blue whales, which are even larger than humans, would presumably fare even worse.Electrofishing temporarily stops a fish's heart.[7] The fish seem to recover, most of the time, but humans—and probably whales—have a harder time with cardiac arrest.It's possible that giving blue whales massive electrical shocks isn't as good an idea as it sounded at first.That's not to say there's no place in science for giving random electric shocks to large aquatic animals. A project at the Denver Wildlife Research Center used electrofishing-style equipment—linked to an infrared camera—to repel beavers, ducks, and geese from selected areas. Apparently, the results were "encouraging."[8]So electrofishing equipment probably can't help you catch blue whales. However, if you're having trouble keeping them out of your backyard pond ...... it's possible the Denver Wildlife Research Center can help you out.[1] This can lead to larger fish being overrepresented in sampling studies.[2] The fish they used in the experiment grew rapidly to a range of sizes, mainly because the larger ones kept eating their smaller siblings.[3] There's been at least one case of dolphin death linked to illegal electrofishing.[4] Actual quote from that paper: "The results for these tests were unsettling ... this observation was so unexpected that we stopped the experiment to recalibrate the equipment."[5] I mean, unfortunately for Madeline. It's fortunate for the whales.[6] While it sounds dangerous, people aren't often killed during electrofishing accidents. The 2000 EPA report "New Perspectives in Electrofishing" comments that "In the United States, since World War II, only about five electrocutions during electrofishing have been documented." I assume they just mean records weren't kept before World War II, but it's technically possible that the war involved so many electrofishing deaths that they need to exclude it from the stats.[7] Until reading this paper, I didn't know clove oil was used as a fish anesthetic. You learn something new every day![8] The equipment kept the beavers away, although they returned as soon as it was turned off. It also worked on ducks and geese, although they had some problems with infrared waterfowl detection. The birds would usually take flight when the equipment turned on, although if it was cold enough, they'd just sluggishly paddle away.

Electrofishing for Whales I used to work on a fisheries crew where we would use an electro-fisher backpack to momentarily stun small fish (30 - 100 mm length) so we could scoop them up with nets to identify and measure them. The larger fish tended to be stunned for slightly longer because of their larger surface area but I don't imagine this relationship would be maintained for very large animals. Could you electrofish for a blue whale? At what voltage would you have have to set the e-fisher?—Madeline CooperSo you want to give endangered whales powerful electric shocks. Great! I'm happy to help. This is definitely a very normal thing to want to do.There are various electrofishing setups, but they all operate on the same general principle: An electric current flows through the water, and also through any fish that happen to be in the water. The electric current, through a few different physical effects, draws the fish toward one of the electrodes and/or stuns them.For a long time, people didn't really notice that electrofishing injured fish at all. For the most part, stunned fish seemed to be fine after a few minutes. However, they frequently suffer from internal damage which isn't obvious from the outside. The electric current causes involuntary muscle spasms, which can fracture the fish's vertebrae. As this paper shows, these kinds of spinal injuries are more common and severe in larger fish.As you mention, for a given electrofishing setup, larger fish are usually more affected than smaller ones.[1]This can lead to larger fish being overrepresented in sampling studies. Why? Well, we don't know. In their comprehensive 2003 study Immobilization Thresholds of Electrofishing Relative to Fish Size, biologists Chad Dolan and Steve Miranda modeled the way electric currents stun fish of different sizes, but caution that "no adequate conceptual system exists to explain the effects of size on electroshock thresholds from the perspective of electric fields."None of these studies dealt with animals anywhere near the size of whales. The largest fish in Dolan and Miranda's study were still quite small. This experiment tested larger fish up to 80cm long,[2]The fish they used in the experiment grew rapidly to a range of sizes, mainly because the larger ones kept eating their smaller siblings. but nothing whale-sized.[3]There's been at least one case of dolphin death linked to illegal electrofishing. Since we don't know exactly why larger fish respond differently, it's hard to confidently extrapolate.Fish are typically[4]Actual quote from that paper: "The results for these tests were unsettling ... this observation was so unexpected that we stopped the experiment to recalibrate the equipment." stunned by equipment delivering about 100 µW of power per cm of body volume, so for a whale, that would be about 20 megawatts.But there's a catch: Most electrofishing is done in fresh water. Unfortunately, blue whales live in the ocean,[5]I mean, unfortunately for Madeline. It's fortunate for the whales. where the salt water conducts electricity much more easily. That might seem like good news for our electrofishing plans, but it turns out to make it much more challenging.Electrofishing works best when the water and the target animals are about equally conductive. In highly conductive saltwater, most of the current flows past the animals in the water rather than through them. This means that ocean electrofishing requires much more power. Using our simple extrapolation, instead of 20 megawatts, we might need a gigawatt. In other words, you'll need to bring a large nuclear generating station.Simple extrapolation is misleading here, since we know that large animals respond to electricity differently. How differently? Well, according to an electrofishing.net post by Jan Dean, a human who fell into the water in front of a typical electrofishing boat could easily die.[6]While it sounds dangerous, people aren't often killed during electrofishing accidents. The 2000 EPA report "New Perspectives in Electrofishing" comments that "In the United States, since World War II, only about five electrocutions during electrofishing have been documented." I assume they just mean records weren't kept before World War II, but it's technically possible that the war involved so many electrofishing deaths that they need to exclude it from the stats. Blue whales, which are even larger than humans, would presumably fare even worse.Electrofishing temporarily stops a fish's heart.[7]Until reading this paper, I didn't know clove oil was used as a fish anesthetic. You learn something new every day! The fish seem to recover, most of the time, but humans—and probably whales—have a harder time with cardiac arrest.It's possible that giving blue whales massive electrical shocks isn't as good an idea as it sounded at first.That's not to say there's no place in science for giving random electric shocks to large aquatic animals. A project at the Denver Wildlife Research Center used electrofishing-style equipment—linked to an infrared camera—to repel beavers, ducks, and geese from selected areas. Apparently, the results were "encouraging."[8]The equipment kept the beavers away, although they returned as soon as it was turned off. It also worked on ducks and geese, although they had some problems with infrared waterfowl detection. The birds would usually take flight when the equipment turned on, although if it was cold enough, they'd just sluggishly paddle away.So electrofishing equipment probably can't help you catch blue whales. However, if you're having trouble keeping them out of your backyard pond ...... it's possible the Denver Wildlife Research Center can help you out.

Would a toaster still work in a freezer?—My Brother, My Brother and Me, Episode 343, discussing a Yahoo Answers questionOn a recent episode of Justin, Travis, and Griffin McElroy's terrific advice podcast, My Brother, My Brother and Me, the brothers pondered a Yahoo Answers question about what would happen if you put a toaster inside a freezer. (The discussion comes around the 36-minute mark.)They have a fun discussion of a few aspects of the problem before eventually moving on to the next question. Since they don't really settle on a final answer, I thought we could help them out by taking a closer look at the physics of freezer toasters.(A quick safety note: If you actually do this, keep in mind that the toaster may melt some of the ice in the freezer, leaving you with a running electrical appliance in a pool of water.)Griffin sums up the situation like this:

Toaster vs. Freezer Would a toaster still work in a freezer?—My Brother, My Brother and Me, Episode 343, discussing a Yahoo Answers questionOn a recent episode of Justin, Travis, and Griffin McElroy's terrific advice podcast, My Brother, My Brother and Me, the brothers pondered a Yahoo Answers question about what would happen if you put a toaster inside a freezer. (The discussion comes around the 36-minute mark.)They have a fun discussion of a few aspects of the problem before eventually moving on to the next question. Since they don't really settle on a final answer, I thought we could help them out by taking a closer look at the physics of freezer toasters.(A quick safety note: If you actually do this, keep in mind that the toaster may melt some of the ice in the freezer, leaving you with a running electrical appliance in a pool of water.)Griffin sums up the situation like this:

What if the entire continental US was on a decreasing slope from West to East. How steep would the slope have to be to sustain the momentum needed to ride a bicycle the entire distance without pedaling?—Brandon RooksToo steep to actually build, sadly. But for the next best thing, I suggest a vacation to the Hawaiian island of Maui.First, the physics. Bikes coast downhill. On a long enough slope, a bike will reach a certain steady coasting speed. On a steep hill, their coasting speed will be faster, and on a gentle slope, they coast more slowly. If the slope is small enough, the bike will slow down and stop.The shallowest slope at which a bike will still roll steadily forward is determined by the bike's coefficient of rolling resistance. In fact, the formula for this minimum slope—measured in terms of vertical drop over horizontal distance—is incredibly simple:\[ \text{Minimum slope} = \text{Coefficient of rolling resistance} \]"Slope equals coefficient of friction"[1] is a handy general rule in physics: The coefficient of friction between an object on a surface is just the shallowest slope at which the object slides.[2]For a nice bike under good conditions, the coefficient of rolling resistance can get as low as 0.002, or 1/500.[3] That means that to travel 500 miles horizontally, you'll need a vertical drop of at least 1 mile. To travel the roughly 2,500 miles from New York to LA, you'd need to start off at least 5 miles up, higher than North America's highest mountain. I suggest bringing oxygen tanks.But be warned—the trip could take a while.A bike's rolling resistance mainly comes from the way the tire[4]​[5]​[6] deforms as it rolls, and it doesn't depend that much on how fast you're going. Air resistance, on the other hand, increases as you speed up, and under most conditions is the main drag force acting on a moving bike. To figure out how fast a bike will coast on a downhill slope, you need to calculate the point at which air resistance balances out the forward pull from gravity. At that point, the bike will stop accelerating. We can do that by using the formula for air resistance:\[ \text{Forward pull from gravity} = \text{Rolling resistance} + \text{Drag force} \]\[ m g \sin(\theta) = g \cos(\theta) C_r m + \tfrac{1}{2} C_d \rho A V^2 \]\[ V = \sqrt{\frac{m g \sin(\theta) - g \cos(\theta) C_r m}{ \tfrac{1}{2} C_d \rho A}} \](V is the speed of the bike, C and C are the coefficients of rolling resistance and air drag, θ is the slope angle, g is the acceleration of gravity, m is the mass of the bike and rider, A is the frontal area of the bike and rider, and ρ is the density of air.)For a very shallow slope of 0.2° or 0.3°, the bike would barely roll, and its top speed would be slower than a walking pace. You would need to add an extra few tenths of a degree to get the speed high enough to balance comfortably, and this would make the LA end of the slope even higher than the already implausible five miles.But still, bicycles are pretty impressive coasting machines.[7] Skis, which are pretty good at sliding, actually have a coefficient of friction about 10 times higher than a bike's rolling resistance.To ski from LA to New York, a skier would need to start off 10 times higher than a bike to make the same trip. Instead of the top of a mountain, they would need to start from near the edge of space. Not only is there no way to build a slope that tall, but ice isn't even stable at those low temperatures, so there'd be nothing to slide on.In practice, the longest horizontal distance you could travel on a bike with an ideal ramp is probably not more than a couple hundred miles, and that would require ideal conditions. In the real world, the longest such trip might[8] be the Haleakala downhill bike ride, which allows you to take a 35-mile trip from near the 10,000-foot summit all the way down to sea level with virtually no pedaling required.(And if you can't make it to Maui yourself, you can at least enjoy the video search results for bicycle into water.)[1] Sliding friction and rolling resistance work in different ways, but the coefficients are equivalent in these types of problems. If you want to be precise, you could use the phrase "coefficient of resistance" for all of them, but "coefficient of friction" is the more common term.[2] The coefficient of static friction is the slope at which the object starts sliding. The (usually lower) coefficient of dynamic friction is the minimum slope at which it keeps sliding once you give it a nudge.[3] You can browse some test data here.[4] And the ground, if you're riding on dirt.[5] And the spokes and frame, if your bike is made of soft clay or something.[6] Why do you have a bike made entirely of soft clay?[7] Trains have steel wheels which roll on smooth rails, so they should have very little rolling resistance. You can work out their coefficients by looking over technical specs or calculating from first principles, but a cleverer way is by watching train-pulling athletic events. Then, with a little calculation involving the limits of human strength and/or direct measurement, you can work out the coefficient from the other end. It turns out that train cars—at least, the kind used in strongman events—have coefficients of rolling resistance barely equal to that of a good bicycle.[8] It's billed as the longest, but I wonder if there's a longer one in some random stretch of gently-sloping downhill road in rural Mongolia or something.

Coast-to-Coast Coasting What if the entire continental US was on a decreasing slope from West to East. How steep would the slope have to be to sustain the momentum needed to ride a bicycle the entire distance without pedaling?—Brandon RooksToo steep to actually build, sadly. But for the next best thing, I suggest a vacation to the Hawaiian island of Maui.First, the physics. Bikes coast downhill. On a long enough slope, a bike will reach a certain steady coasting speed. On a steep hill, their coasting speed will be faster, and on a gentle slope, they coast more slowly. If the slope is small enough, the bike will slow down and stop.The shallowest slope at which a bike will still roll steadily forward is determined by the bike's coefficient of rolling resistance. In fact, the formula for this minimum slope—measured in terms of vertical drop over horizontal distance—is incredibly simple:\[ \text{Minimum slope} = \text{Coefficient of rolling resistance} \]"Slope equals coefficient of friction"[1]Sliding friction and rolling resistance work in different ways, but the coefficients are equivalent in these types of problems. If you want to be precise, you could use the phrase "coefficient of resistance" for all of them, but "coefficient of friction" is the more common term. is a handy general rule in physics: The coefficient of friction between an object on a surface is just the shallowest slope at which the object slides.[2]The coefficient of static friction is the slope at which the object starts sliding. The (usually lower) coefficient of dynamic friction is the minimum slope at which it keeps sliding once you give it a nudge.For a nice bike under good conditions, the coefficient of rolling resistance can get as low as 0.002, or 1/500.[3]You can browse some test data here. That means that to travel 500 miles horizontally, you'll need a vertical drop of at least 1 mile. To travel the roughly 2,500 miles from New York to LA, you'd need to start off at least 5 miles up, higher than North America's highest mountain. I suggest bringing oxygen tanks.But be warned—the trip could take a while.A bike's rolling resistance mainly comes from the way the tire[4]And the ground, if you're riding on dirt.​[5]And the spokes and frame, if your bike is made of soft clay or something.​[6]Why do you have a bike made entirely of soft clay? deforms as it rolls, and it doesn't depend that much on how fast you're going. Air resistance, on the other hand, increases as you speed up, and under most conditions is the main drag force acting on a moving bike. To figure out how fast a bike will coast on a downhill slope, you need to calculate the point at which air resistance balances out the forward pull from gravity. At that point, the bike will stop accelerating. We can do that by using the formula for air resistance:\[ \text{Forward pull from gravity} = \text{Rolling resistance} + \text{Drag force} \]\[ m g \sin(\theta) = g \cos(\theta) C_r m + \tfrac{1}{2} C_d \rho A V^2 \]\[ V = \sqrt{\frac{m g \sin(\theta) - g \cos(\theta) C_r m}{ \tfrac{1}{2} C_d \rho A}} \](V is the speed of the bike, C and C are the coefficients of rolling resistance and air drag, θ is the slope angle, g is the acceleration of gravity, m is the mass of the bike and rider, A is the frontal area of the bike and rider, and ρ is the density of air.)For a very shallow slope of 0.2° or 0.3°, the bike would barely roll, and its top speed would be slower than a walking pace. You would need to add an extra few tenths of a degree to get the speed high enough to balance comfortably, and this would make the LA end of the slope even higher than the already implausible five miles.But still, bicycles are pretty impressive coasting machines.[7]Trains have steel wheels which roll on smooth rails, so they should have very little rolling resistance. You can work out their coefficients by looking over technical specs or calculating from first principles, but a cleverer way is by watching train-pulling athletic events. Then, with a little calculation involving the limits of human strength and/or direct measurement, you can work out the coefficient from the other end. It turns out that train cars—at least, the kind used in strongman events—have coefficients of rolling resistance barely equal to that of a good bicycle. Skis, which are pretty good at sliding, actually have a coefficient of friction about 10 times higher than a bike's rolling resistance.To ski from LA to New York, a skier would need to start off 10 times higher than a bike to make the same trip. Instead of the top of a mountain, they would need to start from near the edge of space. Not only is there no way to build a slope that tall, but ice isn't even stable at those low temperatures, so there'd be nothing to slide on.In practice, the longest horizontal distance you could travel on a bike with an ideal ramp is probably not more than a couple hundred miles, and that would require ideal conditions. In the real world, the longest such trip might[8]It's billed as the longest, but I wonder if there's a longer one in some random stretch of gently-sloping downhill road in rural Mongolia or something. be the Haleakala downhill bike ride, which allows you to take a 35-mile trip from near the 10,000-foot summit all the way down to sea level with virtually no pedaling required.(And if you can't make it to Maui yourself, you can at least enjoy the video search results for bicycle into water.)

