Shoot Down an Asteroid

Would it be possible to stop an asteroid from hitting the earth by firing bullets at it? --Myself

I'll be analyzing one of my own thoughts this time. I'm sure literally everyone^[who?] has wondered about this. For the purposes of this post, I'll assume that we're talking about the asteroid 4942 Munroe. It's big enough to be interesting (6 to 10 kilometers across[1], so I'll go with 8 kilometers), but not big enough to actually destroy the earth. Asteroids typically travel at 25 kilometers per second.[2] Asteroid densities vary widely[3], but let's assume that 4942 Munroe has a density of 4 grams per cubic centimeter. From this, I can calculate that the momentum of 4942 Munroe is 1.28*10^19 kilogram-meters per second.

Now it's time to think about the guns. An AK-47 fires 600 rounds per minute at a velocity of 715 meters per second.[4] Each round weighs 7.9 grams.[5] If one AK-47 is fired straight at the asteroid, the asteroid will lose 715*0.0079*600=3,389.1 kilogram-meters per second every minute. At this rate it would take slightly over 7 billion years to bring 4942 Munroe to a halt. Chances are that there will be no earth to hit by then anyway.

Luckily for humanity, it's possible to do better, but it'll take some thinking. The ideal gun for this sort of task would have massive bullets with high velocity and a high rate of fire. The heavy artillery of World War I and World War II had massive ammunition and often that ammunition had a high velocity. The railway gun Krupp K5 had a shell mass of 255 kilograms and a muzzle velocity of 1120 meters per second. The low firing rate (0.25 rounds per minute) might be a problem, but let's see. 1120*255*0.25=71,400 kilogram-meters per second lost per minute. This would bring the time down to 341 million years, which is actually a lot better than the AK47 (but still impractical). Some cannons are better. The immense V-3 cannon has a far higher rate of fire and muzzle velocity, but only a slightly lower shell size. A V-3 cannon being fired at the asteroid would cause it to lose momentum at a rate of 1,050,000 kilogram-meters per minute, which brings the time down to under 24 million years. The anti-aircraft gun GAU-8 Avenger (link to WP) is slightly superior (13 million years). None of these are going to cut it though.

More modern weapons can do still better. Consider railguns, which are moving from experimental devices into ones with practical uses. The US Navy plans in 2016 to test a railgun with a firing rate of 10 rounds per minute, a muzzle velocity of 2500 meters per second, and a bullet mass of 10.5 kilograms[6] Even that is not enough: the stopping time would be nearly 100 million years. The last thing that I'll try is this Assuming a muzzle velocity of 1000 meters per second, it would take 2.4 million years for one of those to stop 4942 Munroe. Giving one to every person on earth would stop the asteroid in just under three hours, but that wouldn't be practical.

I guess we're doomed if a huge asteroid comes our way. Or not?

Freefall

If you jumped into a hole in the center of the earth, how long would it take to come to a stop? --Sodium

I feel compelled to explain why this is not entirely practical. For one thing, it's entirely likely that such a hole would collapse, but let's assume it's lined with a magic extra-strong material that also keeps the tunnel from reaching temperatures of thousands of degrees. The air pressure would also be a problem. We currently have only 62 miles (100 kilometers) of air above our heads, so having several thousand miles of air about our heads would likely crush us.

With that out of the way, let's turn to the actual scenario. I'll assume that this tunnel is a vacuum (so that the air pressure doesn't crush the jumper [and because physicists like working in a vacuum]) and that it's sealed at both ends (so the tunnel isn't filled with wind). I'll also assume that your aim is good enough that you don't hit any walls, which would (obviously) kill you.

The exact formula for figuring this out is more complicated than traditional gravitational acceleration since the mass that's actually pulling on you will decrease as you approach the center of the earth.[1] On average, the jumper's acceleration will be about 5 meters per second squared, but it does change some.[2] I'll assume that the change in acceleration (jerk) is constant, even though it isn't, to simplify the equations. Because I'm lazy!

