How Tiny Would Donald Trump's Hands Be If They Were Black Holes?
Ryan F. Mandelbaum
Filed to:stupid math
Image: Ryan F Mandelbaum/Alain R/Wikimedia Commons/The White House
Let me tell you a little something about gravity: It's weird. A hundred or so years ago, Albert Einstein realized Isaac Newton's laws didn't work so well for really extreme situations, ones Newton never would have encountered on 17th century Earth. So Einstein said, alright, let's come up with a new theory that looks like Newton's theory, but also works for really big things and really fast things like planets and light—called general relativity. Einstein's theory says mass causes the shape of space and time to change.
General relativity worked super well, so well that it started predicting things. Those include the fact that the orbit of planet Mercury traces a spirograph instead of a circle, and more recently, gravitational waves. But possibly its strangest prediction was black holes—bodies so compact and heavy that light can't escape their gravity. If you got sucked into a black hole, not only would you torn apart, but time would stop as soon as you crossed its so-called "event horizon."
Black holes are a consequence of the mathematics of general relativity. Right around the same time Einstein put forth his theory in 1915, a physicist named Karl Schwarzschild calculated the way spherical stars should change the shape of space. It works really well outside of most stars, but requires a sort of fundamental multiplication of the fabric of time and space by a number that changes based on the stars' mass and radius. If the radius of the star equals twice its mass times a few conversion factors, namely the gravitational constant G divided by the speed of light c squared, a few divide-by-zeros fall out of Schwarzschild's solution. Dividing by zero gets you an infinity, which is a major no-no in physics. Physicists have since gotten rid of most of those pesky infinities by changing the way they looked at a problem, the way you might do calculus differently with a cube than with a sphere.
Inside that star with the radius equaling twice the mass (times a constant), the math physicists came up with to get rid of the infinities says that the shape of space is so warped that no matter what direction a particle travels, the only direction in its future is the center of the black hole.
So, making our own black holes out of every day objects is easy! All we've got to do is start with whatever mass we want (in kilograms) and then multiply it by two, multiply it again by the gravitational constant G (which is a minuscule number), and then divide it by the speed of light squared (which is a gigantic number). Multiplying something by a tiny number and then dividing it by a gigantic number will get you a much much much smaller thing.
Take The Donald's hands. This website I found says that male hands weigh around .65 percent of the human mass, so we'll use .6 for our Commander-In-Chief. He claims to weigh 236 pounds, and I'll give him the benefit of the doubt on that one. That gets us around .642 kilograms. Times two, times G, divided by c squared, that gets us about 10^-27 meters in radius. That is very small, a trillion times smaller than a proton. Such tiny black hole hands!
Even the whole human body would only make a black hole with a radius around 10^-25 meters, a hundred times bigger. A house, at around 50,000 kilograms, would be a black hole with a radius of 10^-22 meters. These black holes are still much smaller than protons, but importantly, all of them are larger than the Planck length, the smallest meaningful length that the laws of physics allow for.
But let's make some bigger black holes. The whole earth squeezed into a black hole would have a 9 millimeters radius or a 18 millimeter diameter, the size of a big toenail. Black hole Saturn would have a radius just under a meter, so it would be around the same size as a fully-grown human. The whole Sun squished up into a black hole would be less than six kilometers, or four miles, across.
All of this is to say, black holes are nuts. If you want to figure out how big you'd be as a black hole, just type (G*(x kg*2))/(c^2) into Google and replace the x with your mass in kilograms. Have fun!
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Science writer at Gizmodo | I like physics and eating