If I shot an infinitely strong laser beam into the sky at a random point, how much damage would it do?

Garrett D.

A lot of the time, if a question includes the word "infinity," the answer is "an infinite amount"—when there's an answer at all.

An infinitely strong laser pointer would deliver an infinite amount of energy to the air in its path, which would in turn radiate an infinite amount of energy in all directions, which would destroy everything. For more on this, see What If #13.

Except that's not really the right answer to your question. Most of our equations don't really work when you put "infinity" in them. So the right answer is "an infinitely strong laser beam isn't a real thing."

But if you made a laser pointer stronger and stronger, the result would look more and more like what I described. This is sort of like the mathematical idea of taking a limit; you can't say what happens at infinity, but you can see how it acts as you get closer and closer to it.

Since we looked at the "destroying the world" consequence in question #13, let's look at the other part of your question: The random aiming.

First of all, if you aimed in a truly random direction, you would have an almost 50% chance of hitting the Earth.

Almost 50%, but not quite. If we assume you're on a spherical Earth, ignoring hills and trees,[1]And ignoring refraction. you have a slightly better chance of missing the ground than hitting it—because you're holding the laser above the surface, and the Earth curves away from you:

If you miss the Earth, 89,999 times out of 90,000, your beam will pass right out of the galaxy without hitting anything. When it does hit something, it will almost always be the Sun or the Moon.

The first time I met astronomer Phil Plait in person, he mentioned a clever trick for calculating the "area" of the sky:[2]"Learn This One Weird Trick,"" he said, "Invented By a Local Schoolteacher!"‌[3]He didn't say that.

The area of a sphere is 4πr². Ok, great, but what's the "radius" of the sky? Well, if the sky is a sphere around us, the radius is "one radian", because that's the radius of anything. But a radian is also 57.3 degrees, which means the sky is 57.3 degrees "away" from us. 4 times pi times 57.3 = 41,253 square degrees.

The Moon and the Sun each take up about 0.2 square degrees, and so the chance of hitting either one of them is about 1 in 180,000. Those aren't great odds, but they're better than the odds of hitting anything else.

To calculate the odds of hitting something else, we can use this handy angular size reference as a shortcut, dividing the rough angular size of the object in the chart by the Earth's total area to see how much of the sky it covers. The odds of hitting one of Jupiter's moons, for example, are on the order of one in a trillion.

Stars are even worse. Your odds of hitting any star at all on your way out of the galaxy are almost zero, even if you aim for the core.

This is good, though! If your odds of hitting a star were high, it would mean the galaxy would be opaque. Since most "lines of sight" would terminate on a star, it would be very hard or impossible to see past our galaxy.[4]There are only a few stars in our galaxy in the Hubble Ultra-Deep Field image. The fact that the night sky is dark is at the core of Olbers' Paradox.[5]I was so tempted to vandalize this article to put a [citation needed] after every claim that the night sky was dark.

If you kept shooting long enough, eventually you'd hit a planet. Neptune would be the hardest to hit, followed by Uranus and Mercury. Pluto would be the hardest, but it might be worth it. An impossibly powerful laser would at least settle that debate.

Could a person walk the entire city of NY in their lifetime? (including inside apartments)

Asaf Shamir

Like the answer to Paint the Earth, the answer to the first part of this question is pretty straightforward to look up.

But what if it weren't? Can we figure out the answer from things we already know? Let's look at a few ways of estimating it.

First of all, how wide is a street? I've never seen one of those flashing crosswalk countdowns signs start with less than 10 seconds; if people walk at a meter per second, most roads are probably at least 10 meters wide.[1]There's a table from the 1892 World Almanac listing the widths of all avenues and streets in Manhattan, as well as the lengths of all the blocks, confirming that even in 1892 the streets were at least 20 meters wide. I found a copy of the table over at the blog Stuff Nobody Cares About.

Most people wouldn't have trouble walking 10 kilometers (6 miles) in a day. If the city were covered in kilometer-long streets laid down edge-to-edge, with no space between them, you could fit a thousand roads side-by-side in 10 kilometers. That means a person could walk back and forth across an entire 10km by 10km grid in, at most, 3 years.[2]On the streets. You have to add another 3 years for the avenues.

I don't know how many 10 km square swatches it takes to cover New York City, but it's probably not very many.[3]Turns out it's a little more than 1 to cover the land and water. And since NYC has some space not occupied by streets, this tells us that the answer to the first part of Asaf's question is almost certainly "yes"—purely from a geometry standpoint.[4]Another way to come at this calculation is to remember that Manhattan streets are numbered, and you never see four-digit numbers.

Here's another approach: I happen to remember that the US Postal Service employs about half a million people. NYC's population is almost 10 million people,[5]The city itself is about 8.5 million, and the metro area is about 20 million. so almost 1 out of every 35 Americans lives there.[6]I remember seeing some California politician boast that California had 14% of the country's millionaires. But 1 in 8 Americans live in California, so that's pretty close to what you'd expect. If New York also has 1 out of every 35 postal employees, that's about 15,000 people.

If all those employees were letter carriers, and they visit every address in the city every workday, that would mean it takes a total 15,000 x 8 hours = 14 person-years to traverse the city—much less than a lifetime! Since lots of postal employees are not letter carriers, and real letter carriers stop frequently, this estimate is probably still much higher than the reality.

Another way: Imagine that each person lives alone in a square room measuring 10 meters by 10 meters, which is about the size of a typical two-bedroom apartment. Furthermore, let's assume that everyone's apartment is on the ground floor with at least one side facing a street. In that case, at a walking speed of 2.5 mph, it would take only 2.4 years to walk past every apartment—which Wolfram|Alpha helpfully points out is roughly 1.4 elephant gestation periods.

Any way we come at this problem, it looks like the answer is "yes"—you can walk down all the streets in New York City. And, indeed, it turns out there are 6,074 miles of road in NYC, which would take a total of a little over 100 days of walking.

Now, what about the second part of Asaf's question—walking through all the apartments?

This one is trickier. As a rule of thumb, a household is overcrowded if it has more people than rooms.[7]There are a bunch of definitions for different family sizes and methodologies, but they all end up in a pretty narrow range. But at the same time, most households don't have more than two rooms per person. Let's assume all households have 1.5 rooms per person.