I can't resist going off-topic to describe some rather interesting facts. As everyone (who's read this far at least) knows that velocity, acceleration, and jerk are the 1st, 2nd, and 3rd derivatives of motion. What you may not know is that jounce (or snap), crackle, pop, lock, drop, shot, and put are the 4th, 5th, 6th, 7th, 8th, 9th, and 10th derivatives of motion, respectively. Just an awesome fact that was worth sharing. I don't know why anyone would use these though.

Anyway, back to business. I wrote a bit of code which tells me the average jerk and also tells me that it would take about 22 minutes to fall to the center of the earth. This implies that it would take 21 minutes, so my math can't be that far off. It doesn't really matter though, since your momentum would carry you all the way back up to the surface, at which point you'd just repeat it all over again.[3]

I wonder how long it would take for a person to get bored of falling assuming they didn't know that they'd never hit the ground...

Apologies

I just want to apologize for the long delay with no posts. I have been busy with other things lately, but I will try to make a new post soon. Thanks,

--Jakob

Saving Electricity

Assuming you could get 100% citizen compliance in this country, and assuming you could come up with a number for "average household" use, then average household energy savings... What amount of energy could be saved, and what might that savings amount to in dollars? -- Sonya

Well, to start idle devices use as much as 10 percent of a typical household's energy use.[1] A typical household uses 10,837 kilowatt-hours per year and there are 116,716,292 households in the United States as of the 2010 US census.[2][3] (There are three random facts in the last two sentences. I love the internet.)

If each one unplugged their idle devices, the total energy saved would be...

...116,716,292*10,837*0.1 = 126,485,445,640 kilowatt-hours, or 3.5162954 exajoules.

That's the raw math, but how much energy is that really? It's more than twice the annual electricity consumption of South Korea and between two and three percent of the annual electricity consumption of the United States. It is also more than 15 times the explosive yield of the largest nuclear bomb ever detonated, the Tsar Bomba.[4]

The cost of all the electricity that would be saved? Well, in residential areas, electricity costs an average of 13.01 cents per kilowatt-hour, as of August 2014.[5] With 126,485,445,640 kilowatt-hours of electricity being saved, the total amount of money saved would be approximately 1.64 trillion cents (more pennies than are currently in circulation), or $16,455,756,477.80. That would look like 16 of these (those are 100 dollar bills) and would take 80 years to print out with a typical printer (again, assuming that you're printing 100 dollar bills).[6]

That sum of money would also be enough money to pay for electricity for a single residence for 11,671,635 years and 211.7 days. Which, by the way, is probably longer than anyone has owned a house for.^{[original research?]}

Penny Statue

How large of a sculpture could you make from melted-down pennies? -Myself

Today I'll be sharing a question that I considered myself: how large of a statue of a person could be made from melted-down US pennies?

While one might think of a penny as a disk, it is technically cylindrical. (OK, technically it's not cylindrical due to the relief images on both sides and whatnot. But that doesn't matter.) The diameter of a penny is 19.05 millimeters and the height of a penny is 1.52 millimeters.[1] From this, it is apparent that the volume of a penny is 285.02 cubic millimeters. So next I needed to find out how many pennies are in circulation. The answer (wait for it):  200,035,318,672.[2]

Given this, the total volume of all pennies currently in circulation is 57 trillion cubic millimeters, or 57,014 cubic meters. That is a lot of cubic meters.^{[citation needed]} It would be enough to fill up 57 Olympic swimming pools and still have enough to fill 14 refrigerators.[3] I love Wikipedia's "orders of magnitude" lists. The average height of an American male over 20 is 69.3 inches.[4] The average width of a human is 18 inches and the average...um...length? thickness? depth? of a human is 9.5 inches.[5] Thus, a person's volume is 11,850.3 cubic inches, or 0.194 cubic meters. Admittedly I fudged this a bit since people aren't rectangular prisms^{[dubious--discuss]}, but it's close enough.

