# NavList:

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

**Re: Moon's angular speed**

**From:**Ken Gebhart

**Date:**2005 Nov 20, 14:35 -0600

On 11/20/05 2:22 AM, "Frank Reed"wrote: > 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 > Frank, Don't you mean 13.2? per HOUR instead of per day? Ken Gebhart