Flood Death Valley Since Death Valley is below sea level could we dig a hole to the ocean and fill it up with water?—Nick TraedenYes! We can do anything we want. We shouldn't do this, though, because it would be gross.Death Valley is an endorheic basin[1]"Big hole" in California. The floor of the valley is about 80 meters below sea level. It contains the lowest point on land in North America[2]Excluding artificial points like mines. and is the hottest place on Earth.[3]If you're about to say "Wait, what about Liby—," then don't worry, I'm with you. Just hang on and read a few more words ahead!Now, if you're the sort of person who's into world records, you might have heard that the hottest place on Earth was Al Azizia, Libya. Al Azizia recorded a temperature of 58.0°C (136.4°F) in 1922, a mark Death Valley has never come close to. So what gives?It turns out Al Azizia has recently been stripped of its record. In 2010, an exhaustive—and definitely a little obsessive—investigation led by Christopher C. Burt convinced the World Meteorological Organization that the Libyan measurement was probably a mistake. This left Death Valley with the record of 56.7°C (134°F), set in 1913. Case closed!Except it's not quite settled. Burt has raised questions about the 1913 record as well, and has gone so far as to catalog a number of historical extremes along with a credibility score for each. The "real" record is probably 53.9°C (129°F). This temperature has been recorded four times, in 1960, 1998, 2005, and 2007—every time in Death Valley.These records were recorded with modern instruments and are considered reliable. They also make sense from a theoretical point of view. Geographers have calculated[4]This Army Corps of Engineers publication cites a couple of sources for this, including a 1963 paper by G. Hoffman. Unfortunately, that paper is in German, which I can't read, so I've just decided to trust that the Army Corps of Engineers writers Dr. Paul F. Krause and Kathleen L. Flood aren't pulling a fast one on me. that the highest possible temperature in ideal spots (in desert basins like Death Valley) during the 20th century is 55°-56°C, so 54°C sounds like a reasonable world record.Now, back to Nick's question.[5]This is nowhere NEAR the record for "most boring digression into world record trivia." That record was recently challenged by IBM computer capable of producing millions of boring pieces of trivia per second, but the machine narrowly lost to reigning human champion Ken Jennings.Since Death Valley is below sea level, we could, as Nick suggests, flood it with seawater. It would take a lot of digging, since there's a lot of Earth in the way. The lowest route to Death Valley is probably by traveling up the Colorado River watershed, along the Arizona border past Quartzsite,[6]Trivia: If you want to reach Quartzsite, Arizona from my school, Christopher Newport University, you just step out onto Warwick Blvd (Rt. 60) and turn left. That's it—Route 60 runs across the country, from the CNU campus in Virginia to I-10 just outside Quartzsite. then northwest[7]Possibly following one of the routes shown on page G34 in this report. past Zzyzx, which is a real place.If you did all that digging, you could create a channel from the Gulf of California to Death Valley, and water would flow in. We can use this handy stream-flow calculator to figure out how wide we'd need to make the channel. A channel 20 meters deep and 100 meters wide should be able to fill it in a few months. A really wide channel—like the kind carved by glacial floods—could fill it in hours.We know it's possible to create this kind of inland sea because we've done it before—by accident. In 1905, irrigation engineers working on the Colorado River made some mistakes. During a flood, the entire Colorado river broke through into the Alamo Canal and flowed directly into the Salton basin to the north. By the time they repaired the canal, two years later, the Salton basin had become the Salton Sea—one of the larger human-caused changes to the world map.The Salton Sea is fed mainly by agricultural runoff, so it's become saline[8]"Salty" and hypereutrophic.[9]"Gross" Large numbers of dead fish, combined with algal decay and unusual chemistry, have created a smell that the US Geological Survey describes as "objectionable," "noxious," "unique," and "pervasive." The sea is a birdwatching hot spot, but also the site of a lot of mass bird die-offs, so kind of a mixed bag if you're into birds. In recent years, the water has been evaporating quickly, leaving behind dried toxic residue which is swept up into dust storms. Work to clean up and rehabilitate the region is ongoing.All in all, the Salton Sea is a mess—and Nick wants to make another one.Nick's Death Valley project would start off connected to the ocean, but without a source of flowing water at the Death Valley end,[10](It's a desert.) the channel would gradually silt up. The link to the ocean would eventually be broken, the sea would start to evaporate, the water would become saline, algae would bloom, and eventually the US Geological Survey would start complaining about the smell.There would be one more consequence to all this. Thanks to the flood of cold ocean water burying the whole region, Death Valley would stop setting temperature records, and someone else would eventually claim to have broken their 129°F record. The Death Valley records would have to be compared to the newer candidates, which would probably use slightly different methods ... and that means one thing:A World Meteorological Organization expert panel!

Sun Bug How many fireflies would it take to match the brightness of the Sun?Luke DotyNot that many! I mean, it's definitely one of those gigantic numbers with lots of zeroes, but in the grand scheme of things, there aren't as many zeroes as you might expect.Our first question: Where does firefly light even come from?Fireflies may look like they're full of glow-in-the-dark goo, but the light they give off actually comes from a thin layer on their surface.[1]You can see some diagrams of the organs here and here. Lots of insects have glowing surface patches, and some of those patches have been studied carefully to calculate their brightness. A 1928 paper on beetles called "headlight bugs"[2]Such a great name. found that their glowing patches, which were a little over a square millimeter in area, emitted about 0.0006 lumens of light. Fireflies have luminous organs (bright patches) that are about the same size as those of headlight bugs,[3]See this paper on some common American fireflies. and their organs tend to have a similar peak brightness per area, so this figure is a good guess for the brightness of a firefly's lantern.Firefly lights aren't "always-on." They blink on and off, with patterns that vary from species to species and situation to situation. These flashes carry information, some of which you can decode using this delightful chart.[4]You can also use LEDs to mess with firefly patterns, which feels strangely invasive.To get the brightest light, let's assume we're using a species with a mostly-on duty cycle—like a headlight bug. How does its 0.0006-lumen light output compare to the Sun?The Sun's brightness is \( 3.8\times10^{28} \) lumens, so by simple division, it would take \( 3\times10^{31} \) of those fireflies to emit the same amount of light. That's a surprisingly small number; adult fireflies weigh about 20 milligrams, which means \( 3\times10^{31} \) fireflies would only weigh about a third as much as Jupiter and 1/3000th as much as the Sun.In other words, per pound, fireflies are brighter than the Sun. Even though bioluminescence is millions of times less efficient than the Sun's fusion-powered glow, the Sun can't afford to be as bright because it has to last billions of times longer.[5]If you like Fermi problems—and silly equations—there's an interesting route you can take to this answer without doing any research on fireflies or the Sun at all. Instead, you can just plug this equation into Wolfram|Alpha: (5 billion years / (4 hours/day * 3 months)) / (1% * (speed of light)^2 / (3200 calories/pound)).

Tatooine Rainbow Since rainbows are caused by the refraction of the sunlight by tiny droplets of rainwater, what would rainbow look like on Earth if we had two suns like Tatooine?—RagaA planet with double suns would have double rainbows.Or rather, quadruple rainbows. Our rainbows here on Earth are already double rainbows—there's a second, fainter bow above the main one. You can't always see this second rainbow, since the clouds need to be just right, so people get excited when they see one.The area between the two rainbows is darker than the area outside because raindrops reflect light more strongly in certain directions. That region has a name, by the way—it's called Alexander's dark band.The first and second rainbows are the only ones you can see easily, but there are actually many more bows beyond those two, each one fainter than the last. Rainbows are formed by light bouncing around in raindrops, and the different bows are formed by different paths the light can take. The main rainbow is formed by the most common paths through the droplet, and other paths—where some of the light bounces around in more unusual ways—make the fainter second, third, fourth, and even fifth rainbows.Usually, only the first and second rainbows are bright enough to see; it was only in the last five years that anyone took pictures of the third, fourth, and fifth rainbows.Rainbows appear on the other side of the sky from the Sun, so to figure out what a double rainbow would look like on a planet with two suns, we need to figure out where the suns usually appear in the sky on that kind of planet.There are planets with two suns out there, although we didn't know that for sure until recently. Double-star planets come in two main varieties:In the first kind of system, the two stars are close together and the planet goes around them far away. This kind of planet is called a circumbinary planet. In the second kind of system, the two stars are farther apart, and the planet orbits one of them[1]Not necessarily the bigger one. while the other stays far away. This kind of planet is called [the other kind of planet].[2]I'm sorry, I've just never learned a good word for these.If you lived on [the other kind of planet],[3]Sorry. the two Suns would spend most of the year in different parts of the sky. Depending on how big they were, they may also be very different in brightness. If you were orbiting the larger star, the smaller one might be no brighter than the Moon,[4]Which would still be bright enough to cast a rainbow! or even look like an ordinary planet or star.Tatooine, in Star Wars, looks like it's probably a circumbinary planet. The two stars appear pretty close together in the sky and similar in color and size, so it seems reasonable to guess they're actually near one another, with Tatooine orbiting both of them.Two suns would create two overlapping rainbows. The main bow of the rainbow is a circle about 84 degrees across, centered in the sky exactly opposite the Sun.[5]This is why you never see more than half of a rainbow above the horizon. If the center of the rainbow were above the horizon, it would mean the Sun was below it behind you, so there wouldn't be sunlight to make a rainbow in the first place. The farther apart the two suns were, the farther apart the rainbows would be. If the two suns were 84 degrees apart, the main bows of the two rainbows would barely touch.A pair of suns 84 degrees apart would be possible around [the other kind of planet], but not around Tatooine-type[6]If Star Wars had just used the other kind of planet, we could use its name for them and solve this problem. circumbinary planets. The reason is simple: A planet orbiting two stars can't get too close to them or its orbit becomes unstable. If it gets too close, the irregular tugging from the gravity of the two stars as they orbit will eventually cause the planet to crash into one of them or get flung out of the system.For a system with two similar-sized stars, this "critical radius" is around six times the distance between the two stars.[7]This is a very rough number; it can range from four to eight depending on the exact arrangement. We've found a lot of planets close to that critical radius, which suggests that maybe they slowly migrate inward until they reach it and are ejected or destroyed. Strangely, we haven't found many big Jupiter-sized planets around binary stars in general; we should be seeing them if they're there, so the lack of them is a mystery. This means that the two suns would never get more than about 20 degrees apart in the sky:This tells us that the two rainbows in a Tatooine-like system would always overlap.[8]Assuming the raindrops are made of water, or something with similar refractive properties. The colors would blend together where the bows crossed, and the dark bands would too.I suppose doubling all the rainbows would also double the number of pots of gold at the end of each rainbow.[9]Come to think of it, do our rainbows have one pot of gold or two? I've never really thought about it. And it's not just pots of gold; I guess we'd need to rethink all kinds of rainbow references.Overlapping rainbows would be beautiful, but definitely a lot more complicated.

Pizza Bird My boyfriend recently took a flight on a plane with wifi, and while he was up there, wistfully asked if I could send him a pizza. I jokingly sent him a photo of a parrot holding a pizza slice in its beak. Obviously, my boyfriend had to go without pizza until he landed at JFK. But this raised the question: could a bird deliver a standard 20" New York-style cheese pizza in a box? And if so, what kind of bird would it take?—Tina NguyenA bird could, possibly, deliver a pizza to a house. Delivering it to an airliner is a lot harder.A 20-inch pizza weighs about 1.8 kg.[1]Citation: I just ordered a pizza to check. I usually steer clear of experimental science in these articles, but am willing to make an exception when it involves eating a bunch of pizza. That's about 100 times the weight of a sparrow, so we're definitely going to need a large bird. There are all sorts of birds bigger than our pizza, including eagles, swans, cranes, pelicans, and albatrosses. However, some of them would do better at pizza delivery than others. To see why, let's take a look at wing shapes.Birds have different types of wings depending on what kind of flying they need to do. Of all the types of wings, the ones best suited for pizza delivery are probably the relatively short-and-broad kind found on many soaring hawks and eagles.[2]Long, thin wings, like those of a gull or albatross, are more aerodynamically efficient in many ways. However, these wings are harder to flap, which makes it difficult for these birds to accelerate quickly. Albatrosses require long "runways" to build up speed before they can lift off.​[3]Here's a live feed of some baby albatrosses nesting in Hawaii. These wings are good for taking off while carrying a heavy load, which is of course necessary for pizza delivery.The largest birds of prey in North America[4]Not counting the California condor, which isn't very good at the kind of hard flapping required to lift heavy loads. And anyway, there are only a few hundred of them in the world—up from 22 in the early 1990's—so someone would definitely notice if you took some for pizza delivery. are the bald eagles[5]Here's a live feed of a bald eagle nest in the US National Arboretum. and golden eagles, which weigh about 4 or 5 kilograms when fully grown. The famous viral video of a golden eagle snatching a toddler is fake, but eagles have been seen to lift some awfully heavy things. Last year, photographer Alex Lamine saw a bald eagle in Georgia carrying a 12-pound (5.4 kg) tree branch, presumably to add to its gigantic nest. The eagle dropped the branch before making it back to the nest, but it definitely proved the bird was capable of flying—at least briefly—while carrying a load equal to its own body weight.As a general rule, though, birds of prey won't try to pick up more than about half of their own weight. This means a half-kilogram peregrine falcon[6]Here's a live feed of a peregrine falcon nest box in Arizona. couldn't pick up our 2-kilogram pizza. A 5-kilogram eagle, on the other hand, probably could.However, picking up a pizza is one thing, but what about delivering it to an airliner?Soaring birds like vultures—and eagles—can ride thermals[7]Thermals, warm columns of rising air, are a phenomenon familiar to both glider pilots and fans of the Animorphs book series. to extreme heights. In tropical regions, where the sunlight-powered thermals are strongest, planes have encountered[8]😞 soaring Rüppell's vultures at altitudes of over 10 kilometers. That's high enough to reach a cruising airliner—but, unfortunately, this kind of soaring flight requires ideal flying conditions. "Having a pizza strapped to you" is definitely not that.So a bird could potentially carry a pizza, but it couldn't fly up to an airliner with it. That's just as well, because there's one more major problem you'd face: Speed.Whether or not a bird can fly as high as an airliner, it definitely can't fly as fast. Even if the person in the plane managed to get the emergency door open, they'd have to find a way to grab the pizza.If you tip a pizza box too far, the cheese runs off one side. This critical angle varies from pizza to pizza and depends greatly on temperature, but let's suppose it's about 45°. That angle tells us that a pizza can handle a maximum sideways acceleration of about 1g.[9]Assuming you've managed to keep the pizza warm at those high altitudes—because what kind of a monster delivers a cold pizza? To accelerate up to an airliner cruising speed of 500 mph, we'll need the acceleration to happen over a distance of over a mile. In other words, we'd need a mile-long mechanism trailing behind the plane to gently reel in the pizza.But wait—those calculations assume sideways acceleration. Pizzas—like humans—handle "face-first" acceleration best. If the pizza were rotated during the handoff, it could survive a much greater acceleration, allowing the grabbing mechanism to be smaller.What kind of face-first acceleration can a pizza survive before it spreads out to fill the bottom of the box? I haven't found any data on that, but if anyone wants to try to sneak a pizza into a centrifuge, go for it. Be sure to take pictures!All in all, if you're in a plane and feel the urge to order a pizza, it's probably easier to just wait until you land. Then, if you really want, you can try to get a bird to deliver it.But don't be surprised if some slices go missing along the way.