The pennies have a volume 293886.5979 times that of a human. The cuberoot of that is about 66.48, so the statue would be 66.48 times taller, 66.48 times wider, and 66.48 times deeper than life-size. Plugging in the numbers shows that this statue would be 384 feet (117 meters) tall, 100 feet (30 meters) wide, and 53 feet (16 meters) deep. In other words, this statue would be large enough to rank among the largest statues ever built, but not large enough to blatantly defy reality.

Derived from this diagram, created by Jdcollins13. Image is licensed under the CC-BY-SA.

(The statue made of pennies is not anatomically accurate or precise)

With the math out of the way, let's turn to the physics of this statue.

These days, pennies are mostly zinc and the density of zinc is 7.140 grams per cubic centimeter and thus 7,140 kilograms per cubic meter according to Theodore Gray's The Elements. With a volume of 57,014 cubic meters, the statue would have a weight of 407,079.96 metric tons. That's a manageable weight, since many structures that size have been built. For instance, the Great Pyramid of Giza is nearly ten times heavier.[6]

This would cause quite a bit of pressure on the feet of the statue. Some source[7] says that the average 19 year old male foot is 26.15 centimeters long. I also estimate based on a chart here that the typical male foot is 10 centimeters wide. Thus, the area of a both human feet combined is 261.5 square centimeters, or 0.02615 square meters. The statue's feet would have a combined area of 1155.72 square meters. Thus, the pressure that the statue would exert on the ground it is standing on would be 352,230 kilograms per square meter, or about 3.453 megapascals. I suspect this may cause some problems, but they could probably be alleviated by putting the statue on a large concrete base.

In case you want to try this, just be warned that it would be pretty expensive (and apparently illegal[8]). The cost of the pennies would only be part of the cost of building the statue, since you'd have to melt the copper and shape it as well.

Atom Or Universe?

Is a person proportionally closer in size to an atom or the universe?

This is a good question for using Fermi Estimation.

A person is about one meter across. At atom is about a hundred picometers across and the universe is about 100 sextillion kilometers across. If we convert these values to scientific notation, an atom is
10^-10 meters across, a person is 10⁰ meters across, and the universe is 10²⁶ meters across. Thus, the universe is 36 orders of magnitude larger than an atom, so an object that is in between the two in size would be 18 orders of magnitude larger than an atom and 36 orders of magnitude smaller than the universe. 26-18 (and for that matter -10+18) is 8, so an in-between object would have a diameter of 100,000,000 meters 100,000 kilometers. This is smaller than Jupiter and Saturn, but larger than the other two gas giants (Uranus and Neptune) and much larger than Earth.[1] It's also probably larger than you are unless you happen to be a gas giant or star (as far as I'm aware, there aren't any reading my blog).

Oh. Right. Sorry. Anyway, I'll bring some real numbers into the equation and see if that changes anything. The atomic radius of hydrogen (the most common atom in the
universe) is 53 picometers[2] so the diameter would be 106 picometers. The average height of an American male over 20 is 69.3 inches[3], or 1.76022 meters. The obeservable universe is 92 billion light years across.[4]

There are 9.4605284 quadrillion meters in a light year, so the observable universe is 8.703686128*10²⁶ meters across. So far, it seems that my Fermi Estimation was
pretty close to the actual sizes (within an order of magnitude or so, which is pretty close considering the roughness of the estimates). Let's plug in these new values.

A hydrogen atom is 1.06*10^-12 meters across, a human is 1.76022*10⁰ meters acorss, and the observable universe is 8.703686128*10²⁶ meters across. Thus, the observable universe is 9.225907296*10³⁸ times the size of a hydrogen atom. Some plugging in of numbers on my calculator shows that an in-between object is 3.037417867*10^19 times the size of a hydrogen atom.
This comes out to 28,654,885.53 meters. It's a bit closer to the size of a human than the result I got with Fermi Estimation. It's twice the size of the largest terrestrial planets and half the size of the smallest gas giants.[5]

Does this make you feel small and insignificant? (You are small and insignificant) Well...

