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This question from 2016 seems to suggest that you need a powerful telescope to get a photo of the stars in such a way that you can use their proper motion to get a timestamp. If this is possible, how would you do it?

For example, Astrometry.net provides a decent first guess given an image of the stars, taken from Earth with a commercial camera. Their own publication says that using tools like WCSFits can provide a better starfield fit to pixels, given Astrometry.net's first guess. Based on this fit, is it possible to get a reasonably good UTC timestamp, if I exclusively work with images taken post-2000, and I know where each image was taken from (i.e. the lat/lon coordinates on Earth)?

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  • $\begingroup$ The star with the highest PM is Bernard's Star, at 10 arcsec per year, or .01" per day. You would be hard pressed to discern a day's movement from atmospheric effects, let alone anything down to the minute or second. $\endgroup$ Commented Mar 1 at 0:43
  • $\begingroup$ Ah, I see. I figured it was worth a shot asking here anyway. $\endgroup$
    – requiemman
    Commented Mar 1 at 0:55
  • $\begingroup$ Please say what the astrometric precision of your images are. i.e. Approximately what is the angular size of pixels on the sky and with what precision (as a fraction of a pixel) can the centroid of a star image be determined? $\endgroup$
    – ProfRob
    Commented May 6 at 7:34

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Asteroids!

There are almost a million identified minor planets out there with pretty well characterized orbital motion.

Your plate solver will give you two things - a coordinate system for your frame, and a way to begin to identify objects that don't correspond to stars.

Once you've got a few candidates, you can use Skyfield's Kepler orbit propagator to quickly get approximate locations of all of them and search for candidates.

Then for those candidates use JPL's Horizons to get much more accurate predictions for their positions as a function of time.

You are well on your way to getting some kind of timestamp, assuming you can find two or three asteroids in your exposure.

Satellites!

There are lots and lots of Earth-orbiting satellites that criss-cross astronomical plates in addition to those pesky Starlinks. Some are in MEO (e.g. GPS, GLONASS, BeiDou, Galileo, there are others) and a whole bunch of them are in GEO. Most of them are in the equatorial plane, but some make big figure eights

enter image description here

For these you use two line element sets and propagate those as a function of time to look for candidates. Again you need several to be sure.

Galilean satellites of Jupiter!

This "clock" is how the speed of light was first measured but alone I don't think you can get an unambiguous measurement - three of the four are in resonance so the frequency of repeats may be too high unless you have a specific time window in mind. Of course if you can also see the stars behind jupiter at the same time, then you have both a "fast clock" and a "slow clock" (Jupiter's orbital motion, from Skyfield or Horizons) so that might work out.

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    $\begingroup$ Aren't asteroids dimmer than stars? I'm trying to think of a way to do this elegantly - maybe plate solve and subtract the sources using Gaia or something similar. However I don't know how I'd differentiate between asteroids, satellites, and noise given only a single image. $\endgroup$
    – requiemman
    Commented Mar 25 at 17:48
  • $\begingroup$ @requiemman I didn't fully appreciate that this must be done with a single image. Asteroids are dimmer than the brightest stars, but starting at say +6 magnitude and higher (dimmer) there are plenty of both asteroids and star (more stars than asteroids of course). The problem with a single image is that it's hard to be certain of the identity of any object that's not where a star is known to be. Usually the speed and direction of motion is used to confirm the identity of an asteroid. I suppose if you have a plate with a lot of high proper motion stars in one field going different directions $\endgroup$
    – uhoh
    Commented Mar 26 at 1:55
  • $\begingroup$ @requiemman you could do a global plate solve, remove low order field distortion and match all the residual errors to proper motions to get an approximate timestamp. Mostly you'll see parallax motion which is repetitive yearly, so the right balance between parallax and proper motion might work in your favor. You didn't mention if one gets to choose where to point the telescope to make the single image, or if it is some random, undocumented "found" plate in some old filing cabinet in a storage room. $\endgroup$
    – uhoh
    Commented Mar 26 at 2:00
  • $\begingroup$ it's just widefield images taken with cell phones, I'm afraid. Assuming that I can platesolve them (which in many cases is impossible!), I don't think anything you suggested is possible. This is akin to the classic 'lost in space' problem, except, of course, you're lost on earth. I do have a few noisy images I've managed to platesolve with astrometry.net which outputs a 'distortion polynomial' - is that related to lower order field distortions? If so, do you have any resources that can help me understand the algorithms to remove these? $\endgroup$
    – requiemman
    Commented Apr 4 at 21:24
  • $\begingroup$ @requiemman I believe that there can be a much, much better solver for cell phone photos. Astrometry.net is super general and searches a huge number of very faint stars, most of which are only visible on long photographic exposures through large telescopes. See answers to How (the heck) does Astrometry.net work? and think about the implications of the title of the paper Astrometry.net: Blind astrometric calibration of arbitrary astronomical images. $\endgroup$
    – uhoh
    Commented Apr 5 at 0:36
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Based on all the discussion under my first answer based on things other than stars that move rapidly, I see that a star-based answer is still desired.

By only observing the proper motion of stars through "normal" strong telescopes on Earth, if you are lucky to have a single exposure with a high proper motion plus high parallax star (they tend to both be bigger the closer the star is), maybe you can get an accuracy of a few months.

The telescopes used to make precision proper motion now are very unusually constructed space telescopes, especially [tab:GAIA].

You might hope for a star with its steady proper motion perpendicular to its oscillating parallax, so that the motion is either a spiral (which still has crossing ambiguities) or with bigger proper motion, like a sine wave.

I'm not an astronomer, but I know there are catalogs you can sort though, especially the GAIA results. You can filter for high parallax and high proper motion and avoid those with proper motion parallel to the ecliptic (which is how parallax moves) and take the top 100 results.

Then you can apply a typical astrometry uncertainty for a "big" astronomical telescope and see what time uncertainty corresponds to the position uncertainty.

I think you are much better of hoping for a single "fast mover" then a general statistical analysis - most stars have very little proper motion.

You might ask a new question about the statistical distribution of proper motions in the GAIA catalog to see if I'm right!

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