# Is it possible to establish a synchronous lunar orbit without using Lagrange points? [closed]

I find this interesting, and so far haven't found anything in an internet search.

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• Do you think on some powered trajectory? – peterh Mar 30 at 15:52
• Synchronous with what? A point on the lunar surface? A point on Earth? – Nathan Tuggy Mar 30 at 17:40
• Can you explain carefully what you mean by "synchronous"? Please edit such an explanation into the question. Otherwise it is not really possible to answer it. – Steve Linton Mar 30 at 17:48
• Possible duplicate of this question on Astronomy.Stackexchange: astronomy.stackexchange.com/questions/20499/… – Dave Gremlin Mar 30 at 17:58
• @SteveLinton "synchronous lunar" ↔ "lunar-synchronous" ↔ "lunasynchronous" ↔ "geosynchronous lunar orbit" ↔ GLEO? – uhoh Mar 31 at 7:34

The Moon’s rotational period is the same as its orbital period: the points on its surface are (approximately) always in the same relationship to Earth. Because of this it is convenient to switch to a frame that rotates with the Earth-Moon system.

Then we're in luck, because now the problem has already been exhaustively explored for us!

Euler found the collinear stationary points L₁ through L₃ and Joseph-Louis Lagrange added the triangular stationary point L₄ and L₅ thereby completing the picture and showing mathematically that these are the only five stationary points in a CR3BP or circular restricted three-body problem. This was briefly mentioned elsewhere as well.

So in a word, no.

For a tidally locked body there are not going to be any points stationary to the surface other than Lagrange points.

If the Moon was spinning (much) faster (i.e. a long time ago), then a stable synchronous orbit may have been possible. But I’m not sure it was ever spinning that fast.

• The Moon was indeed spinning faster long ago, but it could have been tidally locked to a faster rotating Earth. Looks like we are going to have to use Lagrange points through time as well as space. – Oscar Lanzi Mar 30 at 22:21
• The Moon was spinning much faster than it is now a long time ago, but it was also a lot closer to the Earth back then. From everything I've read, the Moon became tidally locked very, very early. If the giant impact hypothesis is at all correct, the Moon formed less than 6 Earth radii from the center of the Earth. This would have made tidal forces on the Moon then over a thousand times stronger than they are now, which in turn would made the tidal locking time very, very short. The Moon has been tidally locked for 4.5 billion years. – David Hammen Mar 31 at 19:54