Tuesday, March 17, 2009

Learned today: Planck Mass, Schwarzschild radius, and BMI

A planck mass is approximately 2.17644 X 10^-8 kilograms. This sounds really small. But it's actually not all that small, as small things go. For instance, a flea's body has a mass of approximately 4000 to 5000 Plank Masses.

Also: Schwarzschild radius (that "rzsch" thing in his name is kind of kewl, isn't it?) This is the radius which, if a given mass is compressed to inside that radius, nothing (that we know about yet) could prevent that mass from continuing to collapse into a black hole. That's kind of kewl. Which is to say that any particular mass has a certain Schwarzschild radius. For instance, the sun has a Schwarzschild radius of ~3 kilometers. To get your head around this, check out this image. This is an actual scale comparison of the sizes of the earth and the sun.

Then consider that the earth has a circumference of ~40,000 km. So you'd have to compress the entire sun down to about 1/13,000 the size of the earth. Or to put it another way, down to a size where it would fit between your house and whatever is 3 km from your house.

Or the Schwarzschild radius of the earth is about ~9 millimeters, or something like the size of a pistachio. Which means if you could compress the entire earth down to the size of a pistachio, it would become a black hole.

Also: the biggest black hole observed to date has a mass equal to about 18 billion suns, and a radius of about 353 AU (Astronomical Unit--the approximate average distance between the earth and the sun), or nearly 10 times the radius of our entire solar system. Kewl.

Using a handy little formula I found, I figured out that Benjamin's Schwarzschild radius is approximately 1.48 X 10^-25 meters.

To me, this illustrates the absurdity of the West's obsession with small weight and small body size in humans. Strangely, if I were compressed to this size, not only would I be a black hole, and be incredibly tiny, but I would also have an enormous body mass index of ~6.757 * 10^26. Probably if being a black hole didn't kill me, having a BMI this big surely would. =)

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