# NavList:

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

**Re: Latitude by Lunar Distance**

**From:**Frank Reed CT

**Date:**2006 Oct 05, 03:10 -0700

Here's an example of fixing your position using angles measured from the Moon to stars only, no altitudes whatsoever. This approach assumes that GMT is a known quantity so its resemblance to historical lunar distance observations is only superificial. I am somewhere southeast of New England, rough DR = 38N, 70W, early in the morning of October 11, 2006. It's the middle of the night and a bit hazy, too. The sea horizon is invisible. But I can see the Moon and some bright stars... At 06:36:00 GMT I look up high in the South at the Moon with Aldebaran below it. With my sextant, I carefully measure the angular distance (Far limb) between the Moon and Aldebaran and find that it is 11d 39.9'. Then I turn to Pollux and measure the distance from that star to the Moon (Near limb this time). I find that the Pollux-Moon lunar distance is 38d 13.1'. The GMT for this sight is 06:39:00 exactly. I believe that my sextant is perfectly adjusted, and I'm skilled at using it, so I trust these angles to the nearest tenth of a minute of arc. With the two "lunar distance" observations above, I can get a fix on my position, both latitude and longitude, accurate to about five nautical miles. I can generate two lines of position for these sights something like the early calculation of Sumner lines by finding the latitude for two given longitudes that yields the exact value for the observed distance at the exact GMT of those observations. For the Aldebaran sight, at longitude 69W, a latitude of 38d 41'N would yield that observed distance. At longitude 70W, a latitude of 38d 46'N would yield the same observed distance. I can draw a line through those two points, and my position must lie along it. For the Pollux sight, in the same way, at longitude 69W, a latitude of 38d 05' produces the correct observed lunar distance, and at longitude 70W, the latitude would have to be 39d 41'. Now I have a second line of position. I can cross them on a chart. My position must be very close to latitude 38d 46', longitude 69d 25'W. This postion is accurate to about five nautical miles if my observations are accurate to the nearest tenth of a minute of arc (and the GMT has no error). I have determined latitude and longitude by measuring angles between the Moon and bright stars. How can this be?? Position-fixing without a horizon?! In fact, there is a horizon involved -- the limb of the Moon. These altitudes are measured from the lunar horizon instead of the ordinary sea horizon. Each "altitude" above the lunar horizon, really a "lunar distance", generates a "cone of position" with its apex at the Moon's center instead of the Earth's center. When those "cones of position" intersect the Earth, they locally create crossing lines of position. And where they cross is where we are... Cool, huh? -FER PS: I should emphasize that this viewpoint on "lunar distances" is radically different from the historical "lunar distance observations" which treated GMT as an unknown. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---