Let's assume it takes 20 seconds to get from the door of a room to the door of the next non-visited room. (Most of the time it will be much less, but sometimes the next non-visited room is on another floor or down the stairs, so it's good to give ourselves some extra time.)

If it takes 5 seconds to walk into a room and back out, then you can visit every room in New York City in 10 years. Even if you only visit rooms for eight hours a day, that's totally plausible to fit into one lifetime.

However, a word of warning to Asaf:

Under NY Penal Code §104.15, entering a dwelling without permission is a class A misdemeanor punishable by up to a year in prison.

So while it might take only 30 years to visit every apartment in New York City ...

... it could take you 2,000 millennia to serve out the resulting prison sentence.

People sometimes say "If I had all the money in the world ..." in order to discuss what they would do if they had no financial constraints. I'm curious, though, what would happen if one person had all of the world's money?

Daniel Pino

So you've somehow found a way to gather all the world's money. We won't worry about how you did it—let's just assume you invented some kind of money-summoning magic spell.

Physical currency—coins and bills—represents just a small percentage of the world's wealth. In theory, you could edit all the property records on Earth to say that you own all the land and edit all the banking records to say you own all the money. But everyone else would disagree with those records, and they would edit them back or ignore them. Money is an idea, and you can't make the entire world respect your idea.

Getting all the world's cash, on the other hand, is much more straightforward. There's a certain amount of cash in the world—it's about $4 trillion—and you want it all.

It won't necessarily do anything for you, since—without the cooperation of the outside world—you probably won't be able to spend it. But maybe you can swim around in it, like Scrooge McDuck in his giant room full of gold.

So you cast your magic spell and summon all the money.

The pile of cash is the size of the Empire State Building, but heavier. You probably don't want to be standing under it, so let's assume you're standing over here, off to the side:

The vast majority of the weight in the pile is coins, and the biggest single contributor is the US penny. Despite periodic efforts to kill off the penny, the US Mint keeps producing more of them.

There are probably 150 billion pennies[1]A 1996 GAO report mentioned a US Mint estimate of the number of pennies in circulation: 132 billion. If you're excited by phrases like "General Accounting Office", "auditing standards", and "Subcommittee on Domestic and International Monetary Policy", you can read the report here.

If you're so excited about penny statistics that the GAO report isn't enough for you, you're in luck: There's another way to derive this number.

We can get an idea of the number of pennies in circulation by looking at all the change in our pockets, counting the dates, and using that to estimate a loss rate. In 1999, some statisticians recorded the dates on 1,000 pennies they had lying around, and published the data in the book Workshop Statistics: Discovery with Data and Fathom, page 389. By plotting the frequency with which they saw pennies of various ages against the frequency we'd expect from US Mint production numbers, we can estimate the rate at which older pennies drop out of circulation per year. Using their numbers, I come up with an estimate of about 190,000,000,000 pennies in circulation.

We can then apply the same formula to previous dates, and come up with a number for 1996, to check against the GAO number. (I have a lot of spare time on my hands.) Surprisingly, this produces an estimate that's still about 190,000,000,000. Either number (190 billion or 132 billion) is probably a reasonable estimate, but if you're serious about your penny statistics—and if you've read this far, you must be—you should probably go with the US Mint guess. After all, they presumably know a thing or two about counting pennies. currently in circulation, for a total weight of over 300,000 tons. In total, US coins and bills are responsible for about 30% of the pile's weight, while the European Union—which has barely been minting coins for a decade—contributes 15%.

Unfortunately for you, the pile doesn't stay a pile for long,[2]When you pour lots of loose material in a heap, it tends to form a cone. Different materials will form cones with different slopes; the steepness of the slope for a given material is called its angle of repose.

I've never found the exact angle of repose for coins—or had enough of them to test it—but a forum poster with the username Master of Coin (who claims to be well-acquainted with "how piles of coins 'slish' about") says that it's probably no more than 5 or 10 degrees. and what seems like a safe distance isn't so safe.

In 1919, a tank of molasses in Boston collapsed. Molasses is thick, so you might think it would flow out slowly, but it didn't. The wave of molasses swept down the streets too fast to outrun, demolishing buildings and killing 21 people.

Something similar happens with the pile of coins. As it collapses, the pile spreads outward, a wave of money carrying a staggering amount of momentum. The pennies, quarters, loonies, and euros scour the landscape in an expanding ring. Within seconds, the wave of coins engulfs you and you die.

There are ways to avoid this. You could, say, build a wall around the coins to contain them. Unfortunately, then you might face a problem worse than death:

Building code violations.

Heavy skyscrapers need ground strong enough to support them. Places with large skyscrapers, like those in Manhattan, need bedrock sturdy enough to hold them up.[3]For a long time, people said that this was why there was a gap in Manhattan's skyline—the bedrock wasn't strong enough to support skyscrapers in the middle. However, a 2011 paper in the Journal of Economic History says that this is a myth, and the bedrock had little influence on the location of skyscrapers. A search through this giant PDF of NYC building codes suggests that if we went ahead with this plan, we would be in serious danger of violating section 1804 ("ALLOWABLE BEARING PRESSURES").

Which makes me wonder: Did Scrooge McDuck ever have to worry about this stuff?

My 12-year-old daughter is proposing an interesting project. She is planning to attach a number of helium balloons to a chair, which in turn would be tethered by means of a rope to a Ferrari. Her 13-year-old friend would then drive the Ferrari around, while she sits in the chair enjoying uninterrupted views of the countryside. Leaving aside the legal and insurance difficulties, my daughter is keen to know the maximum speed that she could expect to attain, and how many helium balloons would be required.

Phil Rodgers, Cambridge, UK

Thanks for getting your dad to send in this question! He said not to worry about the "legal and insurance difficulties," so I think it's safe to assume he's taken care of all that.

Note to police: If you've recently taken into custody two unidentified underage drivers, a stolen Ferrari, and a bunch of helium balloons, the person you're looking for is Phil Rodgers in Cambridge, UK.

