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    Re: Latitude by Lunar Distance
    From: Frank Reed CT
    Date: 2006 Nov 12, 19:21 EST
    Henry H, you wrote:
    "I cannot help but be somewhat amused by the responses to Frank's interesting postings regarding Latitude determination by Lunar distance - whether the concept is old or new notwithstanding. There have been over the years many interesting manipulations of the astronomical or spherical triangle proposed..."
    Well, sometimes it's amusing... :-)
    Of course, it really is all just one "manipulation of the spherical triangle", as you say. At a fundamental level, it's all the same problem. And what's amazing is that even one of the highest tech applications of navigation is very close to this process of "latitude by lunar distance" that I've been talking about. Highest tech, you say?? Sure. How about navigating the asteroid belt...
    Imagine yourself out among the asteroids between Mars and Jupiter. Lots of mini planets, many large enough to see with a good sextant telescope passing within a few hundred thousand miles of your spacecraft. You've brought your sextant and a rather detailed "Deep Space Nautical Almanac", so you're all set. Of course, you have to pop the hatch and go EVA to make this work with a traditional sextant since you can't shoot through windows and expect any kind of reasonable accuracy, but that's ok. As you're floating around outside your capsule, with no horizon and no definition of "vertical" at all, you measure the angles between a couple of nearby asteroids and bright, distant stars. The stars, in fact, could be the 57 traditional navigational stars. There are no corrections required for these angles except those due to instrument error. Each angle places you on a cone of position with its apex at the asteroid's known position at that instant of GMT, very much like the "cones of position" that I drew up for the earth-based Moon observations recently. By measuring two star angles for each of two nearby asteroids, you find that you can only be in one place in space. If the asteroids are each a quarter of a million miles away, similar to the Moon's distance from Earth, and the sextant measures to 0.1 minute of arc accuracy, then the position in space will be accurate to about six nautical miles, just like the terrestrial case I've been talking about. Is this too far out there? Nobody will be navigating the asteroid belt anytime soon, right? Well then, how about a navigating robot...
    From late 1998 through the end of 2001, a small NASA test spacecraft, known as "Deep Space One" maneuvered out into the asteroid belt and eventually photographed Comet Borrelly. This was not covered much in the media at the time since the flyby occurred less than two weeks after 9/11/2001. Deep Space One tested an autonomous navigation system that used the same basic principle of celestial navigation outlined above. But there were some important differences. First, the spacecraft didn't use a sextant of any sort. Since the spacecraft's computer carried a database of stars down to magnitude 9.0, and since you can always see faint stars where there's no atmosphere, you're no longer limited to the bright stars as in traditional celestial navigation. Because you can use faint stars, you never need to measure angles greater than about a degree, and therefore angle measuring is greatly simplified. You use a digital camera in place of a sextant. The computer aboard the spacecraft aimed itself at known nearby asteroids, based on the spacecraft's self-calculated DR position, and then photographed those asteroids against the background of faint, distant stars. It's then a straight-forward matter to "read off" the small asteroid's position in right ascension and declination. The spacecraft then must be somewhere along a ray that starts at the asteroid and extends into space in the opposite direction from the measured RA and Dec. Cross two of those lines of position, and you've got your position fix. This is real celestial navigation applied in space. The sextant has been replaced with a digital camera. The 57 navigational stars have been replaced by 250,000 catalogued stars. The target selection and clearing process are 100% automated. And the horizon, or the limb of the Moon in the case of lunar distances, is replaced by a set of nearby "beacon" asteroids. The technological differences are substantial, but this is the same concept fundamentally as the process for fixing latitude and longitude at known GMT by lunar distance observations that we've been discussing on the list.
    Neat, huh?
    You added:
    "Regardless, I sincerely enjoy Frank's postings"
    Thank you. Glad to hear that.
    42.0N 87.7W, or 41.4N 72.1W.

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