Ephemeris: 04/15/2024 – How the Ancient Greeks tried to measure the distance to the Sun

This is Bob Moler with Ephemeris for Monday, April 15th. Today the Sun will be up for 13 hours and 31 minutes, setting at 8:28, and it will rise tomorrow at 6:55. The Moon, at first quarter today, will set at 4:15 tomorrow morning.

The first quarter Moon tonight reminds me of how the Greeks used the quarter Moon to attempt to determine the distance to the Sun. The idea was to determine when the Moon was exactly at first or last quarter, so the angle of the Sun-Moon-Earth was exactly 90°. The next thing to do was to measure the actual angle between the Sun and the Moon at that instant. It’s a difficult observation. Aristarchus tried and got a result that the Sun was about 19 times the distance of the Moon. The Sun-Earth-Moon angle he got was 87°. Hipparchus measured the Moon to be 60 earth radii away which is near the Moon’s actual distance from the Earth. In actuality the Sun is about 400 times the distance to the Moon.

The astronomical event times given are for the Traverse City/Interlochen area of Michigan (EDT, UT–4 hours). They may be different for your location.

Addendum

A diagram of the measurement Aristarchus tried to make of the distance to the Sun. He got a distance to the Sun of 19.1 times the distance to the Moon, which correlates to an angle between the Moon and the Sun of 87°. The actual distance to the Sun is on the order, rounded up, of 400 times the Moon’s distance from the Earth. So this angle would be impossible to measure 89.85° for that interior angle instead of 87°. Credit: Ancient Greek Astronomy by Denis Erkal