<p>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.</p>
<p>These two masses will want to go in different directions. One of them will &quot;win&quot;. 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.</p>
<p>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.</p>

CC BY-SA 4.0
2023-01-08T15:56:37.013Z
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.
Anders Sandberg
CC BY-SA 4.0
2023-01-08T16:07:39.493Z
Then the most reasonable way to keep a satellite at L1 point and always facing sun is keeping itself rotating with thruster?
Cho
CC BY-SA 4.0
2023-01-08T16:15:55.197Z
Yes. . . Are you aware of [space.se]  this kind of question may also be asked there.  Questions of how to actually manage space craft are better on [space.se]   For example it may be possible to use gyroscopes or something to keep it aligned.
James K
CC BY-SA 4.0
2023-01-08T16:21:27.140Z
Thank you, your answers really helped me a lot :)
Cho
CC BY-SA 4.0
2023-01-09T03:09:19.377Z
My feeling is that for this problem where there are both gravitational forces from two bodies and centrifugal forces present (in the rotating frame) and now the third, extended and potentially rotating (in and out of plane) body can dynamically explore the gradients of those forces, a quick, off-the-cuff answer based on "a pencil on its tip" without using any mathematics nor citing any sources is not justified.
uhoh
CC BY-SA 4.0
2023-01-08T14:25:46.830Z
2023-01-08T14:25:46.830Z
James K
<p>You don’t realize just how wimpy the gravity-gradient effect is. In low Earth orbit, the gravity gradient force is only relevant because it’s an inertial situation, with no other effects overwhelming it. The gravity gradient then falls exponentially with altitude, so a craft in non-low-Earth orbit would need tether-like lengths (not a boom) to be stabilized with a palpable force.</p>
<p>The gravity of the Sun is stronger, but so is the range, and range wins. Wins easily. Meanwhile you’ve also left Earth’s radius of (palpable) influence, by definition. Calculate the length required for a gravity-gradient stabilizer: I’m already supposing, without even doing one bit of math, it’s a length beyond our current technology.</p>

CC BY-SA 4.0
2023-01-10T22:48:08.367Z
Certainly not exponentially. The gravity gradient varies as $r^{-3}$.
Martin Kochanski
CC BY-SA 4.0
2023-01-14T19:52:25.250Z
@Martin Kochanski  So… our GEO birds all launched with gravity gradient booms that were too long? Oh wait, I can cite no GEO comsat with a GG deployable and tip mass, despite having logistical and profit motive. And don’t tell me the Rhyolite/Orion series. Neither comsat companies, let alone Cho, are getting Black funding levels.
caInstrument
CC BY-SA 4.0
2023-01-14T19:55:22.463Z
…and I could also point out that a fractional exponent is an exponent, except flight best practice beats flight demonstration beats a picture beats a thousand words.
caInstrument
CC BY-SA 4.0
2023-01-10T18:02:22.313Z
2023-01-10T18:02:22.313Z
caInstrument
<p>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?)</p>
<p>I came up with a satellite which has two masses each at the end of tethers in opposite direction. But I'm not sure</p>
<ol>
<li>if it is possible,</li>
<li>and if it is possible then one mass is also fine.</li>
</ol>

CC BY-SA 4.0
2023-01-09T03:11:35.643Z
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](https://astronomy.stackexchange.com/a/51546/7982) below the currently accepted answer.
uhoh
<gravity><lagrange-point>
Can a satellite at lagrange point be stabilized with gravity gradient?
Cho
# Can a satellite at lagrange point be stabilized with gravity gradient?

(Asked by: username_0 on 2023-01-08)

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.

**Tags:** gravity, lagrange-point

> **Comments:**
> **username_1**: 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](https://astronomy.stackexchange.com/a/51546/7982) below the currently accepted answer.  

---

## 2 answers

### Answer by username_2 on 2023-01-08. Score: 1 | Accepted answer

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.

> **Comments:**
> **username_3**: 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.  
> **username_0**: Then the most reasonable way to keep a satellite at L1 point and always facing sun is keeping itself rotating with thruster?  
> **username_2**: Yes. . . Are you aware of [space.se]  this kind of question may also be asked there.  Questions of how to actually manage space craft are better on [space.se]   For example it may be possible to use gyroscopes or something to keep it aligned.  
> **username_0**: Thank you, your answers really helped me a lot :)  
> **username_1**: My feeling is that for this problem where there are both gravitational forces from two bodies and centrifugal forces present (in the rotating frame) and now the third, extended and potentially rotating (in and out of plane) body can dynamically explore the gradients of those forces, a quick, off-the-cuff answer based on "a pencil on its tip" without using any mathematics nor citing any sources is not justified.  

---

### Answer by username_4 on 2023-01-10. Score: 0

You don’t realize just how wimpy the gravity-gradient effect is. In low Earth orbit, the gravity gradient force is only relevant because it’s an inertial situation, with no other effects overwhelming it. The gravity gradient then falls exponentially with altitude, so a craft in non-low-Earth orbit would need tether-like lengths (not a boom) to be stabilized with a palpable force.

The gravity of the Sun is stronger, but so is the range, and range wins. Wins easily. Meanwhile you’ve also left Earth’s radius of (palpable) influence, by definition. Calculate the length required for a gravity-gradient stabilizer: I’m already supposing, without even doing one bit of math, it’s a length beyond our current technology.

> **Comments:**
> **username_5**: Certainly not exponentially. The gravity gradient varies as $r^{-3}$.  
> **username_4**: @username_5  So… our GEO birds all launched with gravity gradient booms that were too long? Oh wait, I can cite no GEO comsat with a GG deployable and tip mass, despite having logistical and profit motive. And don’t tell me the Rhyolite/Orion series. Neither comsat companies, let alone Cho, are getting Black funding levels.  
> **username_4**: …and I could also point out that a fractional exponent is an exponent, except flight best practice beats flight demonstration beats a picture beats a thousand words.  

---