I was counting by diameter in the previous examples. But since humans are full of mass and the universe is rather diffuse, maybe counting by mass will bring a more satisfactory result. A typical human weighs 62 kilograms[6], but weights of individuals can vary wildly.^{[citation needed]}. A hydrogen atom weighs 1.673534*10^-27 kilograms.[7] The mass of a hydrogen atom tends not to vary so much. The typical obsevable universe has a mass of 10^53 kilograms (the average of all known observable universes).[8] This figure isn't known to differ from individual to individual.

So the mass of the universe is 5.98*10^79 times heavier than the mass of a hydrogen atom. Thus, an object with a mass in between that of a hydrogen atom and that of the universe would be very roughly 10^40 times heavier than a hydrogen atom, or 1.673534*10^13 kilograms. This result is the best of all. It's far, far smaller than any planet (though obviously nowhere near as small as a person). This Wikipedia article tells me that such a mass would be about as heavy as a fairly large mountain.

I guess that still makes you feel small and insignificant. Oh well.

Atom Smasher

Can you build an atom smasher out of household materials? -Cosmic Cat

Short answer: No.

Long answer:

In a way, you already probably have one in your house. The cathode ray tubes found in televisions and computers use electromagnets to smash electrons into phosphors.[1] But this is another
case where the easiest solution is boring. And we wanted to build an atom smasher out of household materials, not find one in the house.

There are two types of atom smashers (linear and circular; the names are pretty self-explanatory), and both contain a laundry list of parts. They are: electromagnets, which keep the flying particles on the right path; targets, which the flying particles collide with; detectors (self-explanatory); vacuum systems, which keep the atom smasher clean of air; cooling systems (self-explanatory); computers to analyze data, a monitoring system for safety (safety, schmafety), electrical power for the atom smasher; copper tubes for the particles to fly down; klystrons, which are powerful microwave generators; and storage rings to store particles when they're not being used. Oh and, protective shielding so that you won't be killed by deadly radiation. If you forget that, you could have a minor problem on your hands.[2]

The first part of this would be to see if we can buy or build the parts at a reasonable price. Let's start with the particle generator part. The SLAC particle accelerator fires an electron beam at tungsten. I was surprised to learn that you can actually generate an electron beam with a cathode ray tube.[3]
You may not have tungsten in the house, but you can buy it in the form of tungsten shot or welding electrodes (look for ones with green tips), according to Theorore Gray's book The Elements. This will generate positron-electron pairs. Copper tube can be found at hardware stores and it isn't illegal to possess.^{[citation needed]} The problem is that you'll need several miles of it, but with enough money you could probably get that. Next up is a klystron, a microwave generator a million times as powerful
as a microwave oven.[4] I thought this would be impossible to get, but it turns out you can buy them on ebay for a few hundred to a few thousand dollars.[5] You can get a lot of stuff on ebay. Next step: magnets. They are fairly common^{[citation needed]}, so it's probably possible to buy sufficiently powerful ones. Targets can vary, but the simplest ones are probably thin sheets of metal foil. Go look in the kitchen and you'll probably find some. Still stuck? Or, if you insist, you can try gold foil. Detectors are where we get stuck. One typical detector is described as a "barrel-shaped, solid-state detector that stands more than six stories tall and weighs more than 4,000 tons". I don't typically gamble, but I'd gladly bet any amount of money that one of these won't be found in the typical home. Or hardware store. Or ebay.

Sorry.

Faster Than Light

Why can't anything move past the speed of light? --ConorT99

Let's start at slow speeds and work our way up.

One 100-millionth of the speed of light is about 6.7 miles per hour. This is between typical walking speed and typical running speed. Nothing weird happens here. One 10-millionth of the speed of light is 67 miles per hour, roughly the speed of a car on the typical interstate highway. One one-millionth of the speed of light is 670 miles per hour, slightly faster than an average passenger airplane. These speeds are quite common, but if you're in a car, you'll probably fly into the air at that speed.[1] One 100-thousandth of the speed of light is 6706 miles per hour. This is faster than most things made by man, including cars.^{[citation needed]} This is just shy of Mach 9, the speed of NASA's X-43. Even at Mach 3, aerodynamic heating causes temperatures of 500 Fahrenheit[2] , so Mach 9 would likely cause very high temperatures. If you're on earth at least. If you're not on earth...

