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I know that the Sun-Earth system has 5 Lagrange points, and there are five more Earth-Moon associated Lagrange points; so ten in all that are in some way associated with the Earth.

Since Mars has two natural satellites compared to Earth's one, would it have a total of fifteen associated Lagrange points?

Might the points associated with Mars' natural satellites be in any way useful in terms of artificial satellite orbits?

Rickest Rick
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    That is a question for astronomy, not for space exploration. The answer is to be found in Wikipedia here. The mathematics of Langrange points are valid for any large two bodies, even for extrasolar planets and their star. In our solar system they are valid for a planet and the Sun but also for a planet and its moon. – Uwe Mar 15 '18 at 14:52
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    @Uwe Since Lagrange points figure so prominently in the locations and orbits of spacecraft, they are not necessarily off-topic here. It depends to some extent on the motivation of the question, which so far is completely absent here. – uhoh Mar 15 '18 at 14:54
  • This is a MUCH better question! If you asked if the Mars-Deimos or Mars-Phobos Lagrange points were at all useful, then this would be truly about Space Exploration. – uhoh Mar 15 '18 at 14:58
  • My thought is Phobos and Deimos are so small that do their L points even matter? – geoffc Mar 15 '18 at 15:00
  • @Uhoh, I agree, but that seems to be too big of a change to the question. If someone were to have answered the question already, their answer would look to be completely off topic to future visitors, possibly resulting in down-votes to that answer. Even though I'd like to have better questions out in the wild, I also don't want to discourage people from answering my questions! – Rickest Rick Mar 15 '18 at 15:01
  • @RickestRick oh you are of course welcome to roll back. It's just a suggestion. In this case I was pretty sure there would be no answers appearing, considering... To roll back, just click the "edited" button and look back at the edit history. Or I'm happy to do it too. – uhoh Mar 15 '18 at 15:03
  • @geoffc The theory of Lagrange points is only about two large bodies. I think Phobos and Deimos will have also L. points, but the question is about their stability. – Uwe Mar 15 '18 at 15:03
  • @Uwe If the moons are small enough, they will completely cease to be equilibrium points due to gravity from the Sun and Jupiter etc. They will essentially disappear. – uhoh Mar 15 '18 at 15:07

2 Answers2

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The Phobos and Deimos L1 and L2 points are virtually coexistant with the moons themselves. I have seen that the L1 point for Phobos is 10 km above the moon. At that altitude, just build a large tower. L3 does exist for both, but it will be a very small area. L4 and L5 likely exist, and are somewhat larger, but they still won't have a significant effect.

Bottom line is, the 5 Mars-Sun points are all worth something. The moons, while they may exist, they are such a small size that they are not practical for any real use. The stability won't be significantly enhanced by being in one of the Lagrange points.

SE - stop firing the good guys
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PearsonArtPhoto
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    Great answer! Equations and script to calculate the distance found in this answer. – uhoh Mar 15 '18 at 15:16
  • -1 for "just build a large tower". Landing construction materials on Phobos via rockets would kick up a cloud of dust and debris that would last a long time. A tether from MPL1 or MPL2 would be a better way to lower materials to Phobos. A Phobos probe at MPL1 has been proposed. Also MPL1 and MPL2 are about 3.5 km from Phobos' surface. – HopDavid Mar 18 '18 at 04:31
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For tide locked moons the L1 and L2 points could play the same role that planet synchronous points play in Clarke towers.

Simultaneously lowering a tether from MPL1 Phobos ward and extending a tether Marsward can keep the tether hub balanced until the tether reaches Phobos.

enter image description here

The Mars Phobos L1 is a little more than 3 kilometers above Phobos' surface. A tether more than 7 kilometers long would be sufficient to maintain tension.

Soft landings via rockets on Mars' tiny moons would kick up dust and debris. Many particles would be near the moon's escape velocity and remain within the moon's Hill Sphere for a long time. This debris cloud is undesirable.

But using a tether from MPL1 or MPL2, materials can be lowered to the moon's surface without kicking up debris. There is a MPL1 based probe proposed where a tether would lower sensors near the surface of Phobos.

Once a tether is anchored to the moon, it can have a length greater than 7 kilometers. A 1,400 km Marsward tether could drop payloads into an orbit whose periapsis passes through Mars upper atmosphere.

A ~1000 km tether ascending from Phobos and a ~3000 km tether descending from Deimos would enable a Zero Relative Velocity Transfer Orbit (ZRVTO) between the two moons.

enter image description here

Using this ZRVTO the two moons could exchange cargo and passengers while using nearly zero reaction mass.

HopDavid
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