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Elon Musk's own personal Tesla Roadster launched on the Falcon Heavy in November 2018 and unfortunately overshot the orbit of Mars. This short animation shows the trajectory of SpaceX's Roadster. It seems that around October 2020, it'll be fairly close to Mars. I know that a Wikipedia animation is not the most accurate, and that their orbital inclinations are different (Roadster Inclination: 1.077°; Mars' Orbit Inclination: 1.85°). But I'm curious about what will be the closest distance Starman will ever be to Mars? Will it ever enter Mars' Sphere of Influence? I'm talking about the whole orbital life time of this Roadster. Is 2020 really the closest it will be to Mars?

Related: How close will the Tesla Roadster with Starman actually get to Mars?

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    $\begingroup$ BTW, i'm asking from the Tesla Roadster. I need to reach Mars soon. Running out of gas. $\endgroup$
    – Star Man
    Aug 17, 2019 at 0:14
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    $\begingroup$ The Roadster didn't "overshoot" anything. There was no propulsion after the Falcon Heavy second stage, and its payload was never intended to do anything but go into a (hopefully) Mars-crossing orbit. The primary purpose (beyond testing the triple-boosters in real world conditions) was to demonstrate the performance of the second stage after a long duration coast phase, and so it simply burned to depletion, throwing the Tesla as far as it could. $\endgroup$
    – Christopher James Huff
    Aug 17, 2019 at 23:30
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    $\begingroup$ The Roadster is quite a solid chunk of stuff, and so it isn't going to disintegrate. The possibility exists it could be in orbit for billions of years. Over that amount of time, it's impossible to say what its fate will be. Its orbit will slowly change, as will the orbits of everything else in the solar system. It might crash into Mars, or some other major body. It might be ejected from the solar system. It might hit the sun. It might be accreted into a large asteroid. Since you say 'whole orbital lifetime', it's important to point that out. $\endgroup$
    – kim holder
    Aug 18, 2019 at 1:51

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Putting the spacecraft id (-143205) into the JPL HORIZONS ephemeris system produces:

TRAJECTORY: This trajectory is based on JPL solution #10, a fit to 364 ground-based optical astrometric measurements spanning 2018 Feb 8.2 to March 19.1

Trajectory name Start (TDB) Stop (TDB)
-------------------------------- ----------------- ----------------- 
tesla_s10 2018-Feb-07 03:00 2090-Jan-01 00:00

Encounter predictions for s10 (w/radial 1/r^2 non-gravitational acceleration)

Date (TDB)        Body CA Dist  MinDist MaxDist Vrel   TCA3Sg  Nsigs  P_i/p
----------------- ----- ------- ------- ------- ------ ------  ------ ------ 
2018 Feb 08.09690 Moon  .000936 .000936 .000936 3.961     0.41 47509. 0.000
2020 Oct 07.26768 Mars  .049530 .048923 .050242 8.150    27.40 6.63E5 0.000
2035 Apr 22.35934 Mars  .015504 .004378 .027978 8.219   170.47 31247. 0.000
2047 Jan 11.89023 Earth .031919 .031716 .032123 4.493   249.70 78398. 0.000
2050 Mar 19.52949 Earth .119113 .113778 .124369 7.397   538.54 2.61E5 0.000
2052 Sep 05.15606 Mars  .176363 .172469 .180319 5.738   2185.5 8.68E5 0.000
2067 Apr 15.90202 Mars  .043270 .025712 .061471 7.192   1115.0 42565. 0.000
2084 Sep 17.92284 Mars  .116962 .093449 .141170 9.753   787.45 6.55E5 0.000
2085 Jan 01.96490 Earth .083063 .049368 .112186 6.224  5208.9  1.00E5 0.000
2088 Mar 09.95754 Earth .049146 .033491 .063322 5.106  4505.2  1.17E5 0.000

Date = Nominal encounter time (Barycentric Dynamical Time)

CA_Dist = Highest probability close approach distance to body, au

MinDist = 3-sigma minimum encounter distance, au

MaxDist = 3-sigma maximum encounter distance, au

Vrel = Relative velocity at nominal encounter time, km/s

TCA3Sg = 3-sigma uncertainty in close encounter time, minutes

Nsigs = Number of sigmas to encounter body at nominal encounter time

P_i/p = Linearized probability of impact

So from this we can see that the closest approach to Mars is the 2035 April 22 encounter at 0.015504 AU (2319365.39 kilometers) but as you can see by the big difference between the MinDist and MaxDist there is substantial uncertainty in exactly how close to the planet it will go. This is because the measurements of the position don't cover a very large fraction of the orbit and there are a lot of other non-gravitional effects which could affect the orbit over time.

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What is the closest distance SpaceX's Tesla Roadster (Starman) will ever be to Mars?

I predict 0 meters. Musk will capture the Falcon-9 2nd stage adorned with his red Tesla Roadster, bring it to Mars and display it in front of SpaceX Mars headquarters in a similar fashion to the Falcon-9 in front of SpaceX Earth headquarters in Hawthorne.

I think this is inevitable.

[enter image description here

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    $\begingroup$ Seems like a perfectly reasonable thing for a genius Billionaire Playboy Philanthropist to do.... $\endgroup$
    – Criggie
    Oct 25, 2020 at 12:42

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