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According to this answer to When was the last time that Starman/Roadster was seen? it was last seen by Earthlings at least at 2018-03-19 03:22:33 UTC by a 1 meter telescope in South Africa.

  1. Based on known albedo and trajectory, when could Roadster be potentially detectable again by this telescope?
  2. At that time of year, will Roadster's position be viewable at night from this location?
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    $\begingroup$ Who you calling an "Earthling" ? :-) $\endgroup$ Apr 21, 2020 at 11:55

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Starman will be pretty close to Mars in 2035, so if there is any good Martian telescopes then, they will be able to spot it. We could do so in October of this year, but there aren't any telescopes good enough.

From Earth, January 2047 is the most likely time to spot with a 1 meter or smaller telescope. A 1 meter telescope was what last saw Starman. Because of orbital mechanics, any close approach will happen in the winter with Earth, January to March. The next time it will be close is in 2050, I believe March.

We could spot it with Hubble most of the time, if that was even remotely possible to get time on HST for such a thing, or possibly with some of the really big telescopes earlier, but by far 2047 is the most likely time to get a good image of it.

See also an article that I wrote for Ars Technica, with more similar details.

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  • $\begingroup$ I'm curious, how far was Starman when it was last seen? It was launched on 2018-02-06 and last seen about forty days later. Neglecting angles and the position of the Sun for a minute, when would it be that same distance again? $\endgroup$
    – uhoh
    Apr 21, 2020 at 12:00
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    $\begingroup$ It was a bit under 0.1 AU. The next time will be 2047. $\endgroup$
    – PearsonArtPhoto
    Apr 21, 2020 at 12:04
  • $\begingroup$ however, I hope we all agree JWST is totally incapable of spotting starman because 1. It would zoom in waaaaaay too far and 2. because it'd be a total WATSE of the power of webb! $\endgroup$ Sep 6, 2022 at 17:05
  • $\begingroup$ It is totally possible to use JSWT to spot Starman, but it is highly unlikely to be used to do so. And even then, it would only appear as a dot. Totally a waste of power. $\endgroup$
    – PearsonArtPhoto
    Sep 7, 2022 at 19:39

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