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    Re: Photographic lunars
    From: Frank Reed
    Date: 2009 Dec 13, 19:10 -0800

    Peter Monta, you wrote:
    "I've recently become interested in celestial navigation and thought I'd try a lunar distance measurement via digital camera. It seems to work. After skimming the interesting archives of this group, perhaps it's worth sharing the workflow for this."

    Wonderful! Welcome aboard. :-)

    "The two exposures at 1/80 sec and 1/5 sec were used and the center one at 1/20 sec discarded (being the worst of both worlds). All images were taken on a tripod less than a second apart in time (by virtue of the automatic bracketing), so the camera pointing should change very little"

    Aha. That's a very clever approach.

    And you wrote:
    "Having a little experience with the free CCD astrometry pipeline from Astromatic (http://www.astromatic.net/) and the cool work at astrometry.net, I thought the easiest way to reduce the images would be not to try for any "lunar distances" but just to go directly for a lunar position in global coordinates."

    Quite so. This is exactly the right way to work photographic celestial navigation. You're doing something here that's very close to the way celestial navigation is practiced aboard unmanned spacecraft (only one, so far as I know) out among the asteroids. The basic principle is to photograph some nearby object (there are tens of thousands of asteroids with reasonably well-determined orbits against a star field (with the star positions essentially perfect thanks to Hipparcos). Then simple pattern-matching algorithms along with the more specific algorithms for so-called "plate constants" used in astrometry let you read off a highly accurate right ascension and declination for the target asteroid. Then, since you know its three-dimensional coordinates in the Solar System (you can place the asteroid at some point x,y,z for a known value of t), you can draw a line of position extending from that asteroid towards the point on the celestial sphere opposite the value determined from the photograph. Do it again with another asteroid, cross the lines, and there's your position fix. We can do the same thing here on the surface of the Earth with any nearby object taking the place of the asteroids. The Moon is just barely near enough to be useful. There are also thousands of artificial satellites with well-determined orbits which you can use. You photograph any of these at a known time, get the RA and Dec, draw that line out from the known x,y,z of the object, and where it intersects the Earth is your position. In principle, one photo yields a fix.

    And you wrote:
    "astrometry.net can take any image and find out where it's pointed in the sky with no prior information whatsoever. Quite amazing. Feeding it the 1/5 sec image results in a world coordinate system for the whole image, mapping (x,y) pixel coordinates onto (ra,dec). It also estimates lens distortion, which is about 1% in this case. About 50 stars are detected with good coverage over the whole field (except near the moon)."

    For other NavList members, it may be worth mentioning that this sort of analysis has reached a very high level of development in the amateur astronomy community. They've been refining these techniques for almost two decades. They do real astrometric analysis generating "plate constants" which handle the distortions introduced by the optical system. Very high accuracy can be obtained with mid to high-end digital camera equipment.

    You concluded:
    "Now I'm sure one objection to all this is that it requires a stable platform. But with further playing around, maybe some handheld images would be usable if the short exposures were used to derive a "track" of the pointing instability using the sharp lunar images. Could take a stream of, say, 100 images over the
    course of a minute or so, locate the images with the smallest image-to-image movement, then look for (possibly somewhat streaked) star images in the interspersed longer exposures."

    That makes sense. Once you leave the world of "traditional navigation" behind and start using this much technology, anything goes, so you might as well have an automated system taking hundreds of images per minute, catching those moments when the platform is stable. Collecting the good images and dumping the rest, you might get a fix once a minute. Treating those fixes statistically, you can have a system rivaling GPS accuracy in no time at all.


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