Eat the Sun What percentage of the Sun's heat (per day) does the population of Earth eat in calories per year? What changes could be made to our diets for the amount of calories to equal the energy of the Sun?—James Mitchell0.000000000065%.A McDonald's Big Mac contains 540 (dietary) calories of energy, or about 2,250,000 joules. The Sun's output is 382,800,000,000,000,000,000,000,000 joules per second.[1]Also known as watts. This is a rare case of a common-in-America unit which is secretly SI-friendly. Of course, we immediately worked our way around to measuring stored energy in kWh (and mAh), and now everything is terrible again. That's enough to tell us that we're going to have a hard time catching up with the Sun by eating more burgers.Why is this so difficult?Most of the Sun's mass is concentrated in the core, where energy is released as hydrogen fuses into helium. By volume, the Sun's core doesn't actually produce that much energy—a blob of core matter produces about the same amount of energy as the body heat of a reptile of the same size,[2]A Wikipedia factoid also compares the Sun's heat-per-unit-volume to the heat produced by an active compost pile, although the energy production from compost varies with temperature—since a hot compost pile kills off the organisms that do the composting. and less than a warmer-bodied mammal. The Sun is hotter than a reptile because it's so large—all that heat adds up.[3]A large object also has more surface area to radiate heat away, but since surface area is proportional to radius while the amount of heat-producing material is proportional to radius, making things bigger generally makes them hotter.Reptiles may produce heat at approximately the same rate as the stuff in the Sun, but if a reptile doesn't eat for a few weeks or months, it runs out of energy and starves. The Sun, on the other hand, has been burning for billions of years and will last for billions more—because nuclear fusion produces much more energy than metabolizing fat or muscle.How much more? Strangely, we can come up with a pretty decent estimate just from what we know about animals. Animals live a few weeks—or months, in the case of some snakes—on their own stored reserves, while the Sun will last about 10 billion years. That's a difference of about 100 billion-fold. This is roughly similar to the ratio between the energy stored in a snake-meat Big Mac and the energy stored in a Big Mac-sized chunk of the Sun's core.[5]If you calculate out the exact actual ratios here, you'll find that the sun-to-big-mac energy ratio is a bit lower than the sun-to-lizard lifespan ratio. This is partly explained by the fact that animals are full of bones and brains and stuff, and can't efficiently consume their entire body volume as if they were a giant Big Mac.If we want to eat enough food to keep up with the Sun's energy-use rate, we have to eat a lot more. A typical person eats a few thousand calories per day, and we probably can't improve on that too much—we can't all be The Rock. To keep up with the Sun, what we really need is more people.At the end of this article, we imagined a galaxy full of habitable planets, each one hosting 7 billion clones of former solicitor general Ted Olson. (Don't ask.) If the Teds ate a normal diet, the total calorie consumption of that galaxy would still fall short of the Sun. We'd need approximately a thousand galaxies worth of burger-eating Ted Olsons to achieve our goal.It's important to spread this food consumption out across multiple galaxies, because if you gathered all that food in once place, you'd have a big problem. Since food has such a low energy density compared to the Sun, you need a lot of food to keep up with the Sun. Matching a few days' worth of Sun output would require a sphere of hamburgers the size of the Earth, and keeping up with the Sun over its entire lifetime would take a pile of burgers much larger than the Sun. In fact, it would be heavier than the supermassive black hole at the center of the galaxy.[6]Which would promptly create a new black hole. And possibly a new center of the galaxy, for all I know, although I'd want to play with Universe Sandbox for a while before making any sort of guess about how that would play out.The bottom line: If you want to keep up with the Sun's output by feeding people burgers, you'll need to open some intergalactic franchises.

Niagara Straw What would happen if one tried to funnel Niagara Falls through a straw?[1]This question was in reference to this Amazon review of gummy bears—but before you click, be warned that it describes the reviewer's gastrointestinal response to the candy in rather memorable detail.—David GwizdalaOne would get in trouble with the International Niagara Committee, the International Niagara Board of Control, the International Joint Commission, the International Niagara Board Working Committee, and probably the Great Lakes–St. Lawrence River Adaptive Management Committee.[2]Which is, if I'm understanding these organizational charts right, itself a supergroup made up of three committees for individual bodies of water. Also, the Earth would be destroyed.Well, that's not quite right. At the risk of stating the obvious, the real answer is, "Niagara Falls wouldn't fit through a straw."There are limits to how fast you can push fluids through things. If you pump a fluid through a narrow opening, it speeds up. If the fluid is a gas,[3]Gasses are fluids. I know that's weird, but many things are weird. it becomes "choked" when the speed of the gas flowing through the opening reaches the speed of sound. At that point, the gas flowing through the hole can't move any faster—although you can still get more mass to flow through per second by increasing the pressure, which compresses the gas further.For water, a different effect causes it to choke. When a fluid flows through an opening fast enough, the pressure within the fluid drops due to the Bernoulli principle. Water always "wants" to boil, but is held together by air pressure. Without enough pressure, bubbles of steam form in the water. This is called cavitation.When the water is forced through an opening at high speed, cavitation bubbles cause it to become less dense overall. Increasing the pressure—to try to push the water through harder—only makes it boil faster. (See page 17 here for a description of this process.)[4]Valve designers try to avoid creating these steam bubbles, because after the bubbles form, they quickly collapse as the pressure rises back up past the valve, and the force from that collapse can gradually eat away at plumbing. This keeps the total amount of water making it through the opening from rising, even if the water-steam mix moves at a higher speed.Another limit on the water flow rate comes from the speed of sound. You can't use pressure to accelerate water through an opening faster than the speed of sound (in water).[5]It's sort of like a traffic jam—forcing more cars into the back of a traffic jam won't make the ones in the front come out faster. The analogy between traffic jams and choked flows isn't perfect, but I still like it, because it's fun to imagine someone trying to solve traffic jams by using a bulldozer to push more cars into them. However, water very rarely reaches this point, because "the speed of sound in water" is very fast. If you try to make water—which is pretty heavy—go that fast, it tends to start ignoring the turns in your pipes.So how fast does Niagara Falls need to go to fit through a straw, and is it faster than the speed of sound? This is easy to figure out; all we need to know is the flow rate over the falls and how much area it needs to fit through.The flow rate over Niagara Falls is at least 100,000 cubic feet per second, which is actually mandated by law. The Niagara river supplies a total of about 292,000 cubic feet per second to the falls, but much of it is diverted into tunnels to generate electric power. However, since people get mad if you turn off the world's most famous waterfall, they're required to leave at least 100,000 of those cubic feet per second flowing over the falls for everyone to look at. (50,000 at night or during the off-season). Sometime in the next few years, the falls may be turned off for maintanence. And probably to see what cool stuff they can find.(Important note: If you divert the water into a straw, you'll be in violation of the 1950 treaty establishing the "100,000 cubic feet per second" limit. This is monitored by the International Niagara Committee, which consists of one American and one Canadian.[6]Currently, they are Aaron Thompson of Environment Canada and Brigadier General Richard Kaiser of the US Army Corps of Engineers. I'm guessing their enforcement protocol is just some variation on "filing a report," but I like to imagine that they're empowered to physically return the stolen water to the falls by any means necessary. They'll probably be upset with you, as will the other boards I mentioned earlier, so proceed at your own risk.)A typical straw is about 7mm in diameter. To find out how fast the water flows, we just divide the flow rate by that area. If the result is greater than the speed of sound, our flow will probably be choked, which will lead to problems.\[ \frac{100,000\text{ }\tfrac{\text{cubic feet}}{\text{second}}}{\pi\left ( \tfrac{7\text{ mm}}{2} \right )^2}=73,600,000\text{ }\tfrac{\text{meters}}{\text{second}}= 0.25c \]Apparently, our water will be going one-quarter of the speed of light.On the plus side, we don't need to worry about cavitation, since these water molecules would be going fast enough to cause all kinds of exciting nuclear reactions when they hit the walls of the straw. At those high energies, everything is a plasma anyway, so the concepts of boiling and cavitation don't even apply.But it gets worse! The recoil from the relativistic water jet would be pretty strong. It wouldn't be enough to push the North American plate south, but it would be enough to destroy whatever device you were using to create the jet.No machine could actually accelerate that much water to relativistic speeds. Particle accelerators can get things going that fast, but they're typically fed from a small bottle of gas. You can't just plug Niagara Falls into the accelerator input. Or, at least, if you did, the scientists would get awfully mad.Which is for the best, since the power of the particle jet created by this scenario would be greater than the power of all the sunlight that falls on Earth. Your "waterfall" would have a power output equivalent to that of a small star, and its heat and light would quickly raise the temperature of the planet, boil away the oceans, and render the whole place uninhabitable.And yet I bet someone would still try to go over it in a barrel.

Stop Jupiter I understand that the New Horizons craft used gravity assist from Jupiter to increase its speed on the way to Pluto. I also understand that by doing this, Jupiter slowed down very slightly. How many flyby runs would it take to stop Jupiter completely?—DillonMore than we can afford.Spacecraft sometimes perform close flybys of heavy, fast-moving planets, which can let them gain speed without using fuel.[1]It may sound strange that you could gain speed by flying toward a planet and then away from it, since intuitively it seems like any speed you gain from flying toward it, you should lose flying away. But it's not really about gravity at all; gravity assists could work just as well with ropes or springs, if you could make them big enough. When you you fly toward a planet, swing around it, and fly back in the direction you came, it's as if you "bounced off" the planet. If the planet is moving, this bounce can give you an extra kick—like a tennis ball thrown at the windshield of a passing truck. You can check out What If #38 for details—or, at least, a drawing of the tennis ball thing. Due to conservation of momentum, the maneuver also slows the planet down very slightly, but no one really worries about that.Planets don't slow down much during a flyby because they're so much heavier than spacecraft. When New Horizons flew by Jupiter, it gained about 4,000 m/s of velocity, while Jupiter lost about 10 m/s.[2]The geometry is a little complicated, since they were changing both speed and direction. If you want to learn more, look for a copy of this paper; it's a great tutorial.10 meters per second may not sound like much, but it very slightly changed Jupiter's orbit, shortening its year and bringing it slightly closer to the Sun. Thanks to that flyby, by the time the Sun goes supernova, Jupiter's calendar will be several dozen nanoseconds out of sync from where it would be otherwise!"Several dozen nanoseconds out of sync" isn't really satisfying, so we'll definitely need more than one flyby. How many can we pull off?The New Horizons mission cost the US government about \$700,000,000 over the full planned lifetime of the mission from 2001 to 2016. Over that same period, the government spent about \$47,879,840,000,000 on other things. If we cut all the spending on those other things[3]It's probably nothing important. and funneled it all into New Horizons probes, we could have launched 68,000 identical New Horizons probes.This would create some problems. For one, New Horizons carries a chunk of plutonium for power. This chunk—about 10 kg of it—was made from uranium in a reactor. To make enough plutonium for 68,000 New Horizons would require a substantial chunk of the world's uranium reserves.But it gets worse.[4]It always seems to, with plutonium. When NASA launches a spacecraft carrying plutonium, they estimate the odds of a launch accident which would release radioactive material into the atmosphere. Usually, these odds are around 1 in 300. With 68,000 launches, then, we can expect a little over 200 nuclear accidents, which probably isn't good.But it would all be worth it if we could slow down Jupiter! Sadly, 68,000 New Horizons probes aren't nearly enough. We'd still only rob Jupiter of a tiny fraction of its speed. Over the lifetime of the Solar System, the error in Jupiter's calendar would only add up to 2 milliseconds.If we made the spacecraft cheaper, we could send more of them, but sooner or later we'd start running out of materials. We'd definitely run out of fuel for all these rocket launches, but let's assume we've built some kind of space elevator to make launches cheap. We'd run out of uranium (to make the plutonium) pretty quickly, but we could replace the uranium with a chunk of lead—after all, this spacecraft doesn't really need to work.Eventually, though, we'd start running out of lead, too. If we replaced the lead with something else—say, rocks, or old garbage—we'd run out of that, too. At some point, in our desperate attempts to reduce Jupiter's forward speed, we'd be reduced to stuffing handfuls of rocks and dirt into a burlap sack with a NASA logo on the side.Then, believe it or not, we would run out of rocks.The Earth's crust only has so much stuff[5]This is the technical term. in it. Even if we peeled up the upper few dozen kilometers of crust and flung it at Jupiter—and for the record, I do not recommend we do this—it would trim less than a single mile per hour off Jupiter's speed.Really, it makes sense that this plan doesn't work. Earth weighs a lot less than Jupiter,[6]Earth weighs almost exactly pi milliJupiters. so even if we throw the entire Earth at Jupiter, it would still only reduce Jupiter's speed by a fraction of a percent—on the order of a few dozen miles per hour. The situation is similar to the one in the tennis ball analogy from earlier: If you want to stop a truck with tennis balls, the tennis balls need more momentum than the truck, which means they need to be extremely heavy, fast, or both.And at the core, that's the problem with this idea. Gravity assists are just like throwing a tennis ball at a speeding truck, and to stop a truck ...... you need an awfully big tennis ball.

