# NavList:

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

**Re: Lunars.**

**From:**Steven Wepster

**Date:**2001 Jul 04, 8:27 AM

Earlier I wrote > > >> the altitudes of the bodies need not be taken very accurate. << Herbert replied: > As a matter of fact, the altitudes don't have to be taken at all, as they > can be computed. However, the problem with this is that actual refraction > might differ from the tabulated values and hence measuring the altitude > might result in higher accuracy. Has anybody ever investigated this? The altitudes of the bodies are needed for the Clearing of the Distance, i.e. to get rid of the effect of parallax, refraction, and dip in the measured LD. The spherical trigonometry formula (e.g. Krafft, Borda) that you use to actually compute the true LD depends not so much on the altitudes (it is sufficient to have them to a few minutes accurate) but rather on the _difference_ between true and apparent altitudes. These differences must be known as accurate as possible. One of the contributing factors is the refraction; normally there is no other way to get it than to take it from a refraction table. So, wether you use measured or computed altitudes, an error in the refraction will have the same effect. The same applies to dip. Since it is important to have very accurate differences (0.1' is necessary and sufficient) it is wise to include a correction for non-standard atmosphere, table A4 in Nautical Almanac. As I said, it is not necessary to have the altitudes of the bodies themselves to a very high precision. That's why it is at all possible to make use of computed altitudes. Remember that to compute an altitude you need to know your lat and long fairly precicely. On the practical side however, I presume that an Old Salt would prefer to take the altitudes standing on deck with an octant in his hand, than to compute them using log-trig tables. But there are circumstances that it is not practicable to measure them. > > As to the question of an algorithm itself, this depends on the purpose of > the algorithm. For historical research, often the original methods have to > be emulated and the then available ephemeris be used. For modern use, the > fastest and safest algorithm would be right in the spirit of St. Hilaire: > heuristic and iterative. The distance is a function of time. Starting from > a reasonable "assumed time", compute the corresponding "computed > distance", compare it against the "observed distance", make a correction > and iterate until the difference between computed and observed value is > small enough. That is more or less the procedure that Tobias Mayer proposed to use, when he submitted his Lunar Tables to the Board of Longitude in 1754. Quite a cumbersome method, because his tables were for _calculating_ the position of the moon from epoch + mean motion + 14-plus 'equations' (perturbation terms). Imagine that you have to _iterate_ ... It took Maskelyne up to 4 hours to compute a Lunar when on the way to St. Helena in 1761. I don't see what Marc St Hilaire has to do with it. I associate him with the intercept method; quite something different. But maybe he has made other contributions to astronavigation? _Steven