Geometric derivations of distance

[adjkgh]

aristarchus was the greek astronomer who was the first to find out the distance between the Earth and the sun. he observed that when the moon was exactly half full; the Earth (E), moon (M), and sun (S) formed a right triangle with the right angle at the moon.
then how did he found out that the angle MES makes an angle of 87 degrees? (also what was the distance from moon to Earth did he use?) give me derivations.
M-------------S
|_|
|
|
|
|
E


edmond halley used venus and parallax to find the distance between Earth and sun but i don't exactly understand how he did it. could someone please give me some derivations?

thanks.

 

[HallsofIvy]

I wasn't there at the time but I presume Aristarchus measured the angle with something like an Astrolabe.

By the way, since this doesn't seem to me to have anything to do with "Tensor Analysis & Differential Geometry" I am moving it to "General Mathematics"

 

[adjkgh]

oh sorry. i wasnt exactly sure where it should be =/