# Can a satellite at lagrange point be stabilized with gravity gradient?

Assuming that the satellite is big enough and the it is at the Lagrange point between the Earth and the Sun, can this satellite be stabilized with gravity gradient? (which means, can this satellite remain at the Lagrange point while one face towarding the Sun and one facing the Earth?)

I came up with a satellite which has two masses each at the end of tethers in opposite direction. But I'm not sure

1. if it is possible,
2. and if it is possible then one mass is also fine.
• If I were you I would not quickly accept the first answer that's posted. This is actually a sophisticated problem and will need some mathematical analysis in order to analyze. The current answer is just a guess based on intuition and analogy to a much simpler problem. You can always accept it later, but for now why not encourage more users to post an answer by not accepting the first one? See my comment below the currently accepted answer.
– uhoh
Jan 9 at 3:11

No, the mass that is close to the sun will be in a lower solar orbit, and so move ahead, while the mass that is closer to the Earth will tend to trail; it want to enter an Earth orbit.

These two masses will want to go in different directions. One of them will "win". But you are back to the basic problem of stability at the L1 point, it is like balancing a pencil on its tip: any perturbations from the point will tend to move the satellite away from the point and this process is cumulative: the further you are from the point the faster you move away.

Solar orbits near L1 can be achieved, but only with regular station keeping to maintain the satellite's position. There is no way to passively stabilise such an orbit.

• Note that tethered masses could presumably be used to generate force for station-keeping if they are on long rigid extensible struts that can change angle. It just looks like a really messy control problem, especially for lateral station keeping. Jan 8 at 15:56
• Then the most reasonable way to keep a satellite at L1 point and always facing sun is keeping itself rotating with thruster?
– Cho
Jan 8 at 16:07
• Yes. . . Are you aware of Space Exploration this kind of question may also be asked there. Questions of how to actually manage space craft are better on Space Exploration For example it may be possible to use gyroscopes or something to keep it aligned. Jan 8 at 16:15
• Certainly not exponentially. The gravity gradient varies as $r^{-3}$. Jan 10 at 22:48