# NavList:

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

**Re: Old style lunar (in expert hands)**

**From:**Alexandre Eremenko

**Date:**2004 Dec 10, 20:22 -0500

On Sat, 25 Dec 2004, Kieran Kelly wrote: > Eg I own a Wild T1a theodolite. > The Zeiss Yachtsman sextant > and case which I use on expeditions weighs 2.8kgs. > > sextants have survived being bucked right off the back > of a pack horse and > on a recent expedition one travelled 750km on the back of a camel May I ask you what sort of expeditions are you participating in? 750 km with horses, camels and sextant? I did not know that such things still happen in XXI century? Just for fun? Or this sort of surveying still exists? > Also the role of theodolites and sextants > should not be confused. A > theodolite is an instrument of surveying, > a sextant an instrument of > exploration and navigation. Well, I afraid this is based on tradition only:-) It is like Norie's advise for taking lunars: "have a good sextant to measure distances andf a good quadrant to take altitudes":-) You can certainly to all tasks with any of these instruments. > And don't underestimate the accuracy of a > sextant in the hands of an expert. I don't. The best marine sextants allow you READING the scale to 0.1'. I think this is more or less ultimate level of accuracy, even if you average long series. I don't know mych about theodolites, but some allow you to read to a single second, don't they? > "And you can certainly measure lunar or any other > distances with it." Let me make a disclaimer first: I have never held a theodolite in my hands. Only saw them in pictures. I assume your theodolite permits taking altitudes and measuring horizontal angles. Here is how you can measure a lunar distance. Set it firmly on a tripod on any other appropriate platform. Using the levels, insure that the asymuth ring is horizontal. Orientation with respect to the meridian is not essential. Now measure the altutudes of both bodies, and the difference in their azymuths in a quick sequence. Solving the resulting spherical triangle gives you the distance. Remarks. 1. If you don't want to use a calculator, ordinary sight reduction tables can be used to solve the triangle. If someone is really interested I can write the formulas or an algorithm to do it with HO 229 sight reduction tables. 2. That the measurements are not done simultaneously is going to cause a problem, but this difficulty can be overcome (see the Nonlinearity discussion in October for math justification of the procedure). I recommend the following sequence: (point at the first body) read alt1 azymuth1 (turn the scope, point at the second body) read azymuth2 alt2 (turn the scope, point on the first body) and so on. Then take the average of 5-10 azymuths and altitudes, and solve ONE triangle with these average data. To take the averages accurately, you have to TIME the moments when the bodies are on the crossing of your wires, and all measurements have to be reduced to the SAME time. If you can do, say one cycle per minute (both azymuths and both altitudes, once each, in a minute) then averaging 5 observations spread over 5 minutes will surely give you better accuracy than measuring with a sextant. It is very helpful to have an assistant who will read the scales while you point the device. The reduction of such sight is somewhat different from the sextant sight reduction. Different in the way the semidiameters are taken into account. But I can work all details if desirable. Very briefly, the justification is the following: on a 5 min interval, all quantities (altitudes, azymuths and the distance) change as linear functions of time, to VERY high degree of accuracy. So by averaging such sequence of sights you can obtain both altitudes and the difference of azymuths at the average time, as if they were measured simultaneously. If you are using some electronic reduction aids, you can even do quadratic interpolation which will kill the remaining small non-linearity error. Alex.