In my fascinating imagination, I am seeing a space elevator from the vulcano Olympus Mon to the moon Phobos. Phobos also seems to keep spaceships - while a smaller shuttle attaches itself to the elevator and travels down- they can also travel inside Olympus Mon. I was wondering if this is mathematical possible and it seems, it is.
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$\begingroup$ You would have to put Phobos into a much higher orbit, first and even then Olympus Mons is not located on the equator of Mars, so you can't put an object into a stationary orbit right above that place. To compensate for that, you would need, at least, a second elevator cable. It doesn't sound like it's worth doing either, especially since escaping Mars gravity with a rocket is so much easier than launching on Earth. The problem with the space elevator is that where it would be needed, the concept is tough to implement, and where it's easy to implement, one does not really need it. $\endgroup$– CuriousOneCommented Oct 4, 2014 at 3:32
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$\begingroup$ The close votes are a bit harsh. The question is whether a space elevator could be built from Olympus Mons to Phobos. This is a perfectly reasonable question, and the answer is no for the physical reasons explained by CuriousOne. @CuriousOne: do you fancy turning your comment into an answer? $\endgroup$– John RennieCommented Oct 4, 2014 at 5:56
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$\begingroup$ @JohnRennie: If you don't mind. I agree that there is a non-trivial question in there. $\endgroup$– CuriousOneCommented Oct 4, 2014 at 6:33
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$\begingroup$ Related: physics.stackexchange.com/q/33547/2451 $\endgroup$– Qmechanic ♦Commented Oct 4, 2014 at 7:28
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2$\begingroup$ Probably worth mentioning that Kim Stanley Robinson in his Mars trilogy [SPOILERS] decided to position the space elevator between Pavonis Mons (which is very close to the equator) and a smaller asteroid captured for the sole purpose of this enterprise. Phobos and Deimos are larger, and were more suited for other needs (for example military) $\endgroup$– malinaCommented Oct 4, 2014 at 7:58
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1 Answer
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The space elevator probably deserves an entire series of questions (and I am sure there have been plenty of posts), but if we stick to this particular version, there are a couple of problems with it.
First of all, a space elevator needs a counterweight in an orbit that is higher than the areostationary orbit (the Martian equivalent of Earth's geostationary orbit). In case of Mars that orbit lies approx. 17,000km (11,000 miles) above the planet's equator. Phobos is in an orbit with a semi-major axis of just 9376km (5826m miles). It orbits the planet every 7 hour 39 minutes with an orbital velocity of 2.138 km/s, while even an areostationary orbit would require an orbital speed of a mere 1.45km/s. We are therefor tasked to give a large object (the mass of Phobos is 1e16kg) a delta-v on the order of at least 1km/s to get it into place. That requires a lot of energy (and propellant mass), which one could use to launch a lot of payload with conventional rockets, instead!
Anchoring the space elevator over Olympus Mons is also not an easy option. This spot lies at 18.65 degrees North of the equator. Since our counterweight has to be above the equator, we would need a second cable located 18.65 degrees South. Now we have two elevators, but they are both under a slight angle, which doesn't make the design any easier.
If we let go of the particular location and we place a conventional design between a spot on the equator and a smaller counterweight above, we are certainly going to make our lives a little bit easier.
Deimos, on the other hand, is almost in the right place for a counterweight, it seems. With an orbital period of approx. 30 hours and a mass of 1.4e15kg it's a lot closer to what we need than Phobos... except, of course, that we still have to watch out for Phobos cutting our cable every eight hours, which means that we have either to deploy a movable cable (which is not particularly hard compared to the extreme engineering that we already had to do) or we have to use two cables separated by a few degrees, again, so that Phobos can just slip trough our sky-hook!
answered Oct 4, 2014 at 7:16