Okay, on to your question:

Have you ever run with a balloon? It doesn't point straight up. The air rushing past you pushes it down:

How high the balloon goes depends on which force is stronger--the balloon's buoyancy pulling upward, or the wind dragging the balloon backward. If the drag is too strong, the balloon will stay low to the ground and you won't get a good view.

To figure out how fast you can go, let's first figure out how big our cluster of balloons (or one big balloon, which is probably easier) needs to be to lift you.

People your age weigh an average of 43 kilograms, which means you need a balloon 4 meters wide to lift you—that's about the size of a car. (If you don't weigh 43 kilograms, you can put your weight into this formula.)

A 4-meter balloon will be large enough to cancel out your weight. But that's not enough. It just means you wouldn't fall or float—so you'd be towed along the ground behind the car.

To float upward, you need a bigger balloon. A 5 meter balloon will produce 71 kilograms of lift[1]Usually, physics people will make a big deal about how weight and force are different from mass, but in this case, I'm going to resist the urge, because it's easy to just think of everything in terms of weight.​ (here's the formula!). That's enough to cancel out your 43-kilogram weight, plus a few kilograms for the chair and balloon itself.

The balloon will be dragged backward by the air. The faster your friend drives, the more the air will drag the balloon back. You can use this formula to figure out how much "weight" will pull backward on the balloon for different speeds and sizes. Just change the "20 mph" (driving speed) and "5 meters" (balloon size) in the formula.

If the upward pull from the helium is stronger than the backward pull from the wind, the balloon will float at a high angle. If the backward pull is stronger than the upward pull, the balloon will float at a low angle. If you're using a 5-meter balloon, even if you drive only 10 mph, the balloon will float pretty low behind you.

Fortunately, there's a solution: You can make the balloon bigger. As you make the balloon bigger, the buoyancy starts to win out over the drag.[2]The reason is that the buoyancy equation uses diameter^3 but the drag equation uses diameter^2, so if you make diameter bigger, the buoyancy equation grows more.

If you use a 10 meter balloon, the buoyancy is strong enough that you can drive at 20 or 25 mph and still stay pretty high off the ground. A 15 meter balloon is even better; it would let you go 30 mph while still getting a good view.[3]You could make the cable longer, so that even a low angle still gets you high off the ground. But the cable won't be straight; it makes a curve called a catenary. At a low enough angle, making the cable longer would just mean part of it would drag on the ground.

Unfortunately, there's a problem with using larger and larger balloons.

A 15-meter helium balloon plus a 12-year-old can lift 1,895 kilograms. But a Ferrari 458 (plus a 13-year-old) only weighs 1,532 kilograms.

The solution to all this is to ditch the helium. You don't need a balloon. All you need is a kite or a parachute—a surface to act as a wing and redirect that incoming air to push you upward.

In other words, see if your dad will take you parasailing.

How fast could you visit all 50 states?

—as discussed by Stephen Von Worley on Data Pointed

This week's article is a little different. Instead of answering one of your questions, I'm going to look at someone else's answer to a question, and how thinking about that answer raised some new questions of my own. Eventually, the whole thing sucked me down a rabbit hole of calculations from which I barely escaped.

In the summer of 2012, the blog Twelve Mile Circle posted an article about the search for a 24-hour-long Google Maps route that visits as many US states as possible. They found that the maximum was about 19 or 20 states.

If you can visit 19 or 20 states in 24 hours, how long would it take to visit all 50? Stephen Von Worley read the article and did some calculating. He came up with a 6,813-mile route that visited the contiguous 48 states, then wrote an article on Data Pointed discussing how long the journey would take using different types of transportation.

His conclusion:

• • 160 hours by car (plus airline flights to Alaska and Hawaii)
• • 39 hours by private jet (landing in each state)
• • 18 hours by F-22 fighter jet and helicopter (landing in each state)

And he stopped there.

Recently, someone sent me Stephen's article. I enjoyed it, but I got curious: Were there faster ways?

First of all, there are technically faster planes than the F-22. The SR-71 Blackbird is, by some measures,[1]Rocket planes are faster, but only over short distances, and usually don't take off on their own. Orbital rockets are much faster because getting to space is mainly a problem of going as fast as possible.​[2]The X-15 rocket plane, was about twice as fast as the SR-71, and is the only aircraft to fly up to space. the fastest plane. It holds the record for the fastest trip from New York to London. It's fast enough that if you fly it along the Equator going west, even with pauses to refuel, you'll see the Sun rise in the west and set in the east.[3]I just came across this positively stunning firsthand account by Bill Weaver, an SR-71 test pilot. In 1966, Weaver was flying an SR-71 at full speed, Mach 3.18, when it abruptly and catastrophically disintegrated. Somehow, he survived the breakup. He didn't eject; the plane just tore itself apart around him and scattered in all directions. In other words, he suddenly found himself flying along at Mach 3.18 ... without his plane. It's a mind-boggling story. If you relax the requirement to land—so you just need to pass over the borders into the state—an SR-71 using aerial refueling could fly Stephen's route—plus trips to Juneau and Honolulu—in about 7 hours.[4]Or possibly more. It couldn't fly his route exactly, since at full speed the plane's turning radius is something like 100 miles.

And if we're not bothering to land in each state—if we're just trying to through the state's airspace—some new possibilities open up. This is where I got thoroughly nerd-sniped.

Satellites in orbit are an order of magnitude faster than even the SR-71. An object in low Earth orbit can cross the entire US in minutes. Furthermore, a satellite in a polar orbit will eventually pass over every state, since the Earth turns slowly under its orbital path, but hitting all 50 states this way would take many days.

I started to wonder how many orbits were required, and whether a satellite doing carefully planned course corrections could pass over all 50 states faster than the 7+ hours needed by an aircraft.

If you allow the satellite to change course an unlimited number of times, it can just forget about orbits completely, following a twisty course that stays over the US. At that point, it simply becomes a question of how much fuel you're allowing it to have.

Instead, I started considering another version of the problem: What if your satellite that had to coast while near the US, but could fire thrusters on the far side of the Earth once per orbit, putting it on a new course for each pass? How many passes would be required to visit every state then?

