Do Mars' Lagrange Points Exist Near Phobos and Deimos? (2024)

Yes, I forgot to mention that the above query is tied up with my writing - hence it being placed in Physics Forums' SF category.

Do you mean Sun-Mars Lagrange points, or Mars and its satellites?

Both L1 and L2 do exist, but they are not stable ie the probability of anything there is close to zero. Certainly nothing large enough to observe, perhaps some small debris. L4 and L5 probably have something as Mars is fairly close to the asteroid belt and has probably picked up some smaller asteroids that tag along at those two points. Jupiter certainly has them, and any moons, asteroids, or rocks at the L4 or L5 locations are called Trojan satellites.
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Bandersnatch's question is valid, but the points "Mars and its satellites" he is referring to are definitely unstable and nothing (of any size) would be there. Actually the one of the two moons is already inside the Roche limit and if the moon was any larger, it would be torn apart.

The Sun-Mars L1 and L2 are located approx. 1 million kilometers from Mars. They are, as was said, long-term unstable, so you won't find any natural object orbiting there. But you can still put a satellite or a space station around one (likely on a Lissajous orbit), and keep it there artificially with periodic application of thrust.
I don't know how much delta-v is needed, how often, to keep stuff there, but it'll certainly be a bigger problem for larger masses. Depending on hardness of your s-f you could just entirely handwave it, or mention some unspecified on-board ion (or whatever) thrusters that are used for station keeping.

Personally speaking, I'm reluctant to handwave anything at all if I can possibly help it. Still, there's a limit to what might be described as hard-nosed SF and there's been several occasions in the past when I've had to hold my nose and engage in a spot of handwaving - if only to keep things moving. Certainly, the periodic attitude thrusts by a slowly revolving space station would be a convincing enough solution. I gather the ISS has to do this from time to time in order to maintain its orbital path round the Earth, likewise the HST. Well, if it works in reality, why not in fiction?