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    Re: Luni-Solar Distance
    From: Frank Reed
    Date: 2010 Oct 27, 22:36 -0700

    George Huxtable, you wrote:
    "On reflection, I think that Lars has got the matter right. As long as an observation to determine local time has been made, at or near to the time of the lunar, that can provide sufficiently good data on which to base the necessary altitude calculations. In which case, the laborious iteration procedure that I had thought necessary could be circumvented. Thanks to Lars for putting me right."

    It doesn't even need to be particularly close to the time of the lunar. If I get a time sight in the afternoon, I can set my watch to the correct local time and it will still be good many hours later. If the horizon is too murky in the middle of the night, that's one time (at sea) when one might have to resort to calculated altitudes, though I've never come across any calculated altitudes for lunars in any logbooks. This was a method of last resort. Of course, the local time would have to be corrected by the change in longitude from the dead reckoning, but this was a common task in 19th century navigation --nothing that would cause any serious confusion-- and naturally the latitude would have to be corrected in the same way.

    You wrote:
    "Here is the example I asked about, once again-
    "A navigator is somewhere on the Equator, at lat = 0º, and knows it from his previous observations. We know (though he doesn't) that at midnight, 00:00 hrs at the start of 26 March 2005, he is exactly on the Greenwich meridian, at long = 0º, at which moment he takes a precise lunar distance between the Moon's near limb (it's full Moon, so either limb will do) and Regulus, of 36º 48.9'. However, not knowing his exact longitude, he guesses it to be 01º 00'
    East."
    And asked:
    "Can anyone explain to me the most efficient way to go about it, using that lunar calculator?"

    I don't think this example actually illustrates the case you were interested in, but I'll wait for your reply before getting into that. Meanwhile, what you have here is the set up for one of those "lunar lines of position" that I've talked about. You've got a lunar distances observed at a known Greenwich Time. So, just for general interest, I'll describe one way of clearing that to get position information. First, let's set the DR at lat=0, lon=0. Now draw a box around those coordinates with corners at (1N,1E), (1N,1W), (1S,1E), (1S,1W). Clear it at those locations and note the error in the cleared distance at each location. Now by straight linear interpolation, find the coordinates where the error would be exactly zero. You get two points on the north and south side of the box. Draw a line through those points. You'll find that this line runs on an azimuth of around 30/210 true which is perpendicular to the azimuth of Regulus in the sky at that time and passes through a point on the equator just a couple of nautical miles west of the prime meridian. Your observer must be somewhere along that line of position. Actually, of course this is a slice by a "cone of position" where it crosses the Earth. The apex of the cone is at the Moon's center. At this large angle, the side of the cone is nearly a flat plane so over the range of our box around the DR, the LOP is very straight. It's "space navigation" on the surface of the Earth. Shoot another lunar at known GMT and we get a position fix --no altitudes required (or, to put it differently, our altitudes are measured from the horizon of the Moon instead of the Earth's horizon). To emphasize for anyone who hasn't seen this before, this is NOT how lunars were used traditionally. This approach extracts a position fix from lunar distances observed at KNOWN values of GMT.

    -FER

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