# NavList:

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

**Re: Luni-Solar Distance**

**From:**Paul Hirose

**Date:**2010 Oct 30, 15:21 -0700

I wrote: > George's lunar distance is observed from 0°N 0°E at midnight, and also > from 0°N 5°E at 00:15:17 UTC. There are an infinite number of such time > / longitude pairs. Without some additional constraint, there's no way to > know which one is correct. But as George has already noted, a time sight resolves the ambiguity. In this case, a time sight would have measured GHA Aries = 183.538°. (I'll use decimal degrees to make the computation easier.) Let's say the chronometer is 5 minutes slow and the longitude 1° off, so the lunar distance (36.815º, Regulus to near limb) was observed at assumed 2005-03-25 23:55:00 UTC from assumed 0°N 1°E. At the assumed time and place, calculated lunar distance = 36.773°. This value changes +.0052° per minute of time and -.016 per degree of longitude east. At the assumed time and place, calculated GHA Aries = 183.286°. This value changes +.25° per minute of time and +1.00 per degree of longitude east. To make the calculated lunar distance and GHA Aries equal to the observations, the increments are +.042° and +.252°, respectively. The unknown increments in time (∆t) and longitude (∆λ) to attain this goal may be expressed in a pair of linear equations, with coefficients from the paragraphs above. .042 = .0052∆t - .016∆λ .252 = .25∆t + ∆λ The solution is ∆t = 5.00 minutes and ∆λ = -.999 degrees, which we know to be the truth. GHA Aries is linear with respect to time and longitude, so the second equation is practically perfect. Strictly speaking, the .25 coefficient ought to be multiplied by 1.002738 since the rate is sidereal, not solar. But I believe it's not worth the bother because lunar distance is not really a linear function of time and longitude. In this case it was close enough. With larger initial errors this may not be true, and the process would have to be repeated. -- I filter out messages with attachments or HTML.