# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Moon's angular speed**

**From:**Frank Reed CT

**Date:**2005 Nov 20, 03:22 EST

Here's a little trick that might entertain some of you... Suppose you want to know how rapidly the Moon's position in the sky is changing. The average rate is 13.2 degrees per day or 33.0 minutes of arc per hour. But the range is large, running from 29.5 to 38.5 minutes of arc per hour. It turns out that you can get a very good estimate of the actual angular speed (geocentric!) at any moment by looking at the Moon's HP. Since the Moon slows down when it is further from the Earth in accordance with Kepler's Second Law, it might at first seem that the change in angular speed would be directly proportional to the change in horizontal parallax relatve to its mean value of 57.0 minutes of arc, but in fact it's double that. When the Moon is, for example, 1% farther from the Earth, its linear speed is reduced by 1% and in addition, since it is visually further away, the angular rate is reduced by 1% more. So if I look up the Moon's HP in an almanac and find that it's 60.0', that's 3 minutes of arc or 5.3% above average. I double that percentage to get 10.6% and apply that to the Moon's mean angular rate of 33 minutes per hour to get 36.5 minutes per hour. This calculation is accurate to +/-1% at worst and typically accurate to +/-0.5%. Of course, it's not complicated to do a really accurate calculation if you have a computing device handy (you can calculate the actual great circle distance, or you could use a formula from Meeus), but this little method is something that you can do in your head if you have access to the Moon's actual HP for the time in question. Note: I think I've got this all right, but as always, check it out for yourself. -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars