<h3>Asteroids!</h3>
<p>There are <a href="https://en.wikipedia.org/wiki/List_of_minor_planets" rel="nofollow noreferrer"><strong>almost a million</strong> identified minor planets out there</a> with pretty well characterized orbital motion.</p>
<p>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.</p>
<p>Once you've got a few candidates, you can use <a href="https://rhodesmill.org/skyfield/kepler-orbits.html" rel="nofollow noreferrer">Skyfield's Kepler orbit propagator</a> to quickly get approximate locations of all of them and search for candidates.</p>
<p>Then for those candidates use JPL's <a href="https://ssd.jpl.nasa.gov/horizons/app.html#/" rel="nofollow noreferrer">Horizons</a> to get much more accurate predictions for their positions as a function of time.</p>
<p>You are well on your way to getting some kind of timestamp, assuming you can find two or three asteroids in your exposure.</p>
<h3>Satellites!</h3>
<p>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 <a href="https://space.stackexchange.com/a/37454/12102">some make big figure eights</a></p>
<p><a href="https://i.sstatic.net/SwR8L.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SwR8L.png" alt="enter image description here" /></a></p>
<p>For these you use <a href="https://en.wikipedia.org/wiki/Two-line_element_set" rel="nofollow noreferrer">two line element sets</a> and propagate those as a function of time to look for candidates. Again you need several to be sure.</p>
<h3>Galilean satellites of Jupiter!</h3>
<p>This &quot;clock&quot; is <a href="https://en.wikipedia.org/wiki/Speed_of_light#Measurement" rel="nofollow noreferrer">how the speed of light was first measured</a> 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 &quot;fast clock&quot; and a &quot;slow clock&quot; (Jupiter's orbital motion, from Skyfield or Horizons) so that might work out.</p>

CC BY-SA 4.0
2024-03-25T17:48:48.933Z
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.
requiemman
CC BY-SA 4.0
2024-03-26T01:55:49.990Z
@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
uhoh
CC BY-SA 4.0
2024-03-26T02:00:07.033Z
@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.
uhoh
CC BY-SA 4.0
2024-04-04T21:24:04.970Z
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?
requiemman
CC BY-SA 4.0
2024-04-05T00:36:00.317Z
@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?](https://astronomy.stackexchange.com/q/33575/7982) and think about the implications of the title of the paper [Astrometry.net: Blind astrometric calibration of arbitrary astronomical images](https://arxiv.org/abs/0910.2233).
uhoh
CC BY-SA 4.0
2024-04-05T00:41:29.657Z
Once again you did not mention "cell phone" images in your question, but instead you are only slowly revealing the problem over a period of a month, and only in comments. In Stack Exchange a question should work hard to clearly and completely describe the problem. If the problem is limited to cell phone images, then 1) the number of possible stars is reduced by at least a factor of a thousand (and probably closer to a factor of a million!) There are also big constraints on scale (it's not going to be 0.1 arcsec per pixel!). Images could span *as much as* 30-50° but would be bigger than say 1°.
uhoh
CC BY-SA 4.0
2024-04-05T00:53:26.053Z
For example, there are about 10,000 possible stars visible to the human eye, but the USNO-B Catalog (basis of astrometry.net) has over 1,000,000,000 entries! That's one reason why it takes so long to run. **Cell phone images will never be sensitive enough to make use of proper motion unless you are talking about exposures thousands of years apart!** Unless you have a planet or two, or the (not overexposed) Moon against stars, the answer is that (in my opinion) "No, no time stamps from cell phone images". Even if you have a clear horizontal horizon, 2 weeks later and 55 minutes earlier are same
uhoh
CC BY-SA 4.0
2024-04-05T00:55:17.260Z
About the distortion polynomial, you should post a new question so that everyone can see it and someone who may know the answer can answer it. You can add this as "evidence of prior research" https://oa.upm.es/64244/1/INVE_MEM_2019_325014.pdf but say that you don't know which model is used by astrometry.net
uhoh
CC BY-SA 4.0
2024-04-05T12:55:03.340Z
Thanks for the advice. I was investigating whether it was possible to timestamp a single image from a strong telescope, and then wanted to see whether it was possible to extend known solutions to my specific problem. I'll post the question about astrometry.net's distortion polynomial, but I don't expect it to apply at all to my problem.
requiemman
CC BY-SA 4.0
2024-04-06T00:21:35.663Z
@requiemman OK, I see that your interest evolved as more information (in comments at least) available. I added a second answer but it's not exactly a "here's how to do it".
uhoh
CC BY-SA 4.0
2024-03-05T06:15:36.780Z
2024-03-05T06:22:25.257Z
2024-03-05T06:22:25.257Z
uhoh
<p>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.</p>
<p>By only observing the proper motion of stars through &quot;normal&quot; 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.</p>
<p>The telescopes used to make precision proper motion now are very <em>unusually</em> constructed <em>space</em> telescopes, especially [tab:GAIA].</p>
<p>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.</p>
<p>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.</p>
<p>Then you can apply a typical astrometry uncertainty for a &quot;big&quot; astronomical telescope and see what time uncertainty corresponds to the position uncertainty.</p>
<p>I think you are much better of hoping for a single &quot;fast mover&quot; then a general statistical analysis - most stars have very little proper motion.</p>
<p>You might ask a new question about the statistical distribution of proper motions in the GAIA catalog to see if I'm right!</p>

