Starman’s Drive

The only way to avoid knowing that, this week, a bright red, electric sports card with a spacesuit clad dummy at the wheel was launched into interplanetary space was to have become a hermit. The launch was deeply impressive and it seemed only right that the most powerful American rocket since the Saturn V should launch from the same launchpad – 39A – that sent the Apollo XI astronauts to the Moon. What followed, was possibly even more impressive. To see the two booster rockets landing simultaneously at Kennedy was to see the future happening. And then, those images of Starman driving around in a slow spin such that sometimes we saw the Earth behind and sometimes the Earth was reflected in the car door: millions of people watched those images, entranced.

There were a lot of lunchtime discussions about the launch, the PR aspects and the implications of this flight. Even if you thought that there was a bit of showing-off involved, no one could say other than that it was deeply impressive to watch and slickly presented. There has also been some discussion of exactly where the Tesla is headed, with contradictory claims about its final orbit. So then, discussions turned to whether or not the Tesla could be observed leaving Earth orbit and just how bright it might be. I argued that, with its shiny, highly reflective finish, the car would have been quite bright and easy to observe [as you will see below, I was right – the car was surprisingly bright] and was designated to check to see if the Tesla was in the JPL’s Horizons database (https://ssd.jpl.nasa.gov/horizons.cgi) and what its orbit might be.

Horizons does indeed have an orbit solution, there were many observations of the car leaving Earth orbit, despite its southerly trajectory (although this is actually a misleading  effect of perspective, as the orbit is only inclined 1 degree to the ecliptic) and the Tesla even has an official COSPAR designation, making it a formal payload launch.

This is what Horizons has to say about it:

Tesla Roadster (spacecraft): NAIF ID, -143205

Tesla Roadster (AKA: Starman); COSPAR ID, 2018-017A). JPL orbit solution #5

The Horizons description of the mission is:

“Dummy payload from the first launch of SpaceX Falcon Heavy launch vehicle. Consists of a standard Tesla Roadster automobile and a spacesuit-wearing mannequin nicknamed “Starman”.

Also includes a Hot Wheels toy model Roadster on the car’s dash with a mini-Starman inside. A data storage device placed inside the car contains a copy of Isaac Asimov’s “Foundation” novels. A plaque on the attachment fitting between the Falcon Heavy upper stage and the Tesla is etched with the names of more than 6,000 SpaceX employees.

After orbiting the Earth for 5 hours, a third-stage burn was completed at approximately 02:30 UTC Feb 7, placing the dummy payload in a heliocentric orbit having a perihelion of 0.99 au and aphelion ~1.67 au.”

There have been 128 ground-based astrometric observations, spanning February 8.2 to 9.5, during which time it faded from magnitude 10.5 to 16.9. In fact, at the time of the end of the final burn, the Tesla would have been possibly even a naked-eye object from a dark location, with a magnitude around 6.5 and would have been easy to see with binoculars.

The roadster crossed the lunar orbit just before 04:00 on February 8th, about twenty-five and a half hours after its escape burn.

So, as the orbit does goes well past the orbit of Mars (1.52AU), you can argue that, yes, it is into the Asteroid Belt, if only its innermost fringes (people are saying that he was wrong to claim that it would reach the Asteroid Belt).

At midnight tonight (night of February 11/12th) the Tesla will be at 4.1 Lunar Distances and receding at 3.5km/s, having slowed from an initial 6.1km/s. Since escape, the Tesla has been in Southern Hydra, in the morning sky, rising about 2 or 3 hours after local midnight. Right now it is moving almost directly away from the Earth, so its coordinates barely change: RA 14h38m42s, Dec -27°02’16” at midnight tonight and, at magnitude 18.3 is still surprisingly bright and not at all difficult to observe so, with the Moon approaching new, will likely be observed a few more times before it becomes to faint to detect.

How well though do we know where the Tesla and Starman are heading? The timebase for the orbit solution is short and does not include two, very important perturbing effects: one is the effect of light pressure – a highly reflective object experiences a much greater effect from light pressure than one that is dull black because it reverses the momentum of the photons that are hitting it; the second effect is of outgassing – any leaks of gas from the tyres, upholstery, contents of the car, etc. will blow it slightly off course. Without observations over a much longer period of time it is impossible to model either of these effects. They may be tiny, or cancel out, or they could provide a continuous low thrust that changes the orbit slightly, but significantly. Without more observations we will never get a solution to the orbit exact enough to model exactly where it is heading for more than the short term.

