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The planet in my story, Ser, is actually in reality a moon orbiting a larger body called planet Rea. Ser is located in the L1 Lagrangian point, which means it takes the same amount of time to orbit the Sun as Rea does, always staying in between the Sun and Rea. From the perspective on Ser, Rea would not have phases and would always be full and would rise as the sun sets.

The L1, L2, and L3 Lagrangian points are unstable. Satellites in these locations need to regularly use fuel to keep themselves in place. In other words, a regular force needs to stabilize their orbits.

I need a way to explain a stable and completely natural L1 orbit. This does not need to be realistic in the sense of "the chances are a trillion to one", it just needs to be physically possible in a hypothetical sense.

My ideas have included regular perturbations from Rea's inner and outer moons, providing the necessary forces to stabilize Ser's L1 orbit. I believe that it is possible to have a rare, perfectly synchronized system of moons that together keep Ser stabilized in the L1 orbit.


CURRENT MODEL:
Sun Mass: 2.272571428571428571428 × 10^30 kg
Rea Mass: 1.8982 × 10^27 kg
Ser Mass: 2.27268625959933 × 10^25 kg
Rea Semi-major axis: 155037773.469 km
Ser Semi-major axis: 14654840.7502582 km
Rea Orbital Period: 360.312645 days (Earth days)
Ser Orbital Period: 360.312645 days (Earth days)


Constraints:
- Rea orbital period around the Sun = Ser orbital period around Rea = 360.312645 Earth days
- Viewed from Ser, Rea must rise as the Sun sets and must set as the Sun rises. (Part of the established history of Ser is that originally people thought Rea was Ser's moon, when it was actually the opposite.)
- Rea Mass = 1.8982 × 10^27 kg
- Ser Mass = 2.27268625959933 × 10^25 kg

Can Be Changed:
- Sun mass
- Rea orbital distance/semi-major axis
- Ser orbital distance/semi-major axis


Answers must: Calculate and provide information on the necessary forces to keep Ser in an L1 orbit. For an even better answer, improve upon my solar system model to make it more stable and provide insight on its maintainability.

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    $\begingroup$ The issue would seem to be stability over time. What sort of length of stable time period are you looking for? (Bearing in mind nothing is stable indefinitely) Are we talking thousands of years, millions, billions maybe even trillions if you want to push the boat out? $\endgroup$ – We are Monica. Sep 13 at 15:57
  • $\begingroup$ I can choose to go with any amount of time that could explain it properly. $\endgroup$ – overlord - Reinstate Monica Sep 13 at 16:16
  • $\begingroup$ We work here in such a way as to answer well-defined questions with a single identifiable best answer. You've given us a question which needs to be better defined in order to fit with our culture. When you have a moment, please take the tour and visit the help center to get a better idea of how we work. We would need to understand what you need, what your solar system is about, your star, other planets. What's the worldbuilding context that you're striving within? At present, I'm voting to put it on hold to prevent unhelpful answers from being posted 'till you can clarify. Welcome to the forum. $\endgroup$ – We are Monica. Sep 13 at 16:30
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    $\begingroup$ "I believe that it is possible to have a rare, perfectly synchronized system of moons" the n-body problem is decidedly tricky to solve, any near-magical configuration of the sort you're thinking about is vulnerable to peturbations from all sorts of sources that could input enough energy to upset the whole delicate balance. $\endgroup$ – Starfish Prime Sep 13 at 16:43
  • $\begingroup$ More generally, quasi-stable lissajous orbits are a thing, but when the ratio of the bodies involved is a bit small (like, planet:moon, rather than planet:satellite) you might not even manage the quasi- bit. The L4 and L5 points are also not going to be stable for a massive body like a moon. $\endgroup$ – Starfish Prime Sep 13 at 16:54
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An L1 lagrange point is not going to be stable. Even if you get that perfect "trillion to one" set of conditions needed to make it happen between the planet, moon, and star, the movements of other planets, and adjacent stars would not shift in phase with the local system. This means that the L1 will move relative to the planet/moon/star system. When this happens, the "saddle" will shift under your moon to either make it fall in towards the star or out towards the planet.

In other words, it needs some kind of active thrust to compensate for the moving L1 point and Ser can not naturally exist in this manner.

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    $\begingroup$ Rather than “fall into the star or into the planet”, I would guess it falls into an eccentric orbit about one or the other. $\endgroup$ – Anton Sherwood Sep 14 at 19:18

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