NavList:

Frank Reed writes:

> It's interesting to note that images taken at low angular elevations
> also yield an estimate of the vertical from this pattern-matched
> refraction data. So if we leave the Moon out of it, you could use
> three cameras, or more, to photograph the region three to ten degrees
> above the horizon continuously at widely separated azimuths. The
> refraction data will tell you how much the camera is inclined with
> respect to the horizon. Then you have another camera, probably rigidly
> fixed to the others, photographing towards the zenith. The inclination
> data from the low cameras then tell you where the true zenith lies in
> the upward pointing camera. The same pattern matching gives the RA and
> Dec of the zenith. And with a small amount of calculation, you're
> done. You've got a position fix. And the cameras can do this every few
> seconds all night long.

Interesting---I hadn't known of this possibility. A considerable
advantage is that it's unaffected by platform acceleration, unlike
anything that tries to measure the gravity vector. If my arithmetic
is right, moving one arcminute of latitude on the Earth's surface would
change the relative refraction between a near-zenith star and one at
15 degrees elevation by about 0.4 arcsecond. That's a small signal,
but maybe reachable with some averaging.

It seems like the overall refraction amplitude would not need to be
known that well, since one would be comparing delta-refractions across
the whole sky. So static variations from temperature and barometric
pressure should drop out. Any variation over azimuth would be a problem,
though.

Multiple cameras would be fine, but another possibility is to use a single
camera and split its aperture across different areas of the sky with
mirrors on a stable lens-attachment, a la Hipparcos. Maybe an angle
of 70 degrees. This would complicate the orientation process, since
there would be two stellar fields superimposed, but that's just software.

So the upshot seems to be: with just a camera and software, one can
recover UTC from the moon, and the zenith from refraction, and therefore
both latitude and longitude! Starting with nothing---no UTC, no visible
horizon even.

> 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.

I'd be curious as to which satellites are both bright and have orbits
that will remain stable for a long time (years or decades, say). Needing
up-to-date orbital elements would be one dependency it would be nice
to avoid.

This almost rules out anything in LEO. The GEO birds are available 24/7,
but they're dim, mag 12 or so. How bright are the LAGEOS satellites?
[answer from google: also mag 12 or so] The GPS birds are also probably
quite dim (would they bother to optically stealth them?). I guess with any
satellite there's always the risk of maneuvering, but with several being
tracked, an isolated maneuver could be detected and removed from the solution.

Incidentally, I made a mistake with the first email regarding the error---it
is actually almost three arcminutes (rookie mistake with the sexagesimal
units). Turns out the FITS image was flipped and I was using the wrong
limb of the moon on one axis (93% illuminated...). Also the camera's clock
was a little off and the planetarium program I was using had the moon almost
an arcminute away from the position given by the JPL HORIZONS service!
I think I'll try xephem after spot-checking it against JPL. I'm still
convinced that few-arcsecond accuracy is possible.

So still a bunch of loose ends to tie up. I have an automatic scheme
for the lunar position (using saturated pixels only) that seems promising.
Once I have a fully automatic pipeline and reliable lunar ephemerides I'll
try with new images. I plan to reduce the exposure to 1/15 second and open
the lens up to f/2 (which will hurt the star images a little bit and require
more careful focusing). SNR should remain about the same.

Cheers,
Peter Monta

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