FYKOS Year 27 Series 3 Problem 1 — eclipse · FYKOS 27 #27.3.1
Physics · mechanics
Problem
A planet is orbiting around a star on a circular orbit and a moon is orbiting around the planet on a circular orbit in the plane of the planet's orbit. We know that, during the eclipse of the sun the angular size of the moon is the same as the angular size of the sun if observed from the surface of the planet (the moon perfectly covers the sun). Furthermore we know that the planet perfectly covers the moon during the moon's eclipse. Determine the ratio of the radius of the planet R and the moon r, if the distance of the planet from the star is very large compared to the distance of the moon from the planet L and this is in turn larger by several orders of magnitude than the dimensions R, r.