Monday, October 30

Google Calculator is amazing.

Want to calculate the surface temperature of the sun?

Paste this string into google:

((4 pi (1.5 * 10^13 cm)^2 * 0.136 J / (s cm^2 ) / (2 pi^5 * k^4 * 15^-1 * c^-2 * h^-3) ) / (4 pi (7 * 10^10 cm)^2))^0.25

Here's a breakdown of the factors:
10^13 cm is about the distance from the earth to the sun. So, 4 pi r^2 is the surface area of the sphere with that radius.

0.136 J / (s cm^2 ) is the radiant flux of solar energy that we recieve here on Earth. So, multiplying that flux by the area of the earth-orbit-sphere will give you the total radiant power that the sun emits.

Then, we can apply the handy-dandy Stefan-Boltzmann law. The Stefan-Boltzmann "constant" isn't built into google, but Planck's Constant, the speed of light, and Boltzmann's constant are. So, we can put those right into the expression above with the right prefactors and powers.

The radius of the sun is about 7 * 10^10 cm. To scale all the radiant power back to that size, we divide by that surface area, and we're left with something proportional to the fourth power of the black body temperature. Raise the whole thing to the power of 0.25, and you're left with the surface temperature of the sun, approximately.

So cool.

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