# Is the following plausible: a moon at an L1 point orbits a gas giant, which orbits a sun. the moon is submerged in half daylight half moonlight

I'm writing a sci-fi & fantasy novel, I won't get into details, but in essence it's set on a fantasy moon that orbits a gas giant, which orbits a sun. The moon is at an L1 (Lagrange 1) point, and seems like it would be rather stable with the conditions I've created for it in terms of size, distance, etc. The basic premise (that I'm hoping for, anyway) is that one side of the moon exclusively faces the sun and is in constant day-time, while the other face exclusively faces its gas giant, which reflects the light from the sun back to the moon just enough to submerge that face of the moon into a relative twilight. Here is a very basic diagram (evidently not to scale) of what I've thought up:

I just want to ask if this is all plausible? Up for hearing any solutions or explanations, astronomy isn't my forte really but it is so interesting to me :)

L1 Lagrange point is unstable, so it would be too much to expect a moon to appear at that point naturally or stay in it for many million years, but otherwise yes, this setup is possible.

The L1 point is a point of unstable equilibrium, as stated already by Alexander. This means that a body without active control of its orbital parameters would soon move out of that point due to gravitational perturbations.

Moreover, a body in L1 would not be orbiting the planet but the star, which goes against your requirement of "a moon orbiting a planet which is orbiting a star".

Such a settng would be impossible to happen naturally. But if your story is sufficently soft on the Mohs Scale of Science fiction Hardness - TV tropes warning -

https://tvtropes.org/pmwiki/pmwiki.php/Main/MohsScaleOfScienceFictionHardness[1]

Or if your story isn't science fiction at all but a fantasy which happens to be set on another planet (like Eddison's The Worm Ouroboros), you can go ahead and write it anyway.

The L1 point.

In your concept the moon or planet is not orbiting the gas giant planet in the L1 posiiton, it is orbiting the sun in the L1 position relative to the gas giant planet. So your question's title is misleading.

The triangular points (L4 and L5) are stable equilibria, provided that the ratio of M1/M2 is greater than 24.96.[note 1][6] This is the case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller margin, the Earth–Moon system. When a body at these points is perturbed, it moves away from the point, but the factor opposite of that which is increased or decreased by the perturbation (either gravity or angular momentum-induced speed) will also increase or decrease, bending the object's path into a stable, kidney bean-shaped orbit around the point (as seen in the corotating frame of reference).

The points L1, L2, and L3 are positions of unstable equilibrium. Any object orbiting at L1, L2, or L3 will tend to fall out of orbit; it is therefore rare to find natural objects there, and spacecraft inhabiting these areas must employ station keeping in order to maintain their position.

https://en.wikipedia.org/wiki/Lagrange_point#L1_point[2]

Thus it would be extremly improbable that natural forces would keep your planet in the L1 posiiton for the millions of years required for the planet to naturally become habitable for humans or similar beings or to develop higher life forms, or otherwise become an interesting setting for most types of stories.

So it would be a rare coincidence that a planet which had a relatively stable and different orbit for billions of years happened to drift into the L1 position and remain in during the period your story was set in. And it may be easy for sientists in your story to calulate that when the planet leaves the L1 position its new orbit will make it too hot or too cold for life to survive, or even that it will collide with the gas giant planet or the sun or be ejected into interstellar space. Thus a planet which is in the L1 poistion for a relatively short time could face impending doom when it leaves the L1 position.

Of course the planet could be moved to the L1 position and kept there for a long time, perhaps billions of years, by a sufficiently vast project by a sufficiently advanced civilization if they have a reason to. Maybe a science fiction story set on such a planet has become a classic in their society and they decide to create such a planet to honor the story! And possibly a plot point could be a threat by terrorists on the planet to shut off the machinery that keeps the planet in the L1 position.

Or possibly the advanced civilization terraforms the planet to make it habitable, and seeds it with life.

Part two: Becoming Tidally Locked.

You want the planet to become tidally locked.

The planet can not be tidally locked to the gas giant planet because it is not orbiting the gas giant planet. Thus the planet would have to become tidally locked to the star in the system.

But the planet should be orbiting too far from its star to become tidally locked to the star.

A small difference in the mass of stars creates a larger difference in their luminosity. So if a star is 10 percent less massive than the Sun, for example, it will have a luminosity les than 90 of the Sun's luminosity. So a low mass star will have very low luminosity, and its circumstellar habitable zone will be much closer to it than is prob protional to its mass. The distance to a star's circumstellar habitable zone will be prportional to its relative luminosity and not proportional to its relative mass.

So planet's in a dim stars circumstellar habitable zone will orbit very close to that star and where that star's gravity - proportional to the star's mass and not to the star's luminosity - will be very strong, and will swiftly slow down the rotation of the planet and tidally lock it to the star.

So a planet 200,000,000 kilometers from its star as specified in the question would not be tidally locked to the star unless that star was super massive - which would make the star super luminous and the planet super hot, too hot for Earth like life forms.

So one theory might be that the planet originally orbited about 210,000,000 kilometers from the star and had a short day but when it was very young it collided with a massive planet sized object which greatly slowed down the rotation of the planet. It is believed that the strange rotations of Venus and Uranus were caused by such collisions early in the history of the Solar System.

So the planet might now have a day slowed down to just a small bit shorter than its year at a distance of 210,000,000 kilometers. With such a long day already, the comparatively weak tidal interactions with the star might be enough to quickly (astronomically speaking) slow slow down the rotation of the planet a small bit more and make it tidally locked to the star.

Then the gas giant planet which formed much farther from the star might migrate inwards towards the star and eventually take up a permanent orbit at 210,000,000 kilometers from the star. And possible that might force the tidally locked planet to migrate inwards to an orbit at about 200,000,000 kilometers from the star, and then wander into the L1 position of the gas giant planet.

I haven't done any calculations, but I suppose such a scenario could possibly be possible.

Of course that would still require the actions of an advanced ciivlization to keep the planet in the L1 position relative to the gas giant planet for the billions of years necessary for the planet to become interesting for most types of stories.

Or possibly the advanced civilization terraforms the planet to make it habitable, and seeds it with life.

Conclusion:

Your setting is impossible to happen naturally in the real world. Thus it is not suitable for use in a hard science fiction story. But it would be quite acceptable in a very soft science fiction story or in a pure fantasy story set on a distant planet.

• Would there be any stable configuration involving other planets that could fix the planet in this configuration? Or if it were a small star and the planet was much closer? Perhaps the planet is at the L4 or L5 point of another body, which somehow (?) can correspond to the gas giant's L1 point? I can't quite put the tinker toys for that together in my head. – DWKraus Apr 9 at 17:36
• @M. A. Golding, you have something of an alternative of just giving them close orbits and making the gas giant/moon/planet large. It would wobble a little, but the configuration would be stable. – Madman Apr 9 at 17:53