Fire From Moonlight Can you use a magnifying glass and moonlight to light a fire?—Rogier SpoorAt first, this sounds like a pretty easy question.A magnifying glass concentrates light on a small spot. As many mischevious kids can tell you, a magnifying glass as small as a square inch in size can collect enough light to start a fire. A little Googling will tell you that the Sun is 400,000 times brighter than the Moon, so all we need is a 400,000-square-inch magnifying glass. Right?Wrong. Here's the real answer: You can't start a fire with moonlight[1]Pretty sure this is a Bon Jovi song. no matter how big your magnifying glass is. The reason is kind of subtle. It involves a lot of arguments that sound wrong but aren't, and generally takes you down a rabbit hole of optics.First, here's a general rule of thumb: You can't use lenses and mirrors to make something hotter than the surface of the light source itself. In other words, you can't use sunlight to make something hotter than the surface of the Sun.There are lots of ways to show why this is true using optics, but a simpler—if perhaps less satisfying—argument comes from thermodynamics:Lenses and mirrors work for free; they don't take any energy to operate.[2]And, more specifically, everything they do is fully reversible—which means you can add them in without increasing the entropy of the system. If you could use lenses and mirrors to make heat flow from the Sun to a spot on the ground that's hotter than the Sun, you'd be making heat flow from a colder place to a hotter place without expending energy. The second law of thermodynamics says you can't do that. If you could, you could make a perpetual motion machine.The Sun is about 5,000°C, so our rule says you can't focus sunlight with lenses and mirrors to get something any hotter than 5,000°C. The Moon's sunlit surface is a little over 100°C, so you can't focus moonlight to make something hotter than about 100°C. That's too cold to set most things on fire."But wait," you might say. "The Moon's light isn't like the Sun's! The Sun is a blackbody—its light output is related to its high temperature. The Moon shines with reflected sunlight, which has a "temperature" of thousands of degrees—that argument doesn't work!"It turns out it does work, for reasons we'll get to later. But first, hang on—is that rule even correct for the Sun? Sure, the thermodynamics argument seems hard to argue with,[3]Because it's correct. but to someone with a physics background who's used to thinking of energy flow, it may seem hard to swallow. Why can't you concentrate lots of sunlight onto a point to make it hot? Lenses can concentrate light down to a tiny point, right? Why can't you just concentrate more and more of the Sun's energy down onto the same point? With over 10 watts available, you should be able to get a point as hot as you want, right?Except lenses don't concentrate light down onto a point—not unless the light source is also a point. They concentrate light down onto an area—a tiny image of the Sun.[4]Or a big one! This difference turns out to be important. To see why, let's look at an example:This lens directs all the light from point A to point C. If the lens were to concentrate light from the Sun down to a point, it would need to direct all the light from point B to point C, too:But now we have a problem. What happens if light goes back from point C toward the lens? Optical systems are reversible, so the light should be able to go back to where it came from—but how does the lens know whether the light came from B or to A?In general, there's no way to "overlay" light beams on each other, because the whole system has to be reversible. This keeps you from squeezing more light in from a given direction, which puts a limit on how much light you can direct from a source to a target.Maybe you can't overlay light rays, but can't you, you know, sort of smoosh them closer together, so you can fit more of them side-by-side? Then you could gather lots of smooshed beams and aim them at a target from slightly different angles.Nope, you can't do this.[5]We already know this, of course, since earlier we said that it would let you violate the second law of thermodynamics.It turns out that any optical system follows a law called conservation of étendue. This law says that if you have light coming into a system from a bunch of different angles and over a large "input" area, then the input area times the input angle[6]Note to nitpickers: In 3D systems, this is technically the solid angle, the 2D equivalent of the regular angle, but whatever. equals the output area times the output angle. If your light is concentrated to a smaller output area, then it must be "spread out" over a larger output angle.In other words, you can't smoosh light beams together without also making them less parallel, which means you can't aim them at a faraway spot.There's another way to think about this property of lenses: They only make light sources take up more of the sky; they can't make the light from any single spot brighter,[7]A popular demonstration of this: Try holding up a magnifying glass to a wall. The magnifying glass collects light from many parts of the wall and sends them to your eye, but it doesn't make the wall look brighter. because it can be shown[8]This is left as an exercise for the reader. that making the light from a given direction brighter would violate the rules of étendue.[9]My résumé says étendue is my forté. In other words, all a lens system can do is make every line of sight end on the surface of a light source, which is equivalent to making the light source surround the target.If you're "surrounded" by the Sun's surface material, then you're effectively floating within the Sun, and will quickly reach the temperature of your surroundings.[10](Very hot)If you're surrounded by the bright surface of the Moon, what temperature will you reach? Well, rocks on the Moon's surface are nearly surrounded by the surface of the Moon, and they reach the temperature of the surface of the Moon (since they are the surface of the Moon.) So a lens system focusing moonlight can't really make something hotter than a well-placed rock sitting on the Moon's surface.Which gives us one last way to prove that you can't start a fire with moonlight: Buzz Aldrin is still alive.

Saliva Pool How long would it take for a single person to fill up an entire swimming pool with their own saliva?—Mary Griffin, 9th gradeThe average kid produces about half a liter of saliva per day, according to the paper Estimation of the total saliva volume produced per day in five-year-old children, which I like to imagine was mailed to the Archives of Oral Biology in a slightly sticky, dripping envelope.A five-year-old probably produces proportionally less saliva than a larger adult. On the other hand, I'm not comfortable betting that anyone produces more drool than a little kid, so let's be conservative and use the paper's figure.If you're collecting your saliva,[1]This question is gross, by the way. you can't use it to eat.[2]I hope. You could get around this by chewing gum or something, to get your body to produce extra saliva, or just by drinking liquid food or getting an IV.At the rate of 500 mL per day from the paper, it would take you about a year to fill a typical bathtub.A bathtub full of saliva is pretty gross, but that's not what you asked about. For some reason—I don't really want to know why—you asked about filling a pool.Let's imagine an Olympic-sized swimming pool, which is 25 meters by 50 meters. Depths vary, but we'll suppose this one is uniformly 4 feet deep,[3]You can read more of the regulations here; a pool with starting blocks does need a slightly deeper bit near each end, but it can be shallower in the middle. There doesn't seem to be anything in the rules about a maximum depth, so I suppose you can make a pool that continues through to the other side of the Earth, but then you run into trouble when you try to follow the instructions in section FR 2.14 about painting lane markings on the bottom. so you can probably stand up in it.At 500 mL per day, it would take you 8,345 years to fill this pool. That's a long time for the rest of us to wait, so let's imagine you went back in time to get started on this project early.8,345 years ago, the ice sheets that covered much of the northern parts of the world had mostly receded, and humans had just begun to develop agriculture. Let's imagine you started your project then.By 4000 BCE, when the civilizations of the Fertile Crescent had begun to develop in modern-day Iraq, the saliva would be a foot deep, covering your feet and ankles.By 3200 BCE, when writing was first developed, the saliva would creep past your knees.Around the mid-2000s BCE, the Great Pyramid was constructed and early Mayan cultures emerged. At this point, the saliva would be getting close to your fingertips if you didn't lift your arms up.Around 1600 BCE, the eruption of a huge volcano in the Greek island now known as Santorini caused a massive tsunami which devastated the Minoan civilization, possibly causing its final collapse. As this happened, the saliva would probably be approaching waist-deep.The saliva would continue to rise throughout the next three millennia of history, and by the time of Europe's industrial revolution it would be chest-deep, easily enough saliva to swim in. The last 200 years would add the final 3 centimeters, and the pool would finally be filled.It would take a long time, sure. But it would all be worth it, because at the end of it all, you'd have an Olympic-size swimming pool full of saliva. And isn't that, deep down, all any of us really want?[4]No. It is not.

Earth’s atmosphere is really thin compared to the radius of the Earth. How big a hole do I need to dig before people suffocate?—Sam BurkeThe idea here is straightforward: When you dig a hole in the ground, the hole fills up with air.[1] If you dig a big enough hole, most of the atmosphere will flow in, and there won't be enough left outside the hole to breathe.[2]⁠[3]The atmosphere's exact volume is tricky to define, since it gets thinner at higher altitudes and doesn't have a firm boundary. If you compressed the whole thing to the density of normal surface air, it would be about 10 kilometers thick, and take up a volume of 4 billion cubic kilometers. 4 billion km of air is enough to fill a cube 1,000 miles high, which is nearly the volume of the solid core of the Earth. That gives us a rough idea of the scale of our hole.Digging a hole that big will be a challenge. Even a hole the size of Massachusetts would have to be deeper than the diameter of the Earth to fit the whole atmosphere at surface pressure. A hole the size of the entire United States would need to be 400 kilometers deep, much deeper than we could actually dig.[4]But wait! Air pressure changes with height. Air pressure goes down as you rise upward, which you can sometimes notice when your ears pop while driving on a hill or riding in a tall elevator. By the same token, pressure rises when you go downward. The air pressure in a deep mine is much higher than the pressure at sea level.It might seem like the increasing pressure would help us fit more air into the hole. The pressure should compress the air, so a deep hole should be able to fit more than its "fair share" of air. But it doesn't quite work out that way.As you go deeper into the Earth, the rock gets hotter.[5] Under the ideal gas law, pressure compresses air, but heat causes it to expand. In the case of a hole in the Earth's crust, the expansion from the heat of the rocks can actually counteract the compression from the higher pressure. Calculations in this paper⁠[6] show that temperature gradients of more than about 30°C per kilometer will result in no compression at all. If the temperature change is faster than that—as is common in areas with thin crust or volcanic activity—the density of air will actually drop as you go deeper, even as the pressure increases.What if we compress the air some other way?Diving tanks can contain air crushed by a factor of 200. A pile of diving tanks would only have to be a few hundred miles high to hold the entire atmosphere. If we want to compress air further, we can liquify it. Air is mostly oxygen and nitrogen. If we get air cold enough, it turns to a liquid with a density similar to water.If we liquified the whole atmosphere—and for the record, I don't think we should—we could conceivably fit it all in the ground. We'd effectively need to remove a patch of the Earth's upper crust, exposing magma veins and pressurized chambers, and we'd have to somehow seal all those off and keep things cool enough that our storage tanks didn't melt.The excavation would be a near-impossible challenge. But if you somehow solved all the countless engineering problems, you could—in principle—fit the entire liquified atmosphere of the Earth in a 5-mile-deep hole roughly the size of Texas.Although you may not want to use that particular state.[1] The dirt you pile up outside the hole displaces air, so at first you won't have much effect on the surrounding atmosphere, but the effect grows as the hole gets deeper and the pile gets higher. So keep at it![2] You need to remove about 65% of the atmosphere before sea level air becomes too thin to support human life.[3] As this paper points out, it's odd—and likely coincidental—that the highest point on Earth happens to be just about exactly as high as the human high-altitude survival limit.[4] And if you tried to dig up the entire surface of the United States to any depth, people would probably yell at you.[5] Citation: Amiel, J., Eckhart, A. E., Swank, H., (2003) The Core[6] This one is an actual paper and not a trailer for a terrible movie, I promise.

Hide the Atmosphere Earth’s atmosphere is really thin compared to the radius of the Earth. How big a hole do I need to dig before people suffocate?—Sam BurkeThe idea here is straightforward: When you dig a hole in the ground, the hole fills up with air.[1]The dirt you pile up outside the hole displaces air, so at first you won't have much effect on the surrounding atmosphere, but the effect grows as the hole gets deeper and the pile gets higher. So keep at it! If you dig a big enough hole, most of the atmosphere will flow in, and there won't be enough left outside the hole to breathe.[2]You need to remove about 65% of the atmosphere before sea level air becomes too thin to support human life.⁠[3]As this paper points out, it's odd—and likely coincidental—that the highest point on Earth happens to be just about exactly as high as the human high-altitude survival limit.The atmosphere's exact volume is tricky to define, since it gets thinner at higher altitudes and doesn't have a firm boundary. If you compressed the whole thing to the density of normal surface air, it would be about 10 kilometers thick, and take up a volume of 4 billion cubic kilometers. 4 billion km of air is enough to fill a cube 1,000 miles high, which is nearly the volume of the solid core of the Earth. That gives us a rough idea of the scale of our hole.Digging a hole that big will be a challenge. Even a hole the size of Massachusetts would have to be deeper than the diameter of the Earth to fit the whole atmosphere at surface pressure. A hole the size of the entire United States would need to be 400 kilometers deep, much deeper than we could actually dig.[4]And if you tried to dig up the entire surface of the United States to any depth, people would probably yell at you.But wait! Air pressure changes with height. Air pressure goes down as you rise upward, which you can sometimes notice when your ears pop while driving on a hill or riding in a tall elevator. By the same token, pressure rises when you go downward. The air pressure in a deep mine is much higher than the pressure at sea level.It might seem like the increasing pressure would help us fit more air into the hole. The pressure should compress the air, so a deep hole should be able to fit more than its "fair share" of air. But it doesn't quite work out that way.As you go deeper into the Earth, the rock gets hotter.[5]Citation: Amiel, J., Eckhart, A. E., Swank, H., (2003) The Core Under the ideal gas law, pressure compresses air, but heat causes it to expand. In the case of a hole in the Earth's crust, the expansion from the heat of the rocks can actually counteract the compression from the higher pressure. Calculations in this paper⁠[6]This one is an actual paper and not a trailer for a terrible movie, I promise. show that temperature gradients of more than about 30°C per kilometer will result in no compression at all. If the temperature change is faster than that—as is common in areas with thin crust or volcanic activity—the density of air will actually drop as you go deeper, even as the pressure increases.What if we compress the air some other way?Diving tanks can contain air crushed by a factor of 200. A pile of diving tanks would only have to be a few hundred miles high to hold the entire atmosphere. If we want to compress air further, we can liquify it. Air is mostly oxygen and nitrogen. If we get air cold enough, it turns to a liquid with a density similar to water.If we liquified the whole atmosphere—and for the record, I don't think we should—we could conceivably fit it all in the ground. We'd effectively need to remove a patch of the Earth's upper crust, exposing magma veins and pressurized chambers, and we'd have to somehow seal all those off and keep things cool enough that our storage tanks didn't melt.The excavation would be a near-impossible challenge. But if you somehow solved all the countless engineering problems, you could—in principle—fit the entire liquified atmosphere of the Earth in a 5-mile-deep hole roughly the size of Texas.Although you may not want to use that particular state.