I had previously written some code for analyzing airplane routes to help me answer the question in "Flyover States" chapter in the What If book. I repurposed this code to tackle my satellite question.

For a while, the best my math could come up with was a set of six orbits that crossed all 50 states:

I decided that 6 was probably the limit; I just couldn't figure out a way to do it with 5. But I left my computer churning on the problem for an evening, searching through combinations of orbits, and yesterday morning ...

... it came up with a solution that does it in 5.

Those 5 orbits cross over all 50 states ... and DC, for good measure. They're all slightly curved, since the Earth is turning under the satellites, but it turns out that this arrangement of lines also works for the much simpler version of the question that ignores orbital motion: "How many straight (great-circle) lines does it take to intersect every state?" For both versions of the question, my best answer is a version of the arrangement above.

I don't know for sure that 5 is the absolute minimum; it's possible there's a way to do it with four, but my guess is that there isn't. Perhaps there's a way to get just the 48 contiguous states with 4 lines, but I haven't found it yet.

If you want to play with arrangements of lines, you can use the Google Earth path-drawing tool. It's a little clumsy, but it works. If anyone finds a way (or proof that it's impossible) I'd love to see it!

Bringing things back to Stephen's original question, the 5 orbits (four, really, since you could start and end over on the US side) would take just over six hours to complete, including the three maneuvers over the Indian Ocean. In other words, in a spacecraft, you could beat even the fastest airplane.

Of course, those right-angle turns would take a lot of fuel—and, as mentioned before—if you were really trying to set this record, you would just need to get as much fuel as possible and fly a space figure-8 that stayed above the country.[5]Or in a hyperloop, I guess.

Either way, one thing's for sure: In the time I spent doing all that calculation, I probably could have just visited all those states by walking.

But the calculating was fun.

What if everything was antimatter, EXCEPT Earth?

Sean Gallagher

This one doesn't end well for us. But—unlike most scenarios involving the word "antimatter"—the end is surprisingly slow and drawn-out.

The whole universe is matter, as far as we can tell. No one is sure why there's more matter than antimatter, since the laws of physics are pretty symmetrical, and so there's no reason to expect there to be more of one than the other.[1]Although when it comes down to it, there's no reason to expect anything at all.

It's possible that galaxies are made of antimatter, and we just haven't noticed because we haven't tried to touch them. This is a cool idea, but if there are zones of matter and zones of antimatter, we should see a telltale gamma-ray glow from the boundary between the zones. So far, we haven't seen that, although another telescope might help.

If the rest of the universe were swapped out for antimatter, we'd be in trouble. Outer space isn't really "space";[2]As far as I know, it really is "outer", for what that's worth. it's full of a thin gas.[3]Technically, plasma.​[4]Technically, there's also a substantial quantity of solid grains of dust.​[5]Look, there's a bunch of little bits that are hard to see, ok?.​[6]Ok, they're not always hard to see.

The Earth's magnetic field protects us from the solar wind, and would protect us from an anti-solar wind, too. A tiny fraction of the particles from the Sun do reach the Earth, funneled down by our magnetic field, and create the aurora. In this scenario, the aurora would get a lot brighter, but most of the time not bright enough to really cause problems.

Meteorites would be the real problem.

The Earth sweeps up space dust as it travels around its orbit.[7]Unfortunately for us, antimatter is probably attracted to matter by gravity. About 100 tons of dust per day enters the atmosphere in the form of tiny grains, most weighing about 10^-5 grams. An additional similar average per-day amount arrives in giant clumps all at once.

This inflow of antimatter dust would collide with the top of our atmosphere and be annihilated. The interactions between the nuclei and antinuclei and protons and antiprotons would be complex,[8]A lot of the energy would be carried away by neutrinos. but the end result would be a lot of gamma rays, which would turn into a lot of heat. This steady flow of material would be worst around dawn, when your house was facing in the direction of Earth's motion.

The heat and light added by the antimatter would most likely be enough to tip the Earth into a "runaway greenhouse" scenario, turning the Earth into something resembling Venus.

But the big asteroids would get us first. Even a relatively small object like the Chelyabinsk meteor would deliver as much energy as the meteor that killed the dinosaurs.[9]Although it would deliver it to the top of the atmosphere, so in some ways it wouldn't be as bad. Fairly large asteroids enter the atmosphere every few months—mostly unnoticed. If they were all antimatter, each one would trigger a tremendous pulse of energy in the sky and ignite a massive firestorm.[10]If an antimatter meteor is large enough, encountering a cloud could launch some of it backward without completely destroying it. However, it's hard to come up with a practical scenario in which a meteor would exhibit this effect in Earth's atmosphere—unless it were so large that it would have basically destroyed the planet anyway.

Right now, it's still an open question whether any significant percentage of the stuff in the sky is made of antimatter. It's probably not, but we'd need to build another orbiting gamma-ray telescope to really be sure.

However, it's easy to use a telescope to rule out one possibility: That everything in the sky is antimatter.

If you have a telescope, maybe you can get that result published.

When I was about 8 years old, shoveling snow on a freezing day in Colorado, I wished that I could be instantly transported to the surface of the Sun, just for a nanosecond, then instantly transported back. I figured this would be long enough to warm me up but not long enough to harm me. What would actually happen?

AJ, Kansas City

Believe it or not, this wouldn't even warm you.

The temperature of the surface of the Sun is about 5,800 K,[1]Or °C. When temperatures start having many digits in them, it doesn't really matter. give or take. If you stayed there for a while, you'd be cooked to a cinder, but a nanosecond is not very long—it's enough time for light to travel almost exactly a foot.[2]A light-nanosecond is 11.8 inches (0.29981 meters), which is annoyingly close to a foot. I think it would be nice to redefine the foot as exactly 1 light nanosecond. Because we don't have enough unit confusion in the world already.

This raises some obvious questions, like "Do we redefine the mile to keep it at 5,280 feet?" and "Do we redefine the inch?" and "Wait, why are we doing this?" But I figure other people can sort that out. I'm just the idea guy here.

I'm going to assume you're facing toward the Sun. In general, you should avoid looking directly at the Sun, but it's hard to avoid when it takes up a full 180 degrees of your view.

