# NavList:

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

**Re: Lunars: Jupiter's BIG.**

**From:**Herbert Prinz

**Date:**2003 Dec 20, 16:57 -0500

Fred, It would seem that you are applying the least square fit incorrectly. To apply it to the plot of distance versus time is to shoot with guns at sparrows. You can have this cheaper by averaging the time, averaging the distances, and then proceed as if the averaged values where the actual observation - just as you are suggesting. This is what was normally done, and what is feasible to the navigator without electronic tools. To use this technique does not prevent you from plotting the distances versus time to find outlyers. As long as you have the individual distances, that is, because from repeating instruments (such as the Borda circle), one does not get them. However, if you really must apply a least square fit to the given data, (and I could not argue with you if you claim that this is the only rigorous treatment of any set of more than 2 observations), the only correct method is to solve for the watch error for which the sum of the square of the distance residuals becomes a minimum. Besides from being correct, it has the additional benefit that you can combine observations to different objects, in particular observations on either side of the moon, which helps to cancel certain instrument and observation errors. It goes without saying that this has no practical value on the boat. But it could have been used this way in surveying, right before the telegraph was introduced. Herbert Prinz Fred Hebard wrote: > Interestingly, I usually plot the raw distance against the time of > observation and use the least squares fit to pick out a point for > reduction. > I think perhaps the old method of using the mean of the observations > would be better than using a line of best fit, although plotting the > data instantly tells one how good they are. Using the mean, the time > would have been out by 8 seconds, about 2 minutes of longitude.