Fuck it, it's time for: math for fun! In this edition, I'm going to work out the diameter of the sun and moon (maybe) from just some knowledge I happen to have.
Things I know: the sun and moon occupy roughly the same angular size from the surface of the earth (that's why eclipses work the way they do) at about half a degree, the sun is 8 light minutes away, light travels at ~300 million meters per second, and I *think* the moon is about 1 light second away.
Based on those facts, I ought to be able to get pretty damn close for the sun, and if I'm right about the moon, I should be relatively close (at least within an order of magnitude).
First, let's figure out the distance of the sun and moon. The sun is 8 light minutes away, so we take 8 * 60 seconds * 300Mm/s and we get a distance of 144 billion meters away. For the moon, it's just 1 light second, so that's 300 million meters.
Now that we have our distances and their apparent angular diameter, we can set up a right triangle. I like to imagine the base (or adjacent side, technically) is a line from our eye to the center of the object, the opposite side draws a line to the right side of the object, and then the angle of the adjacent and hypotenuse is one half of the angular diameter (since we're only looking at one half of the object).
With that, we can figure out the diameter of the object by taking distance * tan(0.25 degrees) * 2! Thank fuck for trigonometry.
So, how big is the sun? If we plug in 144 billion meters distance we get a diameter of 1,256,645 km. Doing the same for the moon, we get a diameter of 2,618 km.
Those seem to me like they should be ... Roughly on the right order of magnitude at least, even if I have no idea how close they are! So that's cool. Let's see just how close I got.
According to Wikipedia, the sun's diameter is 1,391,400 km -- about 10% off from our estimate. Not half bad! But I'm much less confident about the moon; 1 light second just seems too neat a number to be right.
Wikipedia says the moon's diameter is 3,474 km, which means I was right to be wary of that estimate. That's considerably worse than the sun -- we cut a third off the moon's diameter!
But hey, still within the right order of magnitude. I wouldn't use it for mission planning, but not terrible.