Europa Water Siphon What if you built a siphon from the oceans on Europa to Earth? Would it flow once it's set up? (We have an idea for selling bottled Europa water.)—A group of Google Search SREsNo, but I like where you're going with this.Siphons are neat—they let you pump water up and over a barrier using just a tube and gravity. You can use siphoning to empty swimming pools, fill awkwardly-shaped containers, or get up to all kinds of trouble.[1]I asked some friends to suggest which thing in their house they'd be most upset to find someone siphoning water into. Answers included: Spice drawer, gumball machine, tea collection, bottle of vitamins, watercolor paint set, bag of rice with a cell phone in it, mint-condition instant oatmeal collection, carefully tuned musical glasses, ice hotel, prizewinning sand castle, sodium action figure collection, gremlin cage, Martian soil sample, dehydrated astronaut ice cream, and rack of those water-sensing self-inflating lifeboats.It's not necessarily obvious at first glance, but siphoning works because of air pressure. Before we answer the Europa question, it may help to go over how siphons work.If you take a tube full of water and point the ends down, gravity will try to pull the water down, making it fall out of both sides. If the water did start to fall out, a vacuum would form in the middle, since there's no way for air to get in to fill the gap. Each column of water would then have a vacuum on one side and air on the other, which means it would be pushed back up into the tube.In reality, this doesn't happen; the air pressure stops the vacuum from opening up in the first place, and the water just sits there in the tube. Or, at least, it would if it were perfectly balanced.If the water in one end is slightly lower than the other, then the column of water on that side pushes down harder against the air than the column on the other side. This imbalance causes the water to "tip" and run out of the heavier end.To siphon something, you can just keep feeding more water into the tube on the higher side. As long as the surface of that water is higher up than the place where the water is coming out, the siphon will keep running.If the column of water is more than about 34 feet[2]10 meters​[3]2 giraffes high, the pressure from the weight of the water becomes too strong for Earth's air pressure to counteract, and the water does fall out from both sides and briefly create a vacuum.[4]Although as the pressure drops, the water boils away to fill it, so you can't actually get too close to a pure vacuum this way. However, if you use something like olive oil (or mercury), you can get much closer. This means that on Earth's surface, you can't siphon water over a barrier that's more than 34 feet high. In Denver, where the air pressure is lower, the limit is 28 feet. In a vacuum—in theory—you can't siphon at all.[5]In practice, it turns out siphons do work in a vacuum, at least a little bit, because the "stickiness" of the water keeps it from pulling apart in the middle.Europa has barely any atmosphere, so you won't be able to do much siphoning. But you also can't siphon water out of the atmosphere from a planet in general. A column of atmosphere, which is miles high, pushes down only as hard as a column of water 34 feet high. The water column is smaller because water is much denser than air. As long as the stuff on top is less dense than the liquid below it, you can't use the pressure from the stuff on top to siphon the liquid up above the stuff on top.[6]Most of the time, things sort themselves into layers, with the denser ones on the bottom. Occasionally, in the Earth, layers of dense rock will end up above layers of less-dense oil. This is why—when oil wellheads break—oil can sometimes come spurting out without any help from the pumps.Even if you could generate a lot of pressure, pumping water from Europa's surface would take some work. Europa's gravity is weaker than Earth's, which means lifting something up from the surface of Europa takes less energy, but it's still not easy. The energy required to "climb out of Europa's gravity well" is the same as the energy required to climb up 209 kilometers against Earth's surface gravity. (Earth's gravity well, by comparison, is about 6,379 kilometers "deep"—click on this comic for an illustration.)Once you've lifted the water out of Europa's gravity well, you then have to lift it the rest of the way out of Jupiter's, which is a lot deeper. Then, you have to do more work to push the water on a trajectory where it intercepts Earth. In terms of energy, the whole task is roughly equivalent to lifting the water about 2,500 kilometers in Earth gravity:You could send the water to Earth by launching it from the surface of Europa at about 7 km/s. Conveniently, since Europa has no atmosphere, you don't need to use inefficient rockets to climb up to space. You can launch the water directly from the surface using something simpler, like a coilgun.When the water reaches Earth, it can use atmospheric braking to slow down, and the individual bottles could be steered directly to their targets. Timing the deliveries would be tricky, sure, but it sure would be impressive if you got it right. Plus, you could totally one-up Amazon's drone delivery scheme.At current electricity prices, the launch would cost a minimum of 50 cents (US) per bottle. Of course, getting electricity on Europa is probably a bit more expensive than getting it on Earth,[7]Or would need an awfully long cord. and setting up the purification plant and bottling operation on Europa wouldn't be cheap, to put it mildly.All in all, you're going to have to charge an awful lot per bottle to break even on this whole operation. And if it turns out Europa's water has some weird alien pathogen in it, you might accidentally kill all your customers.[8]And, possibly, everyone else.This may sound like your plan is pretty impractical and unrealistic, especially since there's no point to it all. Water is water. Once you've purified the water on Europa to make it drinkable, it won't be much different from water here on Earth. On the other hand, we ship water around the world from Fiji for no reason, so who knows. Maybe, with the right marketing, this idea could work.

Space Jetta What if I tried to re-enter the atmosphere in my car? (a 2000 VW Jetta TDI). Would it do more environmental damage than it is already apparently doing?—Casey BergBelieve it or not, throwing cars at a planet might be better for the planet than driving them on the surface. But it's hard to say for sure.Volkswagen, as you've apparently heard, has been cheating on pollution tests since 2009. Your car was made before they started cheating, but that doesn't actually mean it pollutes less. Since the 1970s, the US has been tightening the rules around some of the exhaust gasses that create smog, like nitric oxide. By the mid-2000s, when the latest round of standards kicked in, Volkswagen apparently decided it was too expensive to keep up without sacrificing performance. Instead, they modified their cars to cheat on the tests, then lied to customers about how clean their cars were.If you somehow put your car in orbit, then let it re-enter the atmosphere and burn up like a satellite, that would put an end to the tailpipe pollution.On the other hand, burned fragments of your car (and body) would be scattered throughout the stratosphere. So what impact does space debris have on our air?The surprising answer is that no one really knows. Roughly one major piece of space debris, like a satellite or booster rocket, re-enters the atmosphere each day. We talk about them "burning up," but they don't really disappear. Big chunks of them make it to the ground (usually falling in the ocean or landing in the desert somewhere.) Other dust and fragments are scattered throughout the stratosphere, and no one really knows what effect they have on anything.Your car's shockwave would also create nitric oxide, which would—briefly—eat a small hole in the ozone layer. That hole would "close up" quickly, and the overall impact on the ozone layer would be small compared to other sources of ozone depletion.While your car would briefly harm the ozone layer, it would help with global warming. I don't know how long you expect to have your car, but if you drive it another hundred thousand miles, it will emit about 20 or 30 tons of carbon dioxide. By destroying your car, it's true that you'll be literally putting carbon into the atmosphere, but not nearly as much as you would by continuing to drive it.In the end, the real problem isn't the re-entry—it's the launch. Rocket launches have a much larger impact to the environment than re-entry, although it's still small in the grand scheme of things since we don't launch very many rockets.Which raises a final question: What are you and your car doing in orbit in the first place? Are you the only one? Or have all cars been teleported into orbit? If so, we could be in trouble.It's unlikely that any one piece of satellite debris will hit someone. But there are several hundred million passenger cars in the United States alone. If all of them were suddenly shot into orbit and allowed to reenter, it's likely that somewhere between a few hundred and a few thousand people would be injured or killed by falling engine blocks, transmissions, and half-melted axles.On the other hand, about thirty thousand Americans are killed each year in motor vehicle accidents. So while launching all our cars into space—and letting them fall back down and hit us—might sound like a bad idea ...... it's arguably a lot safer than continuing to drive them.

Sunbeam What if all of the sun's output of visible light were bundled up into a laser-like beam that had a diameter of around 1m once it reaches Earth?—Max SchäferHere's the situation Max is describing:If you were standing in the path of the beam, you would obviously die pretty quickly. You wouldn't really die of anything, in the traditional sense. You would just stop being biology and start being physics.When the beam of light hit the atmosphere, it would heat a pocket of air to millions of degrees[1]Fahrenheit, Celsius, Rankine, or Kelvin—it doesn't really matter. in a fraction of a second. That air would turn to plasma and start dumping its heat as a flood of x-rays in all directions. Those x-rays would heat up the air around them, which would turn to plasma itself and start emitting infrared light. It would be like a hydrogen bomb going off, only much more violent.This radiation would vaporize everything in sight, turn the surrounding atmosphere to plasma, and start stripping away the Earth's surface.But let's imagine you were standing on the far side of the Earth. You're still definitely not going to make it—things don't turn out well for the Earth in this scenario—but what, exactly, would you die from?The Earth is big enough to protect people on the other side—at least for a little bit—from Max's sunbeam, and the seismic waves from the destruction would take a while to propogate through the planet. But the Earth isn't a perfect shield. Those wouldn't be what killed you.Instead, you would die from twilight.The sky is dark at night because the Sun is on the other side of the Earth. But the night sky isn't always completely dark. There's a glow in the sky before sunrise and after sunset because, even with the Sun hidden, some of the light is bent around the surface by the atmosphere.If the sunbeam hit the Earth, x-rays, thermal radiation, and everything in between would flood into the atmosphere, so we need to learn a little about how different kinds of light interact with air.Normal light interacts with the atmosphere through Rayleigh scattering. You may have heard of Rayleigh scattering as the answer to "why is the sky blue." This is sort of true, but honestly, a better answer to this question might be "because air is blue." Sure, it appears blue for a bunch of physics reasons, but everything appears the color it is for a bunch of physics reasons.[2]When you ask, "Why is the statue of liberty green?" the answer is something like, "The outside of the statue is copper, so it used to be copper-colored. Over time, a layer of copper carbonate formed (through oxidation), and copper carbonate is green." You don't say "The statue is green because of frequency-specific absorption and scattering by surface molecules."When air heats up, the electrons are stripped away from their atoms, turning it to plasma. The ongoing flood of radiation from the beam has to pass through this plasma, so we need to know how transparent plasma is to different kinds of light. At this point, I'd like to mention the 1964 paper Opacity Calculations: Past and Future, by Harris L. Mayer, which contains the single best opening paragraph to a physics paper I've ever seen:

Proton Earth, Electron Moon What if the Earth were made entirely of protons, and the Moon were made entirely of electrons?—Noah WilliamsThis is, by far, the most destructive What-If scenario to date.You might imagine an electron Moon orbiting a proton Earth, sort of like a gigantic hydrogen atom. On one level, it makes a kind of sense; after all, electrons orbit protons, and moons orbit planets. In fact, a planetary model of the atom was briefly popular (although it turned out not to be very useful for understanding atoms.[1]This model was (mostly) obsolete by the 1920s, but lived on in an elaborate foam-and-pipe-cleaner diorama I made in 6th grade science class.)If you put two electrons together, they try to fly apart. Electrons are negatively charged, and the force of repulsion from this charge is about 20 orders of magnitude stronger than the force of gravity pulling them together.If you put 10 electrons together—to build a Moon—they push each other apart really hard. In fact, they push each other apart so hard, each electron would be shoved away with an unbelievable amount of energy.It turns out that, for the proton Earth and electron Moon in Noah's scenario, the planetary model is even more wrong than usual. The Moon wouldn't orbit the Earth because they'd barely have a chance to influence each other;[2]I interpreted the question to mean that the Moon was replaced with a sphere of electrons the size and mass of the Moon, and ditto for the Earth. There are other interpretations, but practically speaking the end result is the same. the forces trying to blow each one apart would be far more powerful than any attractive force between the two.If we ignore general relativity for a moment—we'll come back to it—we can calculate that the energy from these electrons all pushing on each other would be enough to accelerate all of them outward at near the speed of light.[3]But not past it; we're ignoring general relativity, but not special relativity. Accelerating particles to those speeds isn't unusual; a desktop particle accelerator can accelerate electrons to a reasonable fraction of the speed of light. But the electrons in Noah's Moon would each be carrying much, much more energy than those in a normal accelerator—orders of magnitude more than the Planck energy, which is itself many orders of magnitude larger than the energies we can reach in our largest accelerators. In other words, Noah's question takes us pretty far outside normal physics, into the highly theoretical realm of things like quantum gravity and string theory.So I contacted Dr. Cindy Keeler, a string theorist with the Niels Bohr Institute. I explained Noah's scenario, and she was kind enough to offer some thoughts.Dr. Keeler agreed that we shouldn't rely on any calculations that involve putting that much energy in each electron, since it's so far beyond what we're able to test in our accelerators. "I don't trust anything with energy per particle over the Planck scale. The most energy we've really observed is in cosmic rays; more than LHC by circa 10, I think, but still not close to the Planck energy. Being a string theorist, I'm tempted to say something stringy would happen—but the truth is we just don't know."Luckily, that's not the end of the story. Remember how we're ignoring general relativity? Well, this is one of the very, very rare situations where bringing in general relativity makes a problem easier to solve.There's a huge amount of potential energy in this scenario—the energy that we imagined would blast all these electrons apart. That energy warps space and time just like mass does.[4]If we let the energy blast the electrons apart at near the speed of light, we'd see that energy actually take the form of mass, as the electrons gained mass relativistically. That is, until something stringy happened. The amount of energy in our electron Moon, it turns out, is about equal to the total mass and energy of the entire visible universe.An entire universe worth of mass-energy—concentrated into the space of our (relatively small) Moon—would warp space-time so strongly that it would overpower even the repulsion of those 10 electrons.Dr. Keeler's diagnosis: "Yup, black hole." But this is no an ordinary black hole; it's a black hole with a lot of electric charge.[5]The proton Earth, which would also be part of this black hole, would reduce the charge, but since an Earth-mass of protons has much less charge than a Moon-mass of electrons, it doesn't affect the result much. And for that, you need a different set of equations—rather than the standard Schwarzschild equations, you need the Reissner–Nordström ones.In a sense, the Reissner-Nordström equations compare the outward force of the charge to the inward pull of gravity. If the outward push from the charge is large enough, it's possible the event horizon surrounding the black hole can disappear completely. That would leave behind an infinitely-dense object from which light can escape—a naked singularity.Once you have a naked singularity, physics starts breaking down in very big ways. Quantum mechanics and general relativity give absurd answers, and they're not even the same absurd answers. Some people have argued that the laws of physics don't allow that kind of situation to arise. As Dr. Keeler put it, "Nobody likes a naked singularity."In the case of an electron Moon, the energy from all those electrons pushing on each other is so large that the gravitational pull wins, and our singularity would form a normal black hole. At least, "normal" in some sense; it would be a black hole as massive as the observable universe.[6]A black hole with the mass of the observable universe would have a radius of 13.8 billion light-years, and the universe is 13.8 billion years old, which has led some people to say "the Universe is a black hole!" (It's not.)Would this black hole cause the universe to collapse? Hard to say. The answer depends on what the deal with dark energy is, and nobody knows what the deal with dark energy is.But for now, at least, nearby galaxies would be safe. Since the gravitational influence of the black hole can only expand outward at the speed of light, much of the universe around us would remain blissfully unaware of our ridiculous electron experiment.