In that nanosecond, about a microjoule of energy would enter your eye.

A microjoule of light is not a lot. If you stare at a computer monitor with your eyes closed, then open them and shut them quickly, your eye will take in about as much light from the screen during your reverse blink[3]Is there a word for that? There should be a word for that. as it would during a nanosecond on the Sun's surface.

During the nanosecond on the Sun, photons from the Sun would flood into your eye and strike your retinal cells. Then, at the end of the nanosecond, you'd jump back home. At this point, the retinal cells wouldn't even have begun responding. Over the next few million nanoseconds (milliseconds) the retinal cells—having absorbed a bunch of light energy—would get into gear and start signaling your brain that something had happened.

You would spend one nanosecond on the Sun, but it would take 30,000,000 nanoseconds for your brain to notice. From your point of view, all you would see was a flash. The flash would seem to last much longer than your time on the Sun, only fading as your retinal cells quieted down.

The energy absorbed by your skin would be minor—about 10^-5 joules per cm² of exposed skin. For comparison, according to the IEEE P1584 standard (as quoted on ArcAdvisor.com), holding your finger in the blue flame of a butane lighter for one second delivers about 5 joules per cm² to the skin, which is roughly the threshold for receiving a second-degree burn. The heat during your Sun visit would be five orders of magnitude weaker. Other than the dim flash in your eyes, you wouldn't even notice.

But what if you got the coordinates wrong?

The Sun's surface is relatively cool. It's hotter than, like, Phoenix,^{[citation needed]} but compared to the interior, it's downright chilly. The surface is a few thousand degrees, but the interior is a few million degrees.[4]The corona, the thin gas high above the surface, is also several million degrees, and no one knows why. What if you spent a nanosecond there?

The Stefan-Boltzmann law lets us calculate how much heat you'd be exposed to while inside the Sun.[5]There's also direct pressure from the heavy particles, protons and stuff, bouncing around, but the radiation turns out to be the dominant component.

I'm going to hijack this note to ask another question: How does this transporter work, anyway?

When you teleport somewhere, presumably it does gets rid of the matter that was in the way, so you don't end up combining yourself with whatever was there. A simple solution is to have the teleporters swap matter between the two locations. Kirk gets teleported down to the planet, a Kirk-sized chunk of air gets teleported up to the Enterprise.

So what would happen if an AJ-shaped chunk of Sun-interior gets teleported to snowy Colorado, then we just left it there?

The protons inside the Sun bounce around at speeds of about 350 km/s (about half of the Sun's escape velocity at that depth, for weird and deep reasons.) Freed from their crushingly hot neighborhood, the whole collection of protons would burst outward, pouring light and heat energy into their surroundings. The energy released would be somewhere between a large bomb and a small nuclear weapon. It's not good. You would exceed the IEEE P1584B standard for second-degree burns after one femtosecond in the Sun.[6]Although it wouldn't be a second-degree burn until many picoseconds later, since the definition of a second-degree burn is one which damages some of the underlying layers of tissue—and in the first few femtoseconds, light wouldn't have time to reach the underlying tissue. A nanosecond—the time you're spending there—is 1,000,000 femtoseconds. This does not end well for you.

There's some good news: Deep in the Sun, the photons carrying energy around have very short wavelengths—they're mostly a mix of what we'd consider hard and soft X-rays.[7]<what_if_book_reference>I wonder if there are more soft or hard x-ray photons in the universe.</what_if_book_reference> This means they penetrate your body to various depths, heating your internal organs and also ionizing your DNA, causing irreversible damage before they even start burning you. Looking back, I notice that I started this paragraph with "there's some good news." I don't know why I did that.

In Greek legend, Icarus flew too close to the Sun, and the heat melted his wings and he fell to his death. But "melting" is a phase change which is a function of temperature, a measure of internal energy, which is the integral of incident power flux over time. His wings didn't melt because he flew too close to the Sun, they melted because he spent too much time there.

Visit briefly, in little hops, and you can go anywhere.

If you stripped away all the rules of car racing and had a contest which was simply to get a human being around a track 200 times as fast as possible, what strategy would win? Let's say the racer has to survive.

Hunter Freyer

The best you'll be able to do is about 90 minutes.

There are lots of ways you could build your vehicle—an electric car,[1]With wheels designed to dig into the pavement on turns. a rocket sled, or a carriage that runs along a rail on the track—but in each case, it's pretty easy to develop the design to the point where the human is the weakest part.

The problem is acceleration. On the curved parts of the track, drivers will feel powerful G forces.[2]Which you can broadly call either "centrifugal" or "centripetal" forces, depending on exactly which type of pedant you want to annoy. The Daytona Speedway in Florida has two main curves, and if the vehicles go around them too fast, the drivers will die from the acceleration alone.

For extremely brief periods, such as during car accidents, people can experience hundreds of Gs and survive. (One G is the pull you feel when standing on the ground under Earth's gravity.) Fighter pilots can experience up to 10 Gs during maneuvers, and—perhaps because of that—10 Gs is often used as a rough limit for what people can handle. However, fighter pilots only experience 10 Gs very briefly. Our driver would be experiencing them, in pulses, for minutes and probably hours.

There's a good NASA document on the physical effects of acceleration here, and a particularly helpful chart in Figure 5 here.

But the most fun data comes from John Paul Stapp. Stapp was an Air Force officer who strapped himself into a rocket sled and pushed his body to the limit, taking careful notes after every run. You can read a great essay about him on the Ejection Site. The whole story is fascinating, but my favorite line is, "... Stapp was promoted to the rank of major [and] reminded of the 18 G limit of human survivability ..."

Stapp aside, the data shows that for periods on the order of an hour, normal humans can only handle 3-6 Gs of acceleration. If we limit our vehicle to 4 Gs, its top speed on the turns at Daytona will be about 240 mph. At this speed, the course will take about 2 hours to complete—which is definitely faster than anyone has driven it in an actual car, but not by that much.

But wait! What about the straightaways? The vehicle will be accelerating during the turns, but coasting on the straightaways. We could instead accelerate the vehicle up to a higher speed while on straight segments, then decelerate it back down when approaching the end. This would result in a speed profile like this:

This has the additional advantage that—with some clever back-and-forth maneuvering on the track—the driver can be kept at a relatively constant acceleration through the whole trip, hopefully making the forces easier to endure.

