Watching a solar eclipse, a girl asks her father how much farther away is the sun than the moon.
He says, “As far as I remember, 387 times farther.”
She says, “Then I can figure out how much greater is the sun’s volume than the moon’s.”
He thinks about this and says, “I think maybe you can.”
How about you?
Source: A. Kozlov, the Russian popular science magazine Kvant.
Of course the real situation is more complex than this and certain assumptions must be made. Given that, the 387 figure actually has too many significant figures, but we'll use it anyway.
The assumption is that at a total solar eclipse (total not mentioned in the puzzle) the entire disk of the sun is covered by the disk of the moon. For sake of this puzzle we'll assume the coverage is exact, with no excess coverage by the moon. In actual fact, due to the varying distances to the moon and sun, there are more annular eclipses (ring of sun visible all around the moon that's too far to cover all the sun) than total ones, and total eclipses can more than just barely cover the sun. But the two orbs are approximately the same apparent size in the sky.
In order to make the diameters look the same at 387 times the distance (or is it 388 times as distant in order to be 387 times farther; it doesn't really matter as the approximations account for more fuzziness than that), the volume of the sun must be 387^3 that of the moon. 387^3 is 57,960,603, but that is really going overboard on the significant figures. 388^3 is 58,411,072 in case that is what is meant, but again showing too many significant figures.
Most reasonable estimate: 58 million times the volume.
Posted by Charlie
on 2017-01-24 11:15:52