Jupiter Descending If you did fall into Jupiter's atmosphere in a submarine, what would it actually look like? What would you see before you melted or burned up?—Ada MunroeWe don't know! We've only flown spacecraft into a gas planet's atmosphere twice (both Jupiter). One had no cameras, and one went in at night (and was being disposed of, so wasn't taking pictures anyway).If you took a submarine to Jupiter, it would burn up. Jupiter has a deep gravity well; after falling down toward it from space, you're going very fast. There's no easy way to shed that speed other than slamming into the atmosphere and letting it slow you down, but the entry is about four times faster than the Space Shuttle or Apollo Earth reentries. Only the Galileo probe has survived a Jupiter atmospheric entry.The Galileo probe survived by being a bullet with a big heat shield, and several inches of the shield were burned away before it finished slowing down and started falling vertically by parachute. The probe only sent back about half a megabyte of data to the Galileo orbiter, and had no camera, so we don't know what it saw.We could, I guess, try to do the same thing with a submarine—by mounting a giant heat shield on the front—but it would probably qualify as the most Kerbal vehicle ever built.If our submarine survived, what would we see?[1]I mean, submarines don't usually have a lot of windows, but we at least have a periscope, right?The best pictures we have of Jupiter's atmosphere are probably these carefully processed mosaics of the Great Red Spot, but they're still taken from very far away. At those resolutions, a huge Earth thunderstorm would appear as roughly one pixel. Trying to figure out what Jupiter's clouds would look like from those pictures is like using this to reconstruct these.By combining the pictures with other science data, we've been able to put together a pretty good idea of what Jupiter's atmosphere is like, but there are some pretty big questions still unanswered which make it hard to be too confident about what it would actually look like. For example, you know the Great Red Spot? We don't know what all that red stuff is.Author Michael Carroll has done a lot of thinking about planetary atmospheres, and his book Drifting on Alien Winds vividly describes of what it would be like to descend through Jupiter's clouds. He was also kind enough to answer some of my questions about Jupiter. Here's a rough sketch of what you'd see as you descended through the clouds; for more, definitely check out his book.Jupiter's upper atmosphere (the part we would see before we died) has three main layers—an upper layer of haze and ammonia clouds, similar to cirrostratus clouds on Earth. Below that is a thick, reddish-brown ammonium hydrosulfide cloud layer. The lowest layer consists of white water clouds, which occasionally rise into towering thunderstorms that occasionally push through the middle layer.Between these cloud layers, the air is probably pretty clear. At those levels, it would be less dense than the air on Earth, so you could see a long way. Thanks to Rayleigh scattering, the sky would be blue, and objects far off in the distance would fade to blue just like they do on Earth. But since Jupiter is so huge, we might not see the clouds disappear over the horizon; the towers might just fade off into the distance.We don't really know how accurate these pictures are, though, until we send a camera to fly down into Jupiter's atmosphere and send pictures back.Juno, scheduled to reach Jupiter next year, carries a pretty nice camera,[2]Thank you to Emily Lakdawalla for her helpful background about various spacecraft cameras, including her many thorough spreadsheets. which should give us slightly better-resolution pictures, but it still won't really give us a sense of what the cloud decks look like from within them. For that, we need to send in a probe with a camera—and there's nothing like that on the horizon. There's certainly more science value in visiting Europa than in satisfying our curiosity about the Jovian sky.But with interplanetary cubesats soon to make their debut, who knows—maybe someone out there will put together a camera, heat shield, and parachute, and hitch a ride on the next outer planets mission. And then, finally, we'll get to look at Jupiter's clouds from both sides.

Jupiter Submarine What if you released a submarine into Jupiter's atmosphere? Would it eventually reach a point where it would float? Could it navigate?—KTHNope! Jupiter's pressure, density, and temperature curves are different from ours. At the point in Jupiter's atmosphere where the density is high enough for a submarine to float, the pressure is high enough to crush the submarine,[1]Which makes it more dense. and the temperature is high enough to melt it.[2]Which makes it harder to drive.But there's another problem: Jupiter is a gas giant, but submarines—as you can figure out from etymology—go under water.Air and water are different. This seems straightforward enough, but they're also the same in a lot of ways. They're both "fluids," and some of the same rules apply to each. In some sense, when you look up at the sky, you're looking up from the bottom of a deep sea of air.Things float when they're less dense than the fluid around them. This works the same for balloons in air and boats in water. The late Terry Pratchett wrote a truly beautiful passage about this, in the prologue to his book Going Postal. He says that since water is in many respects a wetter form of air,[3]Sounds reasonable enough to me. as ships sink, eventually they reach a point where the water was too dense to sink any further. This layer forms an underwater surface on which shipwrecks collect, drifting around beneath the waves but far above the sea floor:

New Horizons What if New Horizons hits my car?—Robin SheatThe New Horizons spacecraft is currently flying past Pluto.[1]Ever since astrophysicist Katie Mack pointed out that "New Horizons" appears in the lyrics to A Whole New World, I've gotten it stuck in my head every time I've seen something about Pluto. For the last few days, it's been giving us our first clear look at the world, and it should be making its closest approach at the moment this article is posted. Either that, or hitting your car, I guess.It's hard to imagine how that could happen, even if New Horizons had headed to Earth by mistake. Unless there's been an especially strange freeway accident, your car is currently within the Earth's atmosphere. All that air stops spacecraft from flying into the ground at full speed. But maybe you took a wrong turn and ended up near Charon, or maybe you drove into a freak extremely-low-pressure system, leaving no atmosphere above you. It could happen!​[2]It really, really couldn't.New Horizons is about the size and weight of a grand piano, and is currently screaming along at about 14 kilometers per second. If it hit your car, it would be pretty bad for both vehicles.How fast is 14 kilometers per second? Here's my favorite comparison for putting that speed in perspective: If you were standing at one end of a football field and fired a gun toward the other end, right while New Horizons flew past you, the spacecraft would reach the far end zone before the bullet made it to the 10-yard line.[3]In that same amount of time, a speeding car would travel about an inch.This high speed means that by this afternoon, New Horizons will be on its way out of the Pluto system,[4]People often ask why New Horizons is just doing a flyby, and not sticking around to orbit Pluto. The answer is: If you can figure out a way to do that, go for it. Pluto is really far away, and to get a probe there before your career ends, you have to go really fast. When you're going that fast, it's hard to stop. (At least, if you want to stop in one piece.) and over the coming days and weeks it will let us know what it saw today. It can't talk to Earth and take photos at the same time, so right now it's spending all its time taking pictures and gathering data.Later today, the spacecraft will pause the data-gathering for a moment to send a brief message to Earth. No results—just, "Hey, I'm still alive". If it is still alive, that is. It's flying at terrifying speed through a part of the Solar System we've never visited. There could be, say, a bunch of small rocks there.[5]In case of disaster, New Horizons has sent back a few snapshots and data dumps right before the encounter, so at least we'll have those. Or a car.New Horizons will send the "I'm okay" message in the afternoon, but it takes light four and a half hours to get back to Earth, so it will get here around 8:53pm Eastern US time—so if you're going to have a Pluto party, that's the time to do it. You can tune in to NASA TV to watch the nervous people in mission control wait for the signal. You'll know it worked if there's lots of cheering and hugging.For more details on the mission, check out Emily Lakdawalla's comprehensive Planetary Society post, What to expect when you're expecting a flyby, which has dates, times, and background on all the equipment. (For up-to-the-minute coverage, her Twitter feed is probably the best place to go for updates, context, and excitement.)So what does all this mean for your car?Passenger cars have "crumple zones," which are areas of the car designed to fold up and absorb some of the force of an impact before it reaches the passenger cabin. Unfortunately, in a hypervelocity impact, materials like metal aren't nearly strong enough to hold together. Instead of crumpling, they splash. New Horizons and your car's crumple zone would splash as bits of them passed through each other, and the resulting spray of metal would do the same to the rest of your car. From a distance, it would probably look approximately like this.Here's the good news: NASA will have to pay for your car. Under the Convention on the International Liability for Damage Caused by Space Object, NASA and the US government would clearly be on the hook for the damage. And, since you wouldn't be considered at fault in the accident, in most states insurance companies would be legally prohibited from raising your premiums.The situation would be slightly complicated by the fact that this would be a nuclear accident. New Horizons flies too far from the Sun to use solar panels, so it's powered by the heat from a bunch of lumps of plutonium-238. The container holding the plutonium is sturdy, since it's designed to survive atmospheric reentry (and has done so). However, it's not designed to survive entry into a Chevy. The container and the plutonium inside it would be splattered across the landscape. The US government will not only have to replace your car, it will probably have to replace much of your neighborhood.This has actually happened before. In 1978, the Soviet satellite Kosmos 954, which carried a nuclear reactor, reentered the atmosphere and disintegrated over Canada. The Canadian government spent millions cleaning up the radioactive debris near Yellowknife. They demanded over $6 million (CAD) from the Soviets for the cleanup, and were eventually paid $3 million.Hopefully, New Horizons is currently flying past Pluto. But don't worry; if it somehow hits your car instead, the US government will cover things. To find out which one it is—Pluto or your car—tune in to NASA TV.And watch your driveway.

Spiders vs. the Sun Which has a greater gravitational pull on me: the Sun, or spiders? Granted, the Sun is much bigger, but it is also much further away, and as I learned in high school physics, the gravitational force is proportional to the square of the distance.—Marina FlemingNote: This is a spider-heavy article. I can be a little anxious about spiders myself, so my research for this article involved a lot of opening PDFs while squinting and leaning back from the screen. If you're a serious arachnophobe, you might want to skip this one.In the literal sense, this question is totally reasonable, although it would be easy to rephrase it to be completely incoherent.The gravitational pull from a single spider, no matter how heavy, will never beat out the Sun. The goliath bird-eating spider[1]Wikipedia helpfully notes that despite its name, it "only rarely preys on birds, with the exception of young birds." weighs as much as a large apple.[2]This is correct whether I mean the fruit or the iPhone 6+; the spider weighs about as much as each. Even if, God forbid, you were as close as possible to one of them, the pull from the Sun would still be 50 million times stronger.What about all the spiders in the world?There's a well-known factoid that claims you're always within a few feet of a spider. Is this true? Arachnologist[3]Spiders, not ancient pottery.​[4]Unless the ancient pottery is full of spiders. Chris Buddle wrote a good article on this question; as you might expect, it's not literally true. Spiders don't live in the water,[5]With the exception of Argyroneta aquatica so you can get away from them by swimming, and there aren't as many spiders in buildings as in fields and forests. But if you're anywhere near the outdoors, even in the Arctic tundra, there are probably spiders within a few feet of you.Regardless of whether the factoid is precisely true or not, there are an awful lot of spiders out there. Exactly how many is hard to say, but we can do some rough estimation. A 2009 study actually measured the total mass of spiders in sample areas in Brazil. They found one-digit numbers of milligrams of spider[6]SI unit: the "AAAAAAAAAAAAAAAAAAAAAAAAAAAA", abbreviated "AAAAAA". per square meter of forest floor.[7]That's dry mass; you have to divide by a number around 0.3 to get the live weight. If we guess that about 10% of the world's land area hosts this density of spiders, and there are none anywhere else, we come up with 200 million kilograms worldwide.[8]One survey of fields and pastures in New Zealand and England tended to find two-digit numbers of spiders per square meter. If they each weigh about a milligram, and we assume once again that about 10% of Earth's land supports that density of spiders, that gives a total spider biomass of 100 million to a billion kilograms. That agrees with our first estimate, at least.Even if our numbers are off wildly, it's enough to answer Marina's question. If we assume the spiders are distributed evenly across the surface of the Earth, we can use Newton's shell theorem to determine their collective gravitational pull on objects outside the Earth. If you do that math, you find that the Sun's pull is stronger by 13 orders of magnitude.Now, this calculation makes some assumptions that aren't true. Spider distributions are discrete, not continuous,[9]Spiders are quantized. and some areas have more spiders than others. What if there happen to be a lot of spiders near you?In 2009, the Back River Wastewater Treatment Plant found themselves dealing with what they called an "extreme spider situation." An estimated 80 million orb-weaving spiders had colonized the plant, covering every surface with heavy sheets of web.[10]Which was in turn covered in heavy sheets of spider. The whole thing is detailed in a fascinating and horrifying article published by the Entomological Society of America.[12]The conclusion of the article contains this breathtaking piece of prose:

Digging Downward What would happen if I dug straight down, at a speed of 1 foot per second? What would kill me first?Jack KaunisThis question is the reverse of question #64, which asked how you'd die if you rose steadily at a foot per second. Digging at the same rate would kill you more quickly.After you get through the surface layers,[1]See question #132 for more on that. temperatures rise pretty steadily as you go deeper, a trend that continues all the way to the core.In some areas, where the hot magma[2](Lava.) is closer to the surface, the ground gets hotter more quickly.The Southern Methodist University Geothermal Lab has produced some superb maps showing the temperature of deep rocks in different parts of the United States. If you look at the map of the 3.5 km layer, you see that at that depth, most of the US is colored greenish-yellow, representing temperatures somewhere around 100°C—with one glaring exception. In northwest Wyoming, there's a circle of ground colored bright red, where the rock is much hotter than normal. That circle is the Yellowstone supervolcano.The SMU maps show that even if you avoided digging in Yellowstone, you'd quickly encounter temperatures too hot for an unprotected human. The ground typically gets hotter at an average of about 35°C per kilometer, so at a rate of a foot per second, you'd encounter lethal heat within an hour or two.But wait a moment.Let's say your hole is about a meter wide. At the rate you're digging, you have to remove roughly half a ton of material every second.No human would be capable of lifting that first foot of material out of the hole so quickly, and it only gets worse after that. After a minute of digging, you'd be 60 feet down, and would have to lift all that rock and dirt a huge distance vertically to get it out of the hole. The power required to do that lifting—just after the first minute—would be roughly 150 horsepower.Even if you're not doing the lifting yourself, the way your question is worded makes it pretty clear that you are in this hole. Whatever process you're using is going to require huge amounts of energy to lift all that rock, and that energy is inevitably going to result in the hole being heated somehow. Even if the layer you're digging through wasn't hot when you started, it will be.What if we assume you're protected against the heat from the ground (and the digging mechanism)? Well, in that case, the pressure would become a problem. As you go deeper, air pressure increases. Below about 5 km, the pressure is high enough that oxygen becomes toxic.So what if you're protected against the heat, pressure, and the digging process?Well, at that point, we've redefined the rules so much that I'm not sure it makes sense to try to calculate an answer. The question—"what would kill you if you kept digging downward"—has left the realm of physics and become fantasy.Which, come to think of it, makes the answer perfectly clear.

Space Burial I've often joked I'd like to have my remains put into orbit. Not in a "scatter my ashes" sense, but, like, "throw my naked corpse out the airlock" sense. Honestly, my main motivation is to baffle someone in the distant future, but it's an interesting scientific question: what would happen to my body in orbit over the course of years, decades or centuries?—Tim in FremontThis isn't really relevant, but I have to ask: Is there a reason you specifically wanted your corpse to be naked? Just making things extra weird for the technicians loading up the capsule and/or throwing you out of the airlock?If you tried this, the first thing that would happen to your corpse would be that it would dry out. This would probably start before you made it to space; the dry, climate-controlled air in the pre-launch waiting area would help draw moisture from your body.In the Manual of Forensic Taphonomy, Franklin Damann and David Carter outline the process of human decomposition. According to them, it takes a lot of effort to keep corpses from drying out during the embalming process.[1]The citation they give for that fact is "(C. A. Wacker, pers. comm.)," which I like to think means it was shared in a conversation that totally broke up the dinner party they were both at. In extremely dry environments like the Atacama Desert in Chile, "spontaneous mummification" can occur—and space is even drier than Chile.[2]The space tourism industry has not adopted this as a slogan. Also, "Chile: Not as Dry as Space!" was probably nixed by the Chilean tourism board.Once your body made it to space, this process would ramp up quickly. Most of the "ecology" responsible for decomposing your corpse would be killed off quickly by the drying process (along with the lack of oxygen, temperature swings, and solar radiation levels), so your body wouldn't decay very much. Instead, you'd become a freeze-dried mummy, after losing about 80% of your body weight in water.[3]This is how much liquid you can remove from fresh animal tissue, according to lab experiments reported in Arthur C. Aufderheide's book The Scientific Study of Mummies. That makes sense; after all, according to that commonly-repeated piece of trivia, human bodies are around 70% water.