Keep in mind that the direction of the acceleration will keep changing. Humans can survive acceleration best if they're accelerated forward, in the direction of their chest, like a driver accelerating forward. The body is least capable of being accelerated downward toward the feet, which causes blood to pile up in the head. To keep our driver alive, we'll need to swivel them around so they're always being pressed against their back. (But we have to be careful not to change direction too fast, or the centrifᵫtal[3]Splitting the difference. force from the swiveling of the seat will itself become deadly!)

The fastest modern Daytona racers take about 3 hours to finish the 200 laps. If limited to 4 Gs, our driver will finish the course in a little under an hour and 45 minutes. If we raise the limit to 6 Gs, the time drops to an hour and 20. At 10 Gs—well past human tolerability—it would still take an hour. (It would also involve breaking the sound barrier on the backstretch.)

So, barring dubious concepts like liquid breathing, human biology limits us to Daytona finishing times over an hour. What if we drop the "survive" requirement? How fast can we get the vehicle to go around the track?

Imagine a "vehicle" anchored with Kevlar straps to a pivot in the center, reinforced with a counterweight on the other side. In effect, this is a giant centrifuge. This lets us apply one of my favorite weird equations,[4]See footnote [8] in article #86. which says that the edge of a spinning disc can't go faster than the square root of the specific strength[5](tensile strength divided by density) of the material it's made of. For strong materials like Kevlar, this speed is 1-2 km/s. At those speeds, a capsule could conceivably finish the race in about 10 minutes—although definitely not with a living driver inside.

Ok, forget the centrifuge. What if we build a solid chute, like a bobsled course, and send a ball bearing (our "vehicle") rocketing down it? Sadly, the disc equation strikes again—the ball bearing can't roll faster than a couple km/s or it will be spinning too fast and will tear itself apart.

Instead of making it roll, what if we make it slide? We could imagine a diamond cube sliding along a smooth diamond chute. Since it doesn't need to rotate, it could potentially survive more accelerations than a rolling ball bearing. However, the sliding would result in substantially more friction than the ball bearing example, and our diamond might catch fire.

To defeat friction, we could levitate the capsule with magnetic fields, and make it progressively smaller and lighter to accelerate and steer it more easily. Oops—we've accidentally built a particle accelerator.

And while it doesn't exactly fit the criteria in Hunter's question, a particle accelerator makes for a neat comparison. The particles in the LHC's beam go very close to the speed of light. At that speed, they complete 500 miles (30 laps) in 2.7 milliseconds.

Wikipedia lists about 850 motor racing tracks. The LHC beam could run the equivalent of a full Daytona 500 on each of those 850 tracks, one after another, in about 2 seconds, before the drivers had made it to the first turn.

And that's really as fast as you can go.

What is the farthest from Earth that any Earth thing has died?

—Amy from NZ

With Halloween approaching, I guess it's the season for death-related questions.

The farthest from Earth that any human has died is about 167 kilometers,[1]Plus or minus a kilometer. when three cosmonauts on Soyuz 11—Vladislav Volkov, Viktor Patsayev, and Georgi Dobrovolsky—suffered a depressurization accident while returning to Earth. They were moving at about 7,755 meters per second at the time, which is also the highest forward speed at which any human has ever died.

Volkov, Patsayev, and Dobrovolsky are the only humans who have died in space. Every other fatal space accident—and, for that matter, every other human death of any kind—happened within 70 kilometers of the surface.[2]Morbid list from my notes: The crew of Columbia died at just over 60 km, Pyotr Dolgov died at roughly 24 km, James Zwayer died at 23 km, Michael J. Adams died at 20 km, Ying Chin Wang died at 20 km, and Rudolf Anderson died at between 18 and 23 km. Jack Weeks presumably died somewhere between 20 and 0 km the ocean surface.

But humans don't hold this record.

For starters, there are plenty of test animals which have died in space. But, to be honest, I can't bring myself to collect statistics about them. I mean, at least the human pilots who died had all volunteered and understood what was happening to them. So instead, I'm going to skip straight to the organisms that are the real answer to Amy's question: Microbes.

Spacecraft carry bacteria, although we do our best to sterilize them before and during launch. This sterilization is important, because we don't want to contaminate another planet or Moon with Earth bacteria. There are two big reasons for this—one ethical and one practical. The ethical one is that we don't want to accidentally introduce Earth life that disrupts and/or destroys a native ecosystem. The practical one is that if we find life on some other planet, we don't want to have to struggle to figure out whether it was contamination from one of our probes.

But sterilizing spacecraft is hard. NASA has an employee specifically assigned to this task, and she has possibly the best job title of all time: Planetary Protection Officer.[3]Another competitor for this title is Philip M. Breedlove, who has the job title Supreme Allied Commander.

The Planetary Protection Officer is responsible for avoiding spacecraft contamination, although there are occasionally problems.

A 2008 study of lunar missions estimated that spacecraft carried 1.98x10¹¹ viable microorganisms per vehicle. Spacecraft such as the Voyagers and Pioneers, which were ultimately headed for deep space, were also not fully sterilized—the official planetary protection strategy was "try not to hit any planets."

Voyager certainly carries lots of bacterial spores. If we take the number from the 2008 paper as a (very rough) estimate of the number of microbes Voyager might carry, we can try to figure out how many might still be alive.

Some microorganisms can survive for a long time in a vacuum. One study found that the majority of bacteria that spent six years in space survived—though only if a shade protected them from the Sun's UV light. Other studies have agreed that radiation is the main thing to worry about, and the radiation environment inside a spacecraft is complex. The bottom line is that we just don't know for sure how long bacteria can survive in deep space.

But we can still give part of an answer Amy's question. If we assume that 1 in 1,000 bacterial spores on Voyager were of a space-tolerant variety, and 1 in 10 of those is somewhere on the craft where UV light doesn't reach it, then that still leaves on the order of 10 million viable bacterial spores traveling on Voyager.

