A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Jan 7, 09:09 -0800
Suppose the Moon's HP is 56.8'. That's nearly what it is as I write this, and it happens to be fairly close to the long-term average. This value is equivalent to the SD of the Earth as seen from the Moon. An astronaut standing on the Moon sees the Earth around two degrees across. Today it would be just about 114' across (1.90°). When you keep this in mind, everything else falls into place. The Moon's HP is the Earth's SD as seen from the Moon.
As the Moon moves in and out on its generally elliptical orbit around the Earth, the size of the Earth in the astronaut's sky increases and decreases during a single lunar month. Now suppose our astronaut gets on his phone (great cell service on the Moon) and calls a friend in Boston with a sextant. That friend measures the diameter of the Moon and finds that it's about half a degree across. Why is that not surprising? Well, the Moon is physically about one-quarter the size of the Earth. The Moon is roughly 2,000 miles across while the Earth is roughly 8,000 miles across. So it makes sense.
Our astronaut calls that friend in Boston whenever New England is visible on the Earth's face and checks the Moon's diameter every day. At the same time, the astronaut measures the apparent diameter of the Earth These observers know about "augmentation" so they check the SDs when the Moon is at the same altitude each day seen from Boston and the Earth is at the same altitude seen from our lunar base (not much of a issue on the Moon!). And sure enough, the apparent diameter of the Moon seen from Boston moves (almost, except for augmentation) in lock-step with the apparent diameter of the Earth. The ratio of the SDs is 0.2724 (give or take on that last digit), which they know from Wikipedia (great Internet service up there, too) is identical to the ratio of the Moon's diameter in miles to the Earth's diameter in miles. When the Moon moves away from the Earth, the Moon becomes smaller as seen from the Earth... and the Earth becomes smaller as seen from the Moon.