One 10-thousandth of the speed of light is 67,061 miles per hour. This is close to the speed of the spacecraft Juno as it slingshotted around Earth.[3] Juno is one of the fastest manmade objects[4], so it's clear that we won't be getting anywhere near the speed of light using anything manmade. But who said anything about manmade objects?

I'll skip ahead to relatavistic speeds. Going at 90 percent of the speed of light, strange things start to happen.(Don't ask me why. Ask Albert Einstein instead.) Time dialation would be noticable. Spend 10 minutes at that speed and 20 minutes would have passed for the rest of the world. The Dopper effect would also distort the colors of objects towards the blue end of the spectrum.[5] The mass of an object approaching the speed of light would also increase significantly. A 1-gram object moving at 0.9c would have a mass of 5.26 grams.[6] This would be a problem for any object with substantial mass, since it would take an even larger amount of energy to get an object close to the speed of light than it otherwise would. Luckily, the universe is made full of very small and light things.^{[dubious-discuss]}

A hydrogen atom is pretty light, so it seems like a good particle to start off with. To be specific, a hydrogen atom's mass is one amu. An amu is 1.66*10^-27 kilograms and a hydrogen atom at 0.9999c would  have a mass of 5000 amu or 8.3*10^-24 kilograms. How much power would this take? The formula for watts is kg*m^2/s^3. An object sustaining this speed for one second would trvel 299,762.4788 kilometers. So, plugging in results in a power consumption of 2.48 femptowatts. We can do better. I'll throw in a few more nines. The people reading hypothetical science blogs really like lots of nines, don't they? A hydrogen atom moving at 0.999999999c would have a mass of 500,000,000 amu or 8.3*10^-19 kilograms. The power used would be a quarter of a nanowatt.
Let's try 0.9999999999999999999999999999999999999999999999999999999999999999999999c (I pressed 9 a lot of times just for the hell of it). This is so huge that my TI-84 Plus calculator gets a divide-by-zero error when I try to figure out the mass increase. So that means that there's an effectively infinite mass, which would take infinite energy to move at all. And we're still not even at the speed of light.

Lighter particles (such as neutrinos, the lightest known particles[7]) can get you closer, but they won't get you to the speed of light. To offset the fact that the mass of an object is infinite at the speed of light, a particle would have to have a mass of zero. Photons have no mass, but they still won't get past the speed of light, only to it.

To get past the speed of light, some laws of physics would need to be broken. (DISCLAIMER: If you break the laws of physics in your jurisdiction, I am not responsible)

With that out of the way, let's consider the idea of negative mass. In that case, a 1-gram object traveling at 1.01c would have a mass of -49.75 grams. The problem: negative mass does not exist.[8] But if it is ever created, then it could be used to build an Alcubierre Drive, which can travel faster than light.Come to think of it, if you're willing to break the laws of physics, building a working Alcubierre Drive would be a decent science fair project. Might even win first place.

But if you aren't prepared to take the risk of breaking the laws of physics, is there still a way to do this? Turns out there is! As you may know, light goes at different speeds through different materials. And if you cool sodium atoms down to near absolute zero, they become a Bose-Einstein condensate, and light would travel at a speed of 38 miles per hour.[9] So if you can get something to move as fast as a car through a vat of Bose-Einstein condensate...it'd be going faster than light.

Living On Food Pills

Is it possible to live off of vitamin, mineral, carbohydrate, and protein pills? --Cosmic Cat


I could just Google food pills and see what comes up, but who wants to do that? That would be boring.