If they suffer a death rate of 30% per six years, as in one of the studies, then there would still be a million of them alive after 50 years, dying at a rate of 1 every 10 minutes. On the other hand, the author of the 2008 study speculated that microbes could avoid hits from cosmic radiation for extremely long time periods, and other sources have speculated about survival for thousands or even millions of years. But no one really knows.

For our Voyager bacteria, there's a higher death rate at first, for spores in more exposed positions, and a much lower one for the more protected ones. Today, it's quite possible there are thousands of bacterial spores still alive on Voyager 1 and 2, lurking quietly in the dead of space. Every few hours, days, or months, one of them degrades enough to no longer be viable.

And each one sets a new record for the most distant Earth thing to die.

What if people's incomes appeared around them as cash in real time? How much would you need to make to be in real trouble?

Julia Anderson, Albuquerque, NM

First, let's think about coins.

The US federal minimum wage in the US is \$7.25/hour, which is about \$15,000/year for a full-time job. If you earn the minimum wage, you make a penny every 5 seconds during work hours, or every 20 seconds if you average it over your whole week.

Someone making minimum wage in pennies would earn about 30 lbs of pennies per workday. Two weeks' worth of pay in pennies would fill a small carry-on suitcase. At 150 lbs, the suitcase would probably be too heavy to pick up. However, if they were paid in quarters instead of pennies, two weeks' pay would only weigh about 3 lbs.

If paid in a typical mix of loose change,[1]The makeup of a "mix of loose change" depends on your spending habits. Lots of people have calculated this to estimate the amounts of change in a jar. One of the more careful theoretical calculation I've seen, which considers prices and sales tax, comes from Dan Kozikowski.

Since I've spent way too much time on this question over the years, for the record: If you're ever trying to guess the value of coins in a jar, my suggestion would be \$13.05/lb and \$468/gallon if the person doesn't use quarters for laundry or parking, \$9.53/lb and \$336/gallon if they do, and \$16.75/lb and \$611/gallon if they discard pennies. the US federal minimum wage is about one plastic water bottle full of coins per workday, and the median household earns three or four water bottles per workday.

A CEO of a large company might make \$40,000 per workday. Assuming an 8-hour workday, that's 130 pennies per second. If paid in a mix of loose change, the CEO would earn about a water bottle of coins per minute, and a duffel bag full of loose change every hour, or 600 water bottles per workday:

If you're a CEO working in a 300 ft² office, the change would accumulate on the ground at a rate of about only half an inch per day. (If it were pennies, it would be more like 3" per day). It would mean frequently getting up to adjust your desk so it stayed on top of the pile, and I can't imagine your chair would be too stable, but it seems like it might be manageable.

Lugging those 150-kg duffel bags to CoinStar every hour would be a hassle. If we allowed paper money, things would get easier. A dollar bill has a volume of about 1.55 mL, which means that a CEO paid in dollar bills would only need one large-ish duffel bag for a day's pay.

If paid in \$100 bills, a CEO would only need a couple of duffel bags to carry home their year's salary.

In either case, at 60-70 lbs, a duffel bag full of bills would be a little on the heavy side.

Now, there are people who make a lot more than "typical CEOs".

Mark Zuckerberg, Warren Buffett, and Bill Gates all made in the neighborhood of \$10 billion in 2013. During the workday, that's a duffel bag full of \$100 bills every half-hour.

Going back to our earlier metric, that's 25 water bottles full of change—one minimum-wage worker's daily salary—per second of the workday.

If randomly dispensed from the ceiling in the form of loose change, Mark Zuckerberg's income would pile up at an inch every minute. There would be so many coins hitting the ground per second that it would meld into white noise.[2]The Mark Zuckerberg Money Pump would require over a kilowatt of power just to hoist the coins up to his ceiling and drop them. But that's not a problem. Even a penny is worth enough to pay for the electricity to hoist itself several thousand miles upward. The downward force from the coins falling on Mark's head and shoulders would certainly be annoying, but not debilitating. It would be possible for him to walk around, but if he sat still for an hour, he'd be buried.

It does sound awful.

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.
If our black hole were devouring matter at the Eddington limit, it would be hot enough to sterilize the Earth.

Fortunately, there's not a lot out there for it to eat, so it wouldn't glow very brightly for now. It would spend most of its time drastically altering the orbits of nearby dust particles—one sand grain pushing other sand grains around.[3]Even if it sucked in matter at the rate the Earth—with its much larger "collecting area"—sucks in interplanetary dust, it wouldn't necessarily be a problem for us.

But there would be one interesting effect: In addition to getting darker, Earth would get colder, because moonlight warms the Earth. It's a very tiny contributor to our global energy balance; the Moon is five or six orders of magnitude dimmer than the Sun. But it's there.

Measurements show that global temperature varies with a 28-day cycle; all else being equal, the Earth is hottest during the full moon. It's a tiny difference—small fractions of a degree—but it's there.

But it turns out most of this effect is not due to moonlight. The largest contributor is the fact that the Earth is slightly closer to the Sun during a full Moon:

Calculating the amount of energy radiated back to Earth by the Moon is deceptively tricky. The Moon reflects sunlight, but with some surprising twists. When the Moon is half-illuminated, you might think it would be half as bright as when full—but it's much less bright than that. And once you account for that, there are even trickier effects to deal with, because science is the worst.[4]Like the fact that the waxing Moon is 20% brighter than the waning Moon, or that the Moon is a mild retroreflector. Then, on top of all the weird visible-light effects, the Moon also heats up under the Sun, then radiates that heat as infrared light.

There's a great discussion of the Moon's effect on the Earth's energy budget in this article by Robert Knox. The upshot is that the Moon's infrared heat radiation turns out to affect Earth's temperature about 10 times more than the visible moonlight, but still about 10 times less than the effect from gravity moving Earth closer and farther from the Sun. Knox even quantifies the effect this has on Earth's radiation balance—the presence of infrared moonlight warms the planet by 1.2 milli-degrees Fahrenheit (m°F).

Without moonlight, the planet would cool down slightly. But given the accelerating rate at which we're adding CO₂ to the atmosphere—which changes the Earth's energy balance—we'd make up the difference in a couple of weeks.

