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Ephemeris: 09/29/2025 – First attempts to measure the distance to the Sun

September 29, 2025

This is Ephemeris for Monday, September 29th. Today the Sun will be up for 11 hours and 47 minutes, setting at 7:26, and it will rise tomorrow at 7:39. The Moon, at first quarter today, will set at 11:38 this evening.

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 in this blog are for the Traverse City/Interlochen area of Michigan (Lat 44.7° N, Long 85.7° W; EDT, UT – 4 hours) unless stated otherwise. Times will be different for other locations.

Addendum

A diagram of the measurement Aristarchus tried to make of the distance to the Sun.
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° (89°51′) for that interior angle instead of 87°. Credit: Ancient Greek Astronomy by Denis Erkal.
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