Let's deal with vitamins and minerals first. There are already pills that provide these. A random example includes Vitamin A, some B Vitamins, Vitamin C, Vitamin D, Vitamin E, Omega 3s, iron, calcium, zinc, magnesium, and iodine. Some more Google searching shows that various other dietary minerals can be purchased as supplements. Apparently even arsenic supplements exist. You probably don't want to overdose on those. As one might imagine from the existence  of multivitamins, such a pill would be small enough to consume. Summing up the weights of all the suggested daily values for the various vitamins and minerals (using the tables here and here) comes out to about 11 grams, so it's safe to say that you could make a pill-sized pill that could satisfy your vitamin and mineral needs.


Macronutrients such as carbohydrates and protein are difficult though. The USDA suggests consuming 130 grams of carbohydrates per day, about 30 grams of fiber, again about 30 grams of fat, and an average of perhaps 45 to 50 grams of protein. When we add all these together, we can see that a macronutrient "pill" would not exactly be a pill. More like a blob of stuff weighing about half a pound.

But let's just go with the half-pound blob. There's a simple problem with this: the average American consumes 1996 pounds per year (according to an NPR blog), which comes out to just under 5.5 pounds per day--more than 10 times the weight of our glob of nutrients. That will cause some problems with satiety, or the state of feeling full. If one has early satiety (the state of feeling full after eating a small meal), then this could still work. Early satiety is caused by a lot of nasty diseases, so inducing it isn't something you should try at home. If you do decide to contract a deadly disease, then all I can say is wow, you must be really determined to live on food pills. At least it would work better than breatharianism though.

Antimatter Car

What would be the fuel economy of a car powered by antimatter? --Myself

Note: I originally put this post on pastebin. 

Antilithium is probably the best type of antimatter for fueling a car. It's not a gas like antihydrogen or antihelium, but it's easier to make than heavier anti-elements. So first, I took the density of lithium. Theodore Gray's book The Elements tells me that lithium has a density of 0.535 grams per cubic centimeter. Obviously, antilithium will have the same density. A gallon contains 4000 cubic centimeters (~4 liters * 1000 cubic centimeters in a liter). So a gallon of antilithium would have a mass of 2140 grams. Wikipedia's article on antimatter weapons states that one gram of antimatter could be converted to 180 terajoules of energy. Thus, 2140 grams of antimatter could be converted to 385.2 petajoules of energy. Next, I needed to find the energy in a gallon of regular gas. A PDF from the University of Washington tells me that this number is 130,000,000 joules. 385,200,000,000,000,000/130,000,000 is 2,963,076,923, so antilithium fuel is about approximately 2.963 billion times as efficient as gasoline fuel. But how efficient is gasoline? Obviously, the fuel economy of cars varies hugely, but some blog says that the average fuel economy for new cars in 2013 was 24.9 miles per gallon, so we'll go with that. Multiply 24.9 by 2.963 billion and we get 73,780,615,382.7 miles per gallon.


How far could you get with such a car? Well, the average gas tank is about 16 gallons (so says Yahoo Answers, the very epitome of reliability), so a tank of antilithium would get you 1.18 trillion miles. A lightyear is about 6 trillion miles (thanks, Wikipedia) so a one lightyear trip would require five refills and a drive to Alpha Centauri (the nearest star, 4.2 light years away) would require over 20 refills of antilithium.


There aren't many antilithium stations in interstellar space^{[citation needed]}, but let's suppose there were. Would this drive be worth it? The cost of antihydrogen is $62.5 trillion per gram, according to this. There aren't any estimates (Really! None at all! And this is the Web!) for the cost of antihelium, so I have to blatantly guess. Let's just say that antihelium is ten times as expensive, at $625 trillion per gram. A website implies that antilithium is a million times harder to make, so let's assume it's a million times as expensive. That comes out to $625 quintillion per gram. Going back to the last paragraph, it seems that we'd need 684,800 grams of antilithium to make the trip, so the cost of fuel would be $428 septillion. Let's just say that this is more money than Bill Gates currently has.^{[dubious--discuss]} Oh and, someone would still have to build a highway, since car's don't work well in empty space.^{[citation needed]}