Flagpole So, you're falling from a height above the tallest building in your town, and you don't have a parachute. But wait! Partway down the side of that skyscraper there's a flagpole sticking out, sans flag! You angle your descent and grab the pole just long enough to swing around so that when you let go you're now heading back up toward the sky. As gravity slows you and brings you to a halt, you reach the top of the skyscraper, where you reach out and pull yourself to safety. What's the likelihood this could happen?Rex UngerichtIf you're like me, your first thought on hearing this question was, "That's ridiculous; there's no way that could work."Your first thought is right. But just to be sure, let's take a closer look.Grip strength depends on a lot of factors, like hand slickness and surface material. But for the moment, let's assume Rex's hands are able to grab the pole tightly. What happens to the rest of his body?It's hard to find good numbers on how much force it takes to tear off a person's arm.[1]Which is probably a good thing, to be honest. There are threads on the question on MetaFilter and the Straight Dope message boards, and frequent discussion of the death of Robert-François Damiens,[2]Damiens was tortured to death for attempting to assassinate Louis XV, but a team of horses had trouble tearing him limb from limb. but not too much hard data.For the record, there are lots of studies and lectures on the breaking strength of tendons, which tend to give values of around 50-150 MPa. That's stronger than skin (27 MPa) but weaker than bone (120 MPa). However, to figure out the overall strength of the arm, we need to tally up all the tendons, muscles, and tissues in the wrist, arm, and shoulder, their cross-sectional area, and figure out which parts would be put under strain in what order.Instead, it might be easier to consider people who try to pull off this maneuver in real life: Gymnasts.A gymnast on the uneven parallel bars pushes the human body to its limits while performing maneuvers very similar to Rex's flagpole stunt.[3]In some ways, at least. A 2009 study used 3D motion capture to measure the forces involved in an elite gymnast's routine. They found that the athlete's hands exerted a force of over 3 kN on the bar at the bottom of a swing. In other words, the gymnast was briefly supporting almost 700 lbs of weight.Let's be generous and assume that Rex is even better than the elite gymnast in the study. (After all, the gymnast has to worry about long-term injury, while Rex's concerns are a lot more short-term). Suppose Rex's arms can handle a swing force of over 10 kN, three times more than the gymnast (and twice as much as these guys!). How will he do?Let's see how much force Rex needs to withstand. The "tallest building in town" here in Boston is the 240-meter-tall Hancock Tower; if he jumped off the top, he'd be going nearly 100 mph by the time he was halfway down. At that speed, the force on his arms (speed squared over the radius of his turn[4]Which is effectively somewhere between 1 and 2 meters here.) would be around ... 100 kN.Really, the numbers are just telling us what common sense told us from the start: You can't grab hold of something while going 100 mph, much less swing around it.If you want get a more vivid intuitive sense of the forces involved, consider this: In 2006, GQ put baseball star Albert Pujols in a lab and measured his swing. They clocked the speed of his bat at 87 mph, similar to the speed of the flagpole relative to our falling person.So if you want to pull off Rex's stunt, first go find Albert Pujols, have him swing his bat as hard as you can ... and try to grab it.And remember: You're just trying to stop the momentum of a 31-ounce piece of wood. When you're falling past the flagpole, you're going to be catching your whole body, so it's going to be up to 100 times worse.Good luck!

Hotter than Average I saw a sign at a hot springs tub saying "Caution: Water is hotter than average" with water at about 39°C. Although they were presumably trying to say "hotter than the average swimming pool," this got me wondering: What is the average temperature of all water on the Earth’s surface, and how does that temperature compare to 39°C?—Graham WardYou might be selling the sign-maker short. Whether they explicitly intended it or not, the wording on their sign hints at something kind of profound.The sign is true in the literal sense, in that 39°C is hotter than most water you'll find on Earth. But it's also true in a deeper sense, one that ties together the concept of heat, springs, and averages.For the most part, the temperature of groundwater in an area is equal to the year-round average air temperature of the surface. Water is a terrific absorber of energy, requiring huge amounts of it to change temperature.[1]Which is why pots of it take so long to boil. Underground reservoirs of water tend to warm up and cool down too sluggishly to respond to the comparatively brief winter-summer temperature swings.[2]It also takes a while for heat to work its way downward, so sometimes deep parts of water bodies will reach their maximum temperature when it's winter on the surface. Rock works the same way; if you drill a hole deep into the bedrock, you can see historical temperatures stacked vertically, as waves of heat and cold moving downward.This property makes springs a useful "thermometer" for an area. Instead of spending a year measuring the temperature each day and night, and then calculating the average, you can just stick a thermometer in a spring any time of year.If you look at a map of groundwater temperatures, you'll see it closely resembles a map of year-round average air temperatures (PDF, see page 6).However, this rule only holds true in places where the main energy source heating the groundwater is the same one heating the air—sunlight. While this is true in most areas, in a few geologically-active spots, water is warmed far above this baseline by the flow of energy from deep within the Earth.When the sign at the hot springs told you that the water there was "hotter than average," it wasn't just saying, "This water is hot." In a sense, it was saying, "This water, unlike all the springwater most of us ever encounter, isn't tied to the average summer/winter day/night air temperature for the area. This water is hotter than average."So give the signmakers some credit.

Snow Removal I've long thought about putting a flamethrower on the front of a car to melt snow and ice before you drive across it. Now I've realized that a flamethrower is impractical, but what about a high-powered microwave emitter?—Matt Van OpensBelieve it or not, your flamethrower idea is actually the more practical of the two. The flamethrower also has the advantage that, unlike the microwave, it won't interfere with wifi (unless you aim it directly at the router).I'm writing this article from Boston, which is currently buried under a truly ridiculous amount of snow. We've had more snow in the past 30 days than Anchorage, Alaska usually gets in an entire winter.[1]Meanwhile, Anchorage is on Twitter wondering where their snow went and threatening revenge. Here's a neat visualization of the atmospheric pattern during these polar vortexes. Vortices. Whatever. Our transit system has broken down and our roofs[2]Tolkien prefers rooves. are collapsing. The mayor gave a press conference in which he announced, "I don't know what to say to anybody anymore. Hopefully it will stop eventually."So snow removal is on all our minds.But snow is hard to melt. (And we've been trying[3]I love that tweet because it sort of sounds like it comes from an alternate fairy-tale universe where cities farm snow and snow-melters form the base of the economy.) Your microwave idea certainly sounds like it should be more practical than a flamethrower. Microwaves seem clean and efficient; after all, we don't use flamethrowers in our kitchens.But there's a big problem: Microwaves heat water very well, but they don't really work on ice.Fortunately, there are other ways to get energy into the ice. In addition to your flamethrower suggestion, you could, for example, use infrared heat lamps or lasers.[4]Pick a frequency where snow has a low albedo; otherwise, the FBI may hunt you down for lasering aircraft. But whatever you use, you'll run into another problem: It takes an awful lot of energy to melt snow.Melting a gram of snow takes about 335 joules of energy. To put that another way, a 60-watt lightbulb is capable of melting about a pound of snow an hour.A foot of snow contains roughly the same amount of water as an inch of rain, give or take. Let's assume you've had a decent snowstorm of about a foot[5]For the record, by this standard, Boston has had a "decent snowstorm" every few days for the past month.—meaning an inch worth of water—and that you want to melt a 9-foot-wide swath while driving along at 55 mph.Luckily, this happens to be one of those happy physics situations where we can just multiply together every number we're looking at, and the answer turns out to be the measurement we want:\[55\text{ mph}\times1\text{ inch}\times9\text{ feet}\times\text{water density}\times335\tfrac{\text{J}}{\text{gram}}=574\text{ megawatts}\]Unfortunately, it's not the answer we'd like. The nuclear reactor on an aircraft carrier, for example, produces less than 200 megawatts. To melt snow in front of your car, you'd need three of those.What about your your original flamethrower idea?Gasoline may have a phenomenally high energy density, but it's not high enough. No matter how big the tank on your flamethrower was, you'd run out of fuel constantly.Gas mileage in the US is often measured in "miles per gallon" of gasoline. With your flamethrower guzzling fuel, your mileage would be about 17 feet per gallon.You might be better off dropping the flamethrower entirely. Instead, take a cue from the rail agencies, who use jet-engine-powered snowblowers to clear train tracks.In the end, it's easier to just move the snow out of your way.

Black Hole Moon What would happen if the Moon were replaced with an equivalently-massed black hole? If it's possible, what would a lunar ("holar"?) eclipse look like?—Matt"Not much" and "not much."A black hole the mass of the Moon would have an event horizon about the size of a sand grain. Specifically, according to one of my favorite charts, a black hole moon would be a grain of fine to medium-fine sand, and could pass through a sieve of size ASTM No. 70 or larger. I mean, I guess a black hole with the mass of the Moon would pass right through any sieve, destroying it in the process, but that's neither here nor there.[1]The expression "that's neither here nor there" can be kind of confusing and ambiguous, but I guess that's neither here nor there.Since the Moon's mass and position wouldn't change, the tides on Earth wouldn't change, either. When you're floating outside a spherical mass, its pull on you is the same regardless of whether the mass is concentrated at the center of the sphere or spread out throughout it. If the Sun were replaced by a black hole of the same mass, the Earth's orbit wouldn't change, although life on Earth might.With the Moon gathered into a point, there'd be no moonlight, which would affect the life cycles of all kinds of nocturnal animals. But compared to a lot of the other things we've done, that would be fairly minor. The Earth's orbit is stabilized by the Moon, but the lunar-mass black hole would probably serve the same role.This black hole Moon would be pretty low-profile. If it were much smaller, it would evaporate through Hawking radiation, but a black hole the size of the Moon actually absorbs more energy from the cosmic background radiation than it emits through the Hawking mechanism. Our black hole would really be black.At least, if it didn't eat anything. If the black hole devoured any objects, it would let off a tremendous blast of radiation. Black holes burn brightly as they devour things; the whirlpool of matter heats up as it falls inward, causing it to glow brightly.[2]A black hole can't devour matter too fast, though, because at some point it would be producing so much radiation that it would blast its own "food" away. This is called the Eddington limit.

Zippo Phone What in my pocket actually contains more energy, my Zippo or my smartphone? What would be the best way of getting the energy from one to the other? And since I am already feeling like Bilbo in this one, is there anything else in my pocket that would have unexpected amounts of stored energy?—Ian CummingsThe Zippo lighter easily beats the phone, even though its fuel tank is barely half the size of a large phone's battery, because hydrocarbons are fantastic at storing energy. Gasoline, butane, alcohol, and fat contain a lot of chemical energy, which is why our bodies run on them.[1]I mean, the latter two, at least. You can't eat gasoline.​[2]As far as I know.​[3]Although technically swallowing gasoline may not kill you, according to Utah Poison Control specialist Brad Dahl. However, he cautions that you will find yourself "burping gasoline," which is "not real tasty." (Actual quote.)​[4]Also, if you don't rinse your throat afterward, it will give you chemical burns.How much energy do they contain? Well, let's put it this way: A fully-charged car battery holds barely as much energy as a sandwich.A container of butane the size of a phone battery could, in principle, power the phone about 13 times longer than the battery itself could.[5]In the case of my phone, that could give me as much as three hours. The obvious question, then, is "why doesn't my phone run on propane?"The obvious answer is "because your phone would catch fire," but that's not quite it. See, lithium-ion batteries are also extremely flammable, and a huge amount of effort has gone into making Michael Bay scenarios less common.The truth is more complicated. People have wanted to build various kinds of "fuel cell" batteries for almost as long as we've had portable electronics. The allure of hydrocarbon energy storage continues to this day—if you do a Google search for fuel cell phone charger, you'll find news stories about new products announced every year. Many of them are no longer available.If you really want to power your phone with butane, the current hot project—as far as I can tell from a cursory search—seems to be the kraftwerk portable USB generator, which has made over a million dollars on Kickstarter with several weeks left in its campaign. Of course, a portable battery of the same size could do a lot of the same things, but there are certainly some use cases where the butane charger offers advantages. If you place a premium on reducing weight, or have to go a long time without contact with the power grid, it could be a good option. Let's put it this way: If the phrase "power your phone on butane", makes you think, "hey, that would solve a problem I have!" then go for it.This gives us the answer to Ian's second question. The Zippo lighter has more energy, but getting it into the phone is a little difficult and requires the overhead of a fuel cell or generator. Getting the phone to start a fire, on the other hand, is quite reasonable, although it may require doing bad things to the battery.Ian's third question was "what else in my pocket might contain more energy?" Like Gollum, I have no idea what's in your pocket,[6]Or whether you're happy to see me, for that matter. but I can guess that it might contain one thing with more energy than a battery: Your hand.An adult man's hand weighs about a pound.[7]I wanted to put "citation needed" after that, but to my mild dismay I actually do have a citation. The hand isn't the fattiest part of the body, but if burned completely, it would probably give off about 500 watt-hours of energy, give or take. That's 50 times the energy content of the phone battery, and almost 10 times that of the Zippo. It's also about as much as a car battery.And, for that matter, about as much as a sandwich.

