Question

explain the parallax method determing the size of the moon

Answer 1

Aristarchus (310 - 230 B.C.)

Aristarchus figured out how to measure the distancesto and sizes of the Sun and the Moon. Because he deduced that the Sun was so much bigger than the moon, he concluded that the Earth must therefore revolve around the Sun.

He figured out how to measure the relative distances from the Earth (E) of the Sun (S) and the Moon (M). When the Moon is exactly half full, the angle E-M-S must be exactly 90 degrees. Therefore, a measurement of the angle M-E-S when the Moon is half full will give the ratio of the Earth-Moon distance to the Earth-Sun distance.

Aristarchus measured the angle M-E-S to be 87 degrees, giving the ratio to be 1/19. Actually, the angle is 89 degrees, 51 minutes, giving an actual value of 1/400, that is, the Sun is 400 times further away from the Earth than the Moon is.

Aristarchus' measurement was probably off because first, it is hard to determine the exact centers of the Sun and the Moon and second, it is hard to know exactly when the Moon is half full.

On the other hand, his estimate showed that the Sun is much further away from us than the Moon is.