CC BY-SA 4.0
2024-04-06T00:19:33.947Z
2024-04-06T00:19:33.947Z
uhoh
<p><a href="https://astronomy.stackexchange.com/questions/14497/how-accurately-can-you-tell-the-time-using-a-photo-of-the-stars">This</a> 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?</p>
<p>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 <a href="https://arxiv.org/pdf/0910.2233.pdf" rel="nofollow noreferrer">says</a> that using tools like <a href="https://articles.adsabs.harvard.edu/pdf/2006ASPC..351..204M" rel="nofollow noreferrer">WCSFits</a> 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)?</p>

CC BY-SA 4.0
2024-03-01T00:43:13.107Z
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.
Greg Miller
CC BY-SA 4.0
2024-03-01T00:55:26.080Z
Ah, I see. I figured it was worth a shot asking here anyway.
requiemman
CC BY-SA 4.0
2024-05-06T07:34:27.033Z
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?
ProfRob
<photography><time><astrometry>
Determing timestamp of a photo of the stars using a plate solver
requiemman
# Determing timestamp of a photo of the stars using a plate solver

(Asked by: username_0 on 2024-02-29)

[This](https://astronomy.stackexchange.com/questions/14497/how-accurately-can-you-tell-the-time-using-a-photo-of-the-stars) 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](https://arxiv.org/pdf/0910.2233.pdf) that using tools like [WCSFits](https://articles.adsabs.harvard.edu/pdf/2006ASPC..351..204M) 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)?

**Tags:** photography, time, astrometry
> **Comments:**
> **username_1**: 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.  
> **username_0**: Ah, I see. I figured it was worth a shot asking here anyway.  
> **username_2**: 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?  

---

## 2 answers

### Answer by username_3 on 2024-03-05. Score: 1

### Asteroids!

There are [**almost a million** identified minor planets out there](https://en.wikipedia.org/wiki/List_of_minor_planets) 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](https://rhodesmill.org/skyfield/kepler-orbits.html) to quickly get approximate locations of all of them and search for candidates.

Then for those candidates use JPL's [Horizons](https://ssd.jpl.nasa.gov/horizons/app.html#/) 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](https://space.stackexchange.com/a/37454/12102)

[![enter image description here](https://i.sstatic.net/SwR8L.png)](https://i.sstatic.net/SwR8L.png)

For these you use [two line element sets](https://en.wikipedia.org/wiki/Two-line_element_set) 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](https://en.wikipedia.org/wiki/Speed_of_light#Measurement) 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.

> **Comments:**
> **username_0**: 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.  
> **username_3**: @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  
> **username_3**: @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.  
> **username_0**: 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?  
> **username_3**: @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?](https://astronomy.stackexchange.com/q/33575/7982) and think about the implications of the title of the paper [Astrometry.net: Blind astrometric calibration of arbitrary astronomical images](https://arxiv.org/abs/0910.2233).  
> **username_3**: Once again you did not mention "cell phone" images in your question, but instead you are only slowly revealing the problem over a period of a month, and only in comments. In Stack Exchange a question should work hard to clearly and completely describe the problem. If the problem is limited to cell phone images, then 1) the number of possible stars is reduced by at least a factor of a thousand (and probably closer to a factor of a million!) There are also big constraints on scale (it's not going to be 0.1 arcsec per pixel!). Images could span *as much as* 30-50° but would be bigger than say 1°.  
> **username_3**: For example, there are about 10,000 possible stars visible to the human eye, but the USNO-B Catalog (basis of astrometry.net) has over 1,000,000,000 entries! That's one reason why it takes so long to run. **Cell phone images will never be sensitive enough to make use of proper motion unless you are talking about exposures thousands of years apart!** Unless you have a planet or two, or the (not overexposed) Moon against stars, the answer is that (in my opinion) "No, no time stamps from cell phone images". Even if you have a clear horizontal horizon, 2 weeks later and 55 minutes earlier are same  
> **username_3**: About the distortion polynomial, you should post a new question so that everyone can see it and someone who may know the answer can answer it. You can add this as "evidence of prior research" https://oa.upm.es/64244/1/INVE_MEM_2019_325014.pdf but say that you don't know which model is used by astrometry.net  
> **username_0**: Thanks for the advice. I was investigating whether it was possible to timestamp a single image from a strong telescope, and then wanted to see whether it was possible to extend known solutions to my specific problem. I'll post the question about astrometry.net's distortion polynomial, but I don't expect it to apply at all to my problem.  
> **username_3**: @requiemman OK, I see that your interest evolved as more information (in comments at least) available. I added a second answer but it's not exactly a "here's how to do it".  

---

### Answer by username_3 on 2024-04-06. Score: 0

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!


---