So all in all, the conversion of the Moon to a black hole might not even be that big of a deal.

Unless, of course, it happened on certain days between 1969 and 1972, in which case Nixon would've needed yet another one of those speeches.

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 Opens

Believe 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.

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 Ward

You 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.

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 Ungericht

If 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 theseguys!). 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!

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 Fremont

This 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.

Or is it 65%? Or 80%? The exact number is a little vague, and seems to depend on who you ask. In a footnote in her wonderful book, Stiff: The Curious Lives of Human Cadavers, writer Mary Roach mentioned that she had methodically Googled the phrase "human body is <X> percent water", for X from 0 to 100. She reported a wide range of claims, including several pages asserting that we're 98% water. It's really gratifying to know I'm not the only person who spends a lot of time carefully cataloging weird stuff like that.

What happens next depends on exactly where in space you are.

If you're in an orbit that passes near the Earth, your orbit will quickly decay, and before long you'll re-enter the atmosphere and burn up.

If you're in a slightly higher orbit, you'll last longer, but you'd also be in the zone where space debris was thickest. Impacts with small bits of debris would start to leave pits and scars on your surface; they would often find these on Space Shuttle windows after a flight. Eventually, probably after a few decades, you'd probably have a violent collision with something.

Higher orbits are safer. If you were some distance away from the Earth, near where geosynchronous satellites orbit, there would be less debris to run into. Furthermore, for large, dense objects, orbits out there are stable for a very long time. You could spend centuries drifting among TV broadcast satellites.

If you wanted to last even longer, you could launch yourself away from Earth completely, finding a quiet and stable orbit somewhere in interplanetary space. There, over the course of millennia, you'd be slowly baked by the Sun's radiation and pitted and powdered by micrometeorites.

But if your goal is to weird out future space travelers, that might not be the best plan. Space is big; if someone randomly stumbles on your corpse, it suggests that there must be a lot of people zipping around the solar system. And if space travel has become that common, there will be lots of corpses floating around;[4]Weird that "lots of corpses floating around" is somehow an optimistic prediction about the future of space travel. discovering yours will be more archaeologically exciting than anything. You'll be stuck in a lab or museum somewhere and contribute to someone's research paper—a bland end to your exciting prank.

Unless, of course, you happen to be found by the only people in space even weirder than you.

What would happen if I dug straight down, at a speed of 1 foot per second? What would kill me first?

Jack Kaunis

This 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.

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 Fleming

Note: 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:

  Our recommendations for amelioration included the following general points:
  1) On-site personnel should be reassured that the spiders are harmless and the facility's immense shroud of silk should be presented in a positive light as a record-breaking natural history wonder.

What was the total force of gravity from all those spiders? First we need their mass; according to a paper titled Sexual Cannibalism in Orb-Weaving Spiders: An Economic Model, it's about 20 grams for males and several times that for females.[11]Not to be confused with Trade-off between pre- and postcopulatory sexual cannibalism in a wolf spider, which is a different but equally real paper. So even if you were standing next to the Black River Wastewater Treatment Plant in 2009, the pull of all the spiders inside would still be only 1/50,000,000th that of the Sun.

No matter which way you look at it, the bottom line is that we live our lives surrounded by tiny spiders on a world completely dominated by a gigantic star.

Hey, at least it's not the other way around.

What if New Horizons hits my car?

—Robin Sheat

The 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.

What if you released a submarine into Jupiter's atmosphere? Would it eventually reach a point where it would float? Could it navigate?

—KTH

Nope! 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:

It’s calm there. Dead calm.

Some stricken ships have rigging; some even have sails. Many still have crew, tangled in the rigging or lashed to the wheel.

But the voyages still continue, aimlessly, with no harbour in sight, because there are currents under the ocean and so the dead ships with their skeleton crews sail on around the world, over sunken cities and between drowned mountains, until rot and shipworms eat them away and they disintegrate.

Sometimes an anchor drops, all the way to the dark, cold calmness of the abyssal plain, and disturbs the stillness of centuries by throwing up a cloud of silt.

I love that passage. It's also completely wrong. Ships sink all the way to the bottom. (Sir Terry knew this, as the rest of the passage makes clear, but he's describing how ships work on Discworld, not Earth.)

Air follows the ideal gas law. The more pressure you put on it, the smaller (and denser) it gets.

Water, on the other hand, is pretty much incompressible. When you dive into the ocean, the pressure increases as you go deeper (rising by one atmosphere every 10 meters or so) but the water's density barely changes all the way down to the sea floor.

Buoyancy depends on density, not pressure. There's a point in Jupiter's atmosphere where the pressure is equal to a little more than an Earth atmosphere—which is the pressure a submarine is used to—but the air there is barely a tenth as dense as ours. A submarine in that layer would fall even faster than it would in the air on Earth.

To reach a depth where it could "float" in Jupiter, the submarine would have to go halfway to the center of the planet, where the intense pressure turns the air into a metallic soup that's hotter than the surface of the Sun. The pressure there would be so high that not only would the submarine be crushed, the substances that make it up would probably be converted into new and exciting forms. It's hard to create those kinds of conditions in a lab, so we don't know a lot about how materials behave with that much pressure pushing down on them.

In the sea, on the other hand, the density of the fluid stays relatively constant. That means the submarine can find its appropriate pressure range and float there. In other words, submarines only work because water doesn't follow the ideal gas law.

But there's one more twist: Water sort of does obey the ideal gas law. The equations governing water under normal pressure are similar to the equation for a gas under about twenty thousand atmospheres of pressure. In a sense, this is why water seems incompressible to us—it behaves as if it's already compressed so much that an extra atmosphere or two hardly makes a difference.

So, in some ways, water and air are more similar than they seem, but in the ways that matter for a submarine, they really are different.

Which, of course, brings us back to why it's called a submarine—it operates under a "mare". A vehicle designed to operate beneath a sea of air would be called a subaerine.[5]The "gas" in "gas giant" is from the Greek word for void (χάος, kháos), so maybe a vessel (σκάφη, skáphē) that travels through a gas giant's atmosphere would be a khaoskaphe.

Which, come to think of it, is a perfectly good description of a car.

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 Munroe

We 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.