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I have seen that the original estimate to pass by Mars was about 6 months, but the current trajectory overshot Mars by quite a bit. How long until Starman and the Roadster return to complete their first orbit of the sun?

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  • $\begingroup$ you may want to consider accepting my answer now. $\endgroup$ – uhoh Feb 27 '18 at 5:59
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After seeing the other @MarkAdler comment, I looked and sure enough a projected orbit is in Horizons based on the last, best data from the FH 2nd stage's navigation information.

I get 558 days and I show the math, or at least the Python that extracts the data from Horizons.

Update: JPL Horizons is now providing data based on a refined calculation:

TRAJECTORY:
  This trajectory is based on JPL solution #8, a fit to 330 ground-based 
  optical astrometric measurements spanning 2018 Feb 8.2 to 18.3 

Based on this, the period is now given as 557.1 days, rather than the original 558 days.

This answer will take you to a detailed list of the (now more than) 330 individual astrometric observations of Roadster.

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  • $\begingroup$ Can you provide a margin of error for that orbit ? $\endgroup$ – Antzi Feb 27 '18 at 6:36
  • $\begingroup$ @Antzi No, and you can't either! ;-) The reality of orbits in a realistic solar system is that they are simply not truly periodic. Their orbits never really exactly repeat in either a Barycentric or Heliocentric reference system. However, the number I've provided is the average of the period of the instantaneous osculating orbital elements about the Sun for the next two years, and during that time this value varied by less than about 0.05 days. $\endgroup$ – uhoh Feb 27 '18 at 6:46
  • $\begingroup$ But if you are asking me about the experimental uncertainty based on the errors in the observation, that will be something that can certainly be looked for, though I am not sure how long that will take. You might consider asking that as a separate question, either here or in Astronomy SE. I asked How (the heck) can 2014 MU69's orbit be know well enough for a close flyby by New Horizons? a while ago, so far no good, quantitative answers have been forthcoming. $\endgroup$ – uhoh Feb 27 '18 at 6:50
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2.404 years, by doing the math.

Of course, that assumes that the orbital parameters used were correct. According to many internet sleuths, the C3 value given doesn't match the orbital parameters. The correct value is more likely to be around 1.6 years, according to this tweet.

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  • $\begingroup$ I have it on good authority that the C3 is correct, and the aphelion (misspelled in the tweet by the way) is incorrect. So it did not overshoot Mars much at all. $\endgroup$ – Mark Adler Feb 8 '18 at 6:12

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