Is Lagrange point L1 stable? If I were to place a space station in L1 will it remain in orbit without any difficulty? If there are any difficulties, please mention them here along with any suggestions to overcome the difficulties, if possible.
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L1 is unstable, although you can establish a fairly stable halo orbit around L1 -- but even a halo orbit will require periodic correction.
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3$\begingroup$ In fact, none of the Sun-Earth or Earth-Moon Lagrangian points are stable in the long run, in a real world that includes Venus and Jupiter. They all require periodic correction. $\endgroup$ Apr 6, 2015 at 23:56
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Something parked at L1 is balanced between evenly matched tug-of-war teams.
On one side of the tug-of-war is the moon's gravity and inertia in a rotating frame (what we used to call centrifugal force). On the other side is earth's gravity.
Go a little bit to the left and Earth has the advantage. Move a little bit to the right and the moon and so called centrifugal force get stronger.
So just a tiny nudge destroys this delicate balance. Something at the Earth Moon L1 (EML1) needs station keeping.
If you want something high up that is long lasting and maintenance free, I would suggest a lunar Distant Retrograde Orbit (DRO).
An example of a moon in a DRO is Jupiter's S/2003 J2. According to the Wikipedia article:
Retrograde moons with axes up to 67% of the Hill radius are believed to be stable.
The moon's Hill radius is about 60,000 kilometers. So a lunar retrograde orbit at 40,000 kilometers would be pretty stable.
And in fact a lunar DRO is one of the suggested destinations for the proposed asteroid retrieval mission.
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$\begingroup$ Hello ... thanks !! I'd like to know the difference of both the DRO and Low Lunar Orbit, if possible ! Thanks :D Do let me know which is better for the conditions mentioned hitherto (question) !! $\endgroup$ Apr 7, 2015 at 19:14
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$\begingroup$ The ceiling for a DRO would be 50,000 km from the moon. I believe such an orbit could stick around for decades or centuries. For more stable orbits, lower it to 30 or 40 thousand kilometers. Low lunar orbits would be disrupted by lunar mass concentrations (mascons). The low orbits aren't stable. $\endgroup$– HopDavidApr 7, 2015 at 23:10
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$\begingroup$ can we have a DRO as close as 500 km ? will that be stable ? I need to get it as close as possible .... Please do help, your answers are very convincing ... $\endgroup$ Apr 8, 2015 at 22:21
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$\begingroup$ @AshwinRamachandran I don't the the altitude at which mascons become a destabilizing influence. Perhaps that would be a good question for you to ask. $\endgroup$– HopDavidApr 9, 2015 at 16:33