# NavList:

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

**Frank's formulas, was: Lunars: altitude accuracy**

**From:**Alexandre Eremenko

**Date:**2004 Nov 2, 12:43 -0500

I verified Frank's formulas. They are indeed correct, and I have a rigorous proof of this. (Assuming no refraction). Another way to write them is this: ErDist(MA)=P.cot(dist).cos(MoonAlt).ErMoonAlt, where ErDist(MA) is the error in the cleared distance due to the moon altitude error, and P the numerical value of maximal parallax that is P=0.016; the ratio of the Earth radius to the distance to the Moon. Its reciprocal value is the factor 6' in Frank's formulas. ErDist(SA)=P.csc(dist).cos(StarAlt).ErStarAlt, where ErDist(SA) is the error in the cleared distance due to the star (or Sun) altitude error, and P is the same as before. (csc is cosecant, reciprocal to sine). So indeed everything deteriorates when the distance becomes small; but when the distance is near 90 deg, Moon's alt becomes irrelevant. Furthermore, when the altitude of the Moon or of the star is close to 90 d, this altitude becomes irrelevant:-) Nice formulas, indeed! Alex. On Sun, 31 Oct 2004, Frank Reed wrote: > I general, good (slightly approximate) expressions for the required accuracy > of the altitudes are: > AccuracyBody = 6' * sin(Distance) / cos(BodyAltitude) > AccuracyMoon = 6' * tan(Distance) / cos(MoonAltitude). > I have never seen these expressions in print anywhere.