Afterthought:

Of course, as was pointed out in our lunchtime discussions, as the thrust was applied to the Tesla at the distance of the Earth’s orbit from the Sun, the car will return to its point of origin with every orbit. The rough orbit solution gives an orbital period of 1.53 years so, for every two orbits made by the car, the Earth will make about three, thus the Tesla and the Earth will have returned almost to their starting positions. As a result, it will come close to the Earth every three years, but we do not know how close with such an approximate orbit to work from. Of course, if its period were exactly 1.5 years, it would come almost exactly back to its starting position when the escape burn was made. If the period is a little more, or less than 1.5 years, each return will be a little more distant than the previous one. Depending on the exact period, we may see the Tesla again, in early 2021, or we may lose it forever until some marauding spacecraft encounters it by accident in the distant future, captures it and takes it to a museum.

Update (13th February):

JPL has produced another orbit update for Starman (#6) based on data from February 8.2 to 12.7. Although light pressure and outgassing are still not modelled, the orbit solution is becoming far more reliable, with more than twice the number of observations and three times the timebase of the previous solution.

You can find images, taken by Enrico Pettarin, from Italy, on February 10th, with Starman at 0.00676AU from Earth (2.63 Lunar Distances) here:

http://spaceweathergallery.com/indiv_upload.php?upload_id=142567

The latest orbit has:

q=0.986063

e=0.261849

a=1.335855

Q=1.685648

P=1.544 years

So, it is increasingly obvious that the Tesla is not into a 3:2 orbital resonance with the Earth and, even though there will be a relatively close pass every 3 years, the Tesla will gradually slip further and further away from the Earth with each successive encounter. The other piece of hard data from this new solution is that the orbit does take the Tesla out significantly beyond the orbit of Mars at aphelion, although quite not far enough to be in the Asteroid Belt proper, as the innermost, Hungaria asteroids orbit at about 1.78AU.

Update (February 14th):

There has been another orbit update (JPL #7) although, remarkably, JPL #6 and JPL #7 agree to six places of decimals (the solution is calculated to 16 places, but I have rounded it to the traditional 6), showing that it is already remarkably stable, as the table below shows:

JPL #6 JPL #7
Length of arc 4.5 days 5.2 days
Number of observations 269
Perihelion distance 0.986063 AU 0.986063 AU
Eccentricity 0.261849 0.261849
Semi-major Axis 1.335855 AU 1.335855 AU
Aphelion distance 1.685648 AU 1.685648 AU
Period 1.544 years 1.544 years

My colleague, Ivan Valtchanov points out a paper on Astro-ph on the long-term orbit evolution (https://arxiv.org/abs/1802.04718) of the Tesla. The paper makes various interesting predictions such as a very close Earth encounter in 2091 and that there is a negligible change of a Mars impact in the next million years but, not unreasonably as the car started from a point close to Earth, a quite high probability of Earth impact.

Incidentally, in one million years orbiting, the car would run up around 1015km – around 100 light years – on the clock, which may invalidate its warranty and roadworthiness (my thanks to Jon Brumfitt, Leo Metcalfe and Paolo Pesciullesi for those gems). One suspects though that solar UV will have seriously degraded the paintwork and tyres long before the end of the century.

It would be interesting to see if their prediction of a 2091 close encounter with Earth still stands after the publication of the JPL #7 ephemeris. They are using an orbit based on a very short arc (I think, JPL #5, which was based on little over 1 day of observations – maybe that should be specified more clearly in the paper) whereas now the JPL #7 ephemeris has four times the length of arc and fixes the initial conditions much better. I suspect that they will do some re-calculation and that some of their conclusions may change a little, although not the major conclusion that a Mars impact is unlikely. The interesting part is that they find, not unexpectedly, orbit flips, where a close approach to Earth changes the orbit’s argument of perihelion by 180 degrees, moving it from perihelion at the Earth’s orbit to aphelion at this point and perihelion around the orbit of Venus.

[Update: 19/02/2018]

The latest published image of the Tesla was taken yesterday morning at 8.3 Lunar Distances (http://spaceweather.com/images2018/18feb18/RoadsterAnimation2-5.gif). However, the car is now getting very faint and difficult to observe, only just above magnitude 20. There should be a final orbit update from JPL in the next couple of days, but it seems unlikely that we will get many more observations of the car now.

2 thoughts on “Starman’s Drive

  1. We have a much better orbit solution now, so I have done an update. Nothing fundamental changes, but it hardens-up the data that we had.

    Like

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