NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunar distance accuracy with StarPilot
From: Wendel Brunner
Date: 2026 Mar 7, 18:08 -0800
From: Wendel Brunner
Date: 2026 Mar 7, 18:08 -0800
Regarding the original post on December 3, 2025: I am quite familiar with the methods the Starpath StarPilot calculator uses to compute lunars, based on some detailed descriptions on the Starpath web site, the posted instructions for the star pilot lunar distance function, and some correspondence with David Burch over the years. They do indeed use an iterative method, similar to one I employed to work up lunar distance observations I made as navigator on a small sailboat going to Hawaii. During that voyage we had clouds and fog, but with a brief break in the overcast I was able to get a good series of lunar distances and sun altitudes for averaging. However, I was unable to get any lunar altitude, as fog obscured the horizon beneath the moon.
When I returned home with my log notes, I realized that a lunar distance and the altitude of any body, all timed with the watch we were trying to set to GMT, would be enough to determine GMT and longitude. You have to get your latitude from some sight at meridian passage.
The process is as follows: With the known latitude, assume a GMT for the watch, and calculate the corresponding assumed longitude from the assumed GMT and the observation of the other body - in my case, the sun. Then from the assumed time and corresponding position, calculate the Observed Lunar Distance (OLD) as you would measure it in the sky, including the effects of refraction, augmentation and parallax. This is the inverse of Clearing the Lunar Distance, and in another note I explain more how that is done. Then compare the calculated OLD with the distance measured by the sextant. Adjust the assumed GMT by 120 seconds for each arc minute OLD difference - roughly the average rate of change of the geocentric lunar distance - and adjust the corresponding assumed longitude by 1’ for each 4 seconds time correction. Then repeat the process. After two iterations the calculation converges to within 0.1’ OLD and 12 seconds time, even if the starting point is hundreds of miles off.
I know Frank Reed doesn’t think much of this procedure - understandably, as it is very calculation intense. I haven’t (yet) taken Frank’s Lunar course, but I know there are a variety of simplifying calculation approximations to clear the OLD to the geocentric LD to a quite sufficient accuracy. But despite its drawbacks, this iteration approach has two advantages: 1) It requires just an observation of the OLD and the altitude of any body taken at any convenient time. 2) The process is very suitable for programming into a calculator.
The StarPilot calculator uses this process, but instead of changing the GMT by 120 seconds for each arc minute change of the OLD, they calculate the rate of change of the OLD at the assumed position, and use that rate to change assumed time between iterations. I won’t go here into why that is wrong. Suffice it to say it doesn’t work. The StarPilot converges very poorly on Lunars. Their StarPilot instructions suggest setting the calculator to perform 10 or even more iterations, and even then it often doesn’t converge. I have modeled the StarPilot algorithm and parameters on my own navigation calculator I programmed, and the StarPilot algorithm converges poorly and often gives wrong answers.
StarPilot is an excellent navigation calculator with many useful navigation functions. It is probably the best navigation calculator available on the market. The program gives very accurate positions for the sun, moon and planets, and the TI calculator has plenty of memory to hold the several hundred periodic terms necessary for that precision. But the lunar distance function is flawed.
The process is as follows: With the known latitude, assume a GMT for the watch, and calculate the corresponding assumed longitude from the assumed GMT and the observation of the other body - in my case, the sun. Then from the assumed time and corresponding position, calculate the Observed Lunar Distance (OLD) as you would measure it in the sky, including the effects of refraction, augmentation and parallax. This is the inverse of Clearing the Lunar Distance, and in another note I explain more how that is done. Then compare the calculated OLD with the distance measured by the sextant. Adjust the assumed GMT by 120 seconds for each arc minute OLD difference - roughly the average rate of change of the geocentric lunar distance - and adjust the corresponding assumed longitude by 1’ for each 4 seconds time correction. Then repeat the process. After two iterations the calculation converges to within 0.1’ OLD and 12 seconds time, even if the starting point is hundreds of miles off.
I know Frank Reed doesn’t think much of this procedure - understandably, as it is very calculation intense. I haven’t (yet) taken Frank’s Lunar course, but I know there are a variety of simplifying calculation approximations to clear the OLD to the geocentric LD to a quite sufficient accuracy. But despite its drawbacks, this iteration approach has two advantages: 1) It requires just an observation of the OLD and the altitude of any body taken at any convenient time. 2) The process is very suitable for programming into a calculator.
The StarPilot calculator uses this process, but instead of changing the GMT by 120 seconds for each arc minute change of the OLD, they calculate the rate of change of the OLD at the assumed position, and use that rate to change assumed time between iterations. I won’t go here into why that is wrong. Suffice it to say it doesn’t work. The StarPilot converges very poorly on Lunars. Their StarPilot instructions suggest setting the calculator to perform 10 or even more iterations, and even then it often doesn’t converge. I have modeled the StarPilot algorithm and parameters on my own navigation calculator I programmed, and the StarPilot algorithm converges poorly and often gives wrong answers.
StarPilot is an excellent navigation calculator with many useful navigation functions. It is probably the best navigation calculator available on the market. The program gives very accurate positions for the sun, moon and planets, and the TI calculator has plenty of memory to hold the several hundred periodic terms necessary for that precision. But the lunar distance function is flawed.