Tug of War Would it be possible for two teams in a tug-o-war to overcome the ultimate tensile strength of an iron rod and pull it apart? How big would the teams have to be?—Markus AndersenA couple dozen people could pull a half-inch iron rod apart.Tug-of-war, a simple game in which two teams try to pull a rope in opposite directions, has a surprisingly bloody history.I don't mean that there's some kind of gruesome historical forerunner of modern tug-of-war.[1]Although it's definitely an ancient sport, so I'm sure people have come up with all kinds of horrific variations over the centuries that I don't really want to spend hours reading about. Humans seem to be creative when it comes to that kind of thing. I mean that modern tug-of-war involves a lot more death and mutilation than you might expect—precisely because people underestimate how few people it takes to break "strong" things like heavy rope.As detailed in a riveting article in Priceonomics, recent games of tug-of-war have resulted in hundreds of serious injuries and numerous deaths—all caused, one way or another, by ropes snapping. In particular, this seems to happen when large groups of students try to set a world record for largest tug-of-war game. When a rope under many tons of tension suddenly snaps, the recoiling ends can—and do—cause a terrifying variety of injuries.Before we answer Markus's question, it's worth noting that the physics of tug-of-war can be a little tricky. It seems like common sense that the "stronger" team has an advantage, but that's not quite right. To win, you need to resist sliding forward better than the other team. If you can't resist sliding, then increasing your arm strength means you'll just pull yourself forward. Since sliding friction is often proportional to weight, tug-of-war on many surfaces is simply a contest over who's heavier.[2]Champion tug-of-war teams focus on body angle, footwork, digging into the ground, and timing pulls to throw off the other team. The strongest team in the world would lose a tug-of-war with a six-year-old and a sack of bricks, as long as the sack had a firm grip.So, how much force can tug-of-war players exert?A 2011 paper analyzing the immune systems of several "elite tug-of-war players"[3]The paper notes that "Few studies have been done to examine the effects of [the] tug-of-war sport on physiological responses," which seems likely enough to me. measured their average pull force (on a school gym floor) to be about 102.5 kilograms-force, or about 1.5x their body weight.The ultimate tensile strength of cast iron is about 200 megapascals (MPa), so we can use a simple formula to figure out how many players would be needed to break one.\[ \text{People required}=\frac{\pi\times\left(\tfrac{1}{4}\text{ inch} \right )^2\times200\text{ MPa}}{102.5\text{ kg}/\text{person}}\approx25\text{ people} \]Two teams of 25 people[4]I originally wrote 25 people total, forgetting that two people pulling with 100 units of force each will produce 100 units of tension on the rope, not 200! Thank you for Gordon McDonough for pointing this out. could probably pull a half-inch iron bar apart. An inch-thick iron bar could be torn in half by teams of 101 people,[5]People often play tug-of-war with their dogs. Going by weight alone, 30 humans would probably be about evenly matched against 101 dalmatians. and a 2-inch-diameter bar would need over 400. It's hard to have a tug-of-war with something thicker than about 2 inches. Since you're not allowed to install handles on the rope,[6]Or wrap it around your hand, for reasons which will become clear if you read some of the articles on tug-of-war injuries. it has to be narrow enough to grip easily.While "400 people" may be the limit for plain iron bars, there are much stronger substances out there. Common types of steel, for example, have a tensile strength about 10 times that of cast iron. Common half-inch rebar, for example, would in theory take teams of over 200 people to pull apart, compared to 25 for cast iron. Other substances are even stronger; a half-inch shaft made from high-grade steel or a polymer like Kevlar (or, theoretically, a solid silicon crystal) could handle the pulling force from teams of anywhere between 500 and 800 competitive tug-of-war players.If we limit ourselves to a two-inch diameter rope, which seems to be about the maximum size for tug-of-wars,[7](William Safire returns from the grave to point out that it should really be tugs-of-war.) then the maximum number of tug-of-war players given a super-strong rope like Kevlar is in the neighborhood of 10,000.[8]Or several times that many, if they're not very athletic.If we figured out how to manufacture large ropes out of graphene ribbons, which have tensile strengths over 10 times higher than existing materials, we could theoretically support a tug-of-war between teams of up to 100,000 players each. Such a rope would be over 200 miles long, and could stretch from New York to Washington.If our experience with nylon ropes failing is any indication, when the graphene finally snapped, the death toll could be enormous among both players and bystanders. Lengths of graphene would crack across the landscape like bullwhips, slicing down forests and demolishing buildings.In the end, trying to develop stronger ropes leads only to greater danger to everyone, both participants and bystanders. In the ultimate game of tug-of-war ...... the only winning move is not to pull.

Stairs If you made an elevator that would go to space (like the one you mentioned in the billion-story building) and built a staircase up (assuming regulated air pressure) about how long would it take to climb to the top?—Ethan AnnasA week or two, if you're a champion stair-climber. Or 12 hours if you're on a motorcycle.A tower to space would be very different from a space elevator. A space elevator would be about 100,000 kilometers tall, while a tower "to space" would only need to be 100 kilometers. As Ethan mentions, it would need to be pressurized, with an airlock every few miles.A stairway to space[1]If there's a bustle in your hedgerow, well, uh, boy, I don't know what to tell you. I guess ask it to leave? would have about half a million steps. World-champion stair-climbers[2]or "towerrunners" like Christian Riedl or Kristin Frey can travel roughly a Mount Everest's height in a day; Riedl set the half-day record last October by climbing 13,145.65 meters in 12 hours. At that pace—taking the other twelve hours to rest, eat, and sleep each day—it would take him a little over a week to reach the top.Climbing all those stairs would burn calories, which would mean you'd need to carry food. It turns out that the most efficient food you can carry, in terms of calories per pound, is butter—which is why Arctic explorers carry so much of it.Suppose your backpack holds 9 liters. Climbing 10 stairs burns about a calorie, which means climbing all the way up to space will burn about 72,000 calories. If you fill your backpack with butter, it would hold almost enough calories to get you to the top.However, since it would take you weeks to climb all those stairs, you'd also need your normal dietary allowance of 2,000 calories (three sticks of butter) per day. Combining that with the 72,000 calories just from climbing the stairs, and you'd probably need to upgrade to a more serious 16-liter backpack. If you fill that backpack with butter, it will let you carry around 110,000 calories,[3]Coincidentally, about the amount you get from eating a human body. which should be enough to get you to the top if you're really dedicated.If you didn't want to eat 35 pounds of butter,[4]For whatever weird reason. you could try getting to the top by motorcycle. Based on how quickly this rider ascends 45 stairs, a motorcycle could conceivably make it to the top in a day.Ok, so you got to the top. Now what? Getting up to space isn't that hard, after all—the hard part is getting into orbit, and the tower doesn't help you very much with that.So what else could you do?Michael Longuet-Higgins was a research professor at the University of Cambridge and an expert in fluid dynamics, bubbles, and unusual types of waves.[5]Given his apparent research interests, this video would blow his mind.​[6]Or this one, or this gadget, or this. In 1953, Dr. Longuet-Higgins was shown, by a colleague, an "interesting toy" which had recently appeared on the market. This toy, "Slinky," had some unusual properties. The professor immediately set to work analyzing it, and wrote up his results in a paper.Dr. Longuet-Higgins first determined through mathematical modeling that the rate at which the Slinky descends steps should depend only on the properties of the spring itself, and not the size or shape of the stairs. He and his colleague conducted a series of experiments "on five different flights of stairs, of various dimensions, in Trinity College, Cambridge." Their conclusion: The Slinky descended a constant rate of about 0.8 seconds per step.[7]Except on some wide, flat stairs, where the Slinky "came to rest after three or four steps at most," which gives me a wonderful mental image of two disappointed British professors at the bottom of a staircase.​[8]Sadly, this was before the invention of the StairMaster. Fun fact: After a surprise StairMaster management shakeup in 2011, for some reason not a single newspaper ran the headline "StairMaster CEO steps down".

Bowling Ball You are in a boat directly over the Mariana Trench. If you drop a 7kg bowling ball over the side, how long would it take to hit the bottom?Doug CarterIt is a good thing you mentioned the weight, because of a very surprising fact:Most bowling balls float.It's true. Bowling balls all have about the same volume, so they all displace the same weight in seawater—12.13 lbs, or about 5.5 kg. But their weights vary substantially, from as little as 6 lbs to a max of 16. Only the balls that weigh more than 12.13 lbs will sink."Hang on a moment," the serious bowlers reading this are saying, "most bowling balls are at the heavy end of that range. The usual range is more like 14-16 lbs for men and 10-14 lbs for women. Maybe the average women's ball floats, but the overall average ball surely sinks."This is definitely true for serious bowlers, but for casual bowlers, it might be better to define the "average" ball using the distribution on the rack of balls at the local bowling alley. These house balls often list the weight on them, so rather than go to a bowling alley, I just sifted through all the Flickr photos of bowling balls and tallied up all the visible weights. The average was 10½ lbs.So at the very least, for most people, the average bowling ball they've picked up in their lives probably floats. If nothing else, this makes the popular simile "sank like a bowling ball"—which appears in a number of books—seem a little poorly chosen.[1]In defense of the authors of Volume 53 of North Dakota Quarterly, the simile they used is, "sank like a bowling ball in whipped cream," which is perfectly reasonable. On the other hand, How To Hook a Man (And a Baby) and The Year's Work in Lebowski Studies are on their own.But Doug's bowling ball is 7 kg (15.5 lbs), making it plenty heavy enough to sink in the ocean. How fast will it fall?Small falling spheres in viscous (goopy) liquids (like hair gel) exhibit weird behaviors and sometimes complex oscillation, but bowling balls falling through water are pretty straightforward. Their falling speed is determined by the drag equation and their weight (accounting for buoyancy). For Doug's bowling ball, that terminal velocity will be roughly 1.3 meters per second, which means it will take two hours and 20 minutes to reach the bottom. That's plenty of time to enjoy a two-hour movie.A 13-pound bowling ball, which is much closer to neutrally buoyant in seawater, would take four and a half hours to reach the bottom. On the other hand, a bowling ball made of solid iron would reach the bottom in half an hour.A bowling ball made of lead would reach the bottom in 23 minutes, and a bowling ball made of solid gold would make it in 17. However, a bowling ball made of solid gold would also weigh more than the average bowler.[2]At least, I think it would, but I can't think of a way to sample the weight of the average bowler without getting punched. A bowling ball made of solid osmium, the heaviest naturally-occurring element, would weigh 120 kilograms, and could sink to the bottom of the Mariana Trench in just 16 minutes.But what if you got the weight wrong? What if the bowling ball you were using turned out to be 7 pounds, not 7 kilograms? Or maybe it's 10.5 pounds—the "average" bowling ball, at least according to a dubious Flickr sample.In that case, the ball would never reach the bottom. Instead, it would drift sideways with the currents. We can track what course it would take using the Adrift.org.au ocean plastic tracking tool. The bowling ball would first drift west, past Luzon in the Philippines, then probably north along the coast of China, turning right at Japan and heading out over the Pacific.Sometime in the summer of 2018, it would approach the coast of California. Most likely, it would follow the coast for a little while, then become swept up in the great Pacific garbage patch.However, it's possible that it would be swept up on shore instead. If, during those three years, Doug took his boat from the Mariana islands to Los Angeles, found a nice, sheltered cove, and set up ten carefully weighted bowling pins just below the surface, then there is a tiny, tiny chance ...... that he could succeed in bowling the single most improbable strike of all time.

Lunar Swimming What if there was a lake on the Moon? What would it be like to swim in it? Presuming that it is sheltered in a regular atmosphere, in some giant dome or something.Kim HolderThis would be so cool.In fact, I honestly think it's cool enough that it gives us a pretty good reason to go to the Moon in the first place. At the very least, it's better than the one Kennedy gave.Floating would feel about the same on the Moon as on Earth, since how high in the water you float depends only on your body's density compared to the water's, not the strength of gravity.Swimming underwater would also feel pretty similar. The inertia of the water is the main source of drag when swimming, and inertia is a property of matter[1]♬ BILL NYE THE SCIENCE GUY ♬ independent of gravity. The top speed of a submerged swimmer would be about the same on the Moon as here—about 2 meters/second.Everything else would be different and way cooler. The waves would be bigger, the splash fights more intense, and swimmers would be able to jump out of the water like dolphins.This[2]Not this one. The other one.​[3]The simplest approach, which gives us an approximate answer, is to treat the swimmer as a simple projectile. The formula for the height of a projectile is:

Microwaves I have had a particular problem for as long as I can remember. Any time I attempt to heat left over Chinese food in a microwave, it fails to heat completely through somewhere. Usually the center but not always and usually rice, but often it will be a small section of meat. It's baffling and has made me automatically adjust heating times to over 2 minutes. In most cases this tends to heat the bowl or plate more than the food. So I suppose the question is what is the optimal time to heat left over Chinese food in the microwave, how about an 800 watt microwave?—JamesThis is a great question. Since the answer isn't too hard to find by Googling, normally I would skip it, but the answer is also something that I never really learned while growing up, so I'd like to try to answer it, for the sake of anyone else out there like me who spent years confused by microwaves.First, the disclaimer: I am not an expert on food preparation or food safety. Actual experts on food safety can be found at US Department of Agriculture, which publishes a good FAQ page on microwave oven safety.Now, on to James's question.There are a couple of different effects that cause microwaves to heat food unevenly.The first one is that microwaves have hot and cold spots. You can see this by filling a microwave with damp thermal paper, marshmallows, chocolate, or—possibly best of all—appalams.The reason microwaves don't cook evenly comes straight from physics. When you continuously feed waves into a space—which is what microwaves do—you'll often have some "dead" spots:In two dimensions, you get a similar but more complicated pattern.These dead spots are the reason microwaves are designed with rotating platters—the idea is that each part of the food will pass through at least one hot spot. Microwave designers use a lot of tricks to try to vary the pattern to minimize dead spots, but no one does it perfectly; all microwaves will heat at least a little bit unevenly.The second major reason for cold spots in microwaved food is something touched on in last week's article: Microwaves aren't absorbed very well by ice.At first, this doesn't seem like a problem, right? It just means that if your food is partly or entirely frozen, you just need to microwave it longer. But when you do that, something interesting happens.When ice melts, it turns to water, which does absorb microwaves very well. When the first pockets of ice turn to water, they start absorbing more microwaves and heating very quickly, even though the ice around them hasn't even melted. Those melted parts can easily heat enough to start cooking the food while other parts are still frozen.This means that if you defrost frozen meat in your microwave, it could be hot to the touch over most of its surface, but still have a solid chunk of ice in it somewhere. If it does, when you plop it on the stove,[1]Or in a pan on the stove, or whatever. the thawed parts might finish cooking before the frozen parts have even started to warm up, giving you a large chunk of raw meat in the middle of your steak.This starts to explain some of the weird instructions commonly seen on microwavable food.When instructions say let stand for 1-2 minutes, it's not just to protect your mouth from hot food—it's giving the hot and cold spots time to equalize, so the whole thing will be sufficiently heated throughout. And if some part of the food doesn't conduct heat well (e.g. rice) or contains a lot of chunks of ice (e.g. frozen fruit or meat) they also might tell you to stir midway through cooking. This helps to transfer the heat more evenly into the food, move food away from cold spots, and also break up chunks of ice and mix them with warmer pockets of water to help melt them.This helps us explain why James is so perplexed. He's adjusting the obvious variable—total cooking time—and no matter what value he chooses, he's getting bad results.The solution is to mess with other variables. First, he can redistribute the heat by pausing halfway through microwaving to stir the food. Second, for things that are harder to stir, he can give the heat time to equalize on its own. If he microwaves his food for a short period, waits a moment, then zaps it again, the heat will have time to spread from the hot spots to the cold spots in between zaps, resulting in more evenly-heated food.And that brings us to one last surprising[2]This was surprising to me, anyway; I used microwaves for almost 20 years before I realized it. aspect of microwaves: Power level.It turns out that "turning the microwave off every so often to let the food cool" is exactly what the "power level" setting does! Choosing a lower power level doesn't actually change the strength of the microwaves; it just means that the microwave generator won't be running the whole time. When you cook something on 50% power, you may notice the microwave's sound changing every so often; that's the dynamo turning on and off.[3]The length of these on/off periods (duty cycle) is surprisingly long, partly because switching off and on is hard on the magnetron. This is also the reason why, if you normally cook something for 2 minutes on 50% power, cooking it for 1:30 won't necessarily deliver 75% as much heat like you'd expect. While it's on, the microwave is running at full power. In effect, the microwave is just automating the tedious task of zapping something a bunch of times on "high" for 10 seconds each and letting it sit for a while in between.So my advice to James is simple: Use a lower power level, stir your food partway through microwaving, and let it sit for a few minutes before you eat it.And FYI, if you cut a grape in almost in half and microwave it, you'll create bursts of plasma. (You also might damage your microwave, so do it at your own risk.)This has nothing to do with your question. I just wanted you to know.