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Elon Musk made another characteristic splash recently with his plan to launch a Falcon Heavy into orbit around Mars, with the bonus payload of his personal Tesla Roadster inside.

Of course, it's an experimental launch, and quite possibly might blow up on launch. If it doesn't, it will head into orbit around Mars, apparently indefinitely.

Musk was quoted in the above article as saying it

"Will be in deep space for a billion years or so if it doesn’t blow up on ascent"

Assuming he means Mars orbit when he says "deep space", and assuming the rocket makes it there, how long would it actually stay in orbit, without refueling or any kind of human interference? I would assume the rocket might have some fuel left for correcting its trajectory, and it would need far less than, say, the ISS in LEO, where there's more drag due to Earth's dense atmosphere. But would it really last a billion years? Or will its orbit degrade and its body disintegrate before then?

I admit I am imagining a stereotypical circular orbit around Mars... could Elon be talking about a larger Elliptical orbit akin to a comet? In that case, I imagine there are even more variables that would make a billion-year lifespan unpredictable.

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    $\begingroup$ I think the car will not orbit mars but rather be send in an orbit that intersect with mars orbit. I don’t think the falcon heavy upper stage can pull off anything like that. $\endgroup$ – Antzi Dec 2 '17 at 16:49
  • $\begingroup$ The shape of the orbit (circular vs. elliptical) isn't what determines orbital lifetime, it's the distance from the planet, and thereby how much or how little drag is induced by the atmosphere, that determines (excluding other interference) how long an orbit will last. In fact, an elliptical orbit will decay sooner than a circular one, since the lower end is always closer to the planet than an equivalent circular path. Eventually the lower end gets into the atmosphere - as happened to Galileo at Jupiter and Cassini at Saturn, then it's bye bye satellite in a ball of flame... $\endgroup$ – FKEinternet Dec 3 '17 at 0:18
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    $\begingroup$ Might want to ask in astronomy how long Phobos and Deimos have been in orbit of Mars $\endgroup$ – JCRM Dec 3 '17 at 10:10
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    $\begingroup$ @TylerH here: syfy.com/syfywire/elon-musk-on-the-roadster-to-mars as a quote: No, it’s not going to Mars. It’s going near Mars. He said it’ll be placed in “a precessing Earth-Mars elliptical orbit around the sun.” $\endgroup$ – Dragongeek Dec 4 '17 at 15:58
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    $\begingroup$ @uhoh got it - that's "never" happened to me ... ( and I've got a bridge for sale ;) ) $\endgroup$ – FKEinternet Dec 5 '17 at 16:02
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The Falcon Heavy has no capability to put a passive object (i.e. without its own propulsion) into Mars orbit. The lifetime of the second stage is on the order of 8 hours. After the cruise to Mars, the batteries on the stage will be dead.

So there's no option to change the trajectory once you get to Mars. The best they can do is aim the rocket in the general direction of Mars, for an elliptical heliocentric orbit that intersects Mars' orbit.

They would have to modify the stage to allow it to function in Mars orbit: Larger batteries, thermal management, insulation for the main propellant tanks to reduce boiloff, custom software for the Mars orbit injection burn. All that sounds like too much effort for a one-off demonstration mission.

More importantly: they're doing this mission as part of the certification effort for Falcon Heavy. That means they need to demonstrate the standard stage. Modifying the stage for this mission would make the mission useless.

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  • $\begingroup$ Cryogenic propellants are quite a technology challenge to store for periods of many months, even non-sub-cooled. But as far as power is concerned, couldn't one could simply add an extra 100 kg battery with good long-term storage (in exchange for removing the roadster's seats and doors perhaps?) and shut down nearly all power usage for the trip, something like how Rosetta and New Horizons did? I'm assuming the Roadster's own battery was already removed for weight considerations; I don't think those hold charge long enough. $\endgroup$ – uhoh Dec 6 '17 at 0:38
  • $\begingroup$ Li-ion batteries (such as Teslas use) can certainly hold a charge for months, if nothing is draining them. Furthermore, I wouldn't really expect them to bother removing the car's batteries; the entire weight of a Roadster is far below what FH is supposed to be able to get to Mars. Now, with that said, the batteries will become useless if they get too cold, and keeping them warmed will certainly deplete them long before reaching Mars, so there is definitely a limit to how long the car will be able to play Space Oddity to itself. $\endgroup$ – CBHacking Dec 6 '17 at 5:18
  • $\begingroup$ See my amended answer. $\endgroup$ – Hobbes Dec 6 '17 at 8:44
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    $\begingroup$ @uhoh I really doubt weight was a concern. The Falcon Heavy can send at least an 8 ton vehicle ("Red Dragon") to the surface of Mars. I doubt a 1.5 ton vehicle would cause it any issues at all, just in the general direction. $\endgroup$ – PearsonArtPhoto Jan 9 '18 at 15:05
  • $\begingroup$ @CBHacking Li-ion batteries also tend to drain much faster in the cold. If there's no insulation on the batteries, I would imagine they would probably be long dead before they near Mars, even if they are fully charged to begin with and don't have anything actively drawing power from them during the trip. $\endgroup$ – TylerH Feb 6 '18 at 19:29
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The short answer is, it really does depend heavily on the orbit. It is not exactly known at this time what kind of orbit it will be in, but there are some requirements if it is to last as long as Musk claims. If the periapsis of the orbit is fairly high, like several thousand kilometers, and the apoapsis is reasonably low, it could stay for an extremely long time, quite possibly over a billion years as Musk tweeted. This would take a good bit of $\Delta$v, however, compared to a simple low-periapse, eccentric orbit.

Phobos, which orbits at about 6000km, is predicted to either break up or impact Mars in about 50 million years. So we'll need a higher orbit than that. If this car is going to enter Martian orbit, they would most likely bring their periapsis very low, likely below 1000km, because the lower your periapsis, the faster you go at that point, and the faster you're moving, the more power you can get for a given amount of thrust (by the Oberth effect). This, of course, means you can use less fuel to get captured. So the best way to get into a super-stable orbit is to come in on a very close approach, burn retrograde to get captured, coast to apoapsis, and use the remaining fuel to raise your periapsis to a respectable altitude. I have not crunched the numbers on how much $\Delta$v it will actually have or how much it will need, however.

So, either there is going to be enough leftover fuel in that second stage (or I suppose maybe it's a third stage now?) to be able to get it into an orbit with a high periapsis, which could indeed last over a billion years, or he's only doing a flyby, or perhaps it won't actually last over a billion years. I don't know which of these is the case, but it will be easy enough to tell which of these is the case if it sends videos or pictures back, which I'm sure it will.

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