# NavList:

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

**Re: Exercise #14 Multi-Moon LOP's**

**From:**Frank Reed

**Date:**2009 May 2, 23:14 -0700

George H wrote previously: "Now, I don't know how that program operates, internally, and I doubt whether Jeremy or Frank know either. It seems worthwhile, then, to ask some probing questions about the value of such an exercise, before building on to such an insecure foundation, as Frank has done." Insecure foundation? You're way off, George. As for the supposed "black box", most of these software packages do exactly the same thing: they use the least squares solution for multiple sights provided in many sources, including every copy of the Nautical Almanac for some twenty-odd years. The calculational details are not the point of all this. The POINT is that you can get a good fix with a series of sights over a fairly brief period of time. This is not widely known among celestial navigation enthusiasts/practitioners. In a (typical) rapid-fire fix, the error ellipse will be aligned with its long axis perpendicular to the mean azimuth of the sights (quite comparable to lat/lon at noon, by the way). The error in this direction is given approximately by (3/2)*S/(sqrt(N)*A) where S is the standard deviation of the observations themselves, N is the number of sights, and A is the range of azimuth in the sights (azimuth expressed as a pure number, "in radians"). So take Jeremy's moon sights in his "Exercise #14". First, we need the standard deviation of observations. Jeremy has posted quite a few cases, and he gets pretty good sights, with s.d. around 0.5 minutes of arc. In this particular set, N is 11, A is 0.1 (5.5 degrees is a tenth of a radian). So the standard deviation "cross-range" would be 2.3 nautical miles. Pretty good. In the direction towards the object, the error ellipse "down-range" has a width of about S/sqrt(N). We're not generally worried about the error in this direction, but it's worth mentioning that you would bump up againt systematic error fairly quickly. So if the equation says your error is 0.05 nautical miles in that direction, don't take it seriously. -FER PS: The factor (3/2) above may be wrong. I got that twice, but a third time I found (4/5). Whatever that constant is, it is "of order unity" --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---