Lagrange Points regarding a moon 1.5 times the mass of Earth's Moon and one 0.75 times the mass of Earth's Moon

Working on a lunar orbit system. As place holder numbers, two moons are orbiting a planet equal to earth's mass. One moon, Selenara, is 1.5 times the mass of Earth's moon, and the other, Thoth, is .75 times the mass of Earth's moon. I want these two moons to have the same orbital period/lunar month--as in, it takes them each thirty days to complete their cycle.

Primary Question: How can I place the moons to make their orbits viable? I am interested in them preferably sharing the same lunar month, but if better options exist I would like to know.

Desired outcomes: I would prefer for both moons to be visible in the sky simultaneously at some points of the month, however I also wanted them to be in different points in their phases, which I suspect isn't possible.

If it is impossible, I want them at opposite orbits to each other(as in, while one is on the sun facing side of the planet, the other is on the night side).

Other Notes: Selenara, the bigger planet, is meant to support some life. Life was terraformed here at some point, and I need it to be viable. Any issues that orbital mechanics might cause should be avoided.

• There's probably the core of a good question here, but a few problems currently - the [science-based] and [internal-consistency] tags are mutually exclusive, as per the descriptions of each - please remove one of them, probably the latter. Also note that it is one question per post - it isn't clear if your primary question is about Lagrange points or how to arrange for 2 moons with the same orbital period to exist (and somehow be visible simultaneously and directly opposite each other in orbit???) The requirements appear to be directly contradictory, please rephrase. Commented Jun 1 at 8:17
• Lagrange points only really work if the two orbiting bodies are sufficiently different in mass - a good rule of thumb is the larger should be between 25 and 100 times the size of the smaller. If they're too close in size, the gravitational influence of the smaller on the larger becomes significant, and their orbit is much more chaotic. Commented Jun 1 at 8:24
• Question has Thoth at two different mass ratios.
– Ash
Commented Jun 1 at 9:34
• @cadence do you know if that's the case over astronomically short time scales? It may not matter if the orbital synchronicity will soon desynchronize, or even if Littlemoon is a recent chance capture soon to be ejected, or even if the whole system is soon doomed to a fiery demise, if "soon" is fifty thousand years from now.
– g s
Commented Jun 1 at 14:57
• @Ash Thanks, I resolved that error now. Commented Jun 1 at 17:21

I want these two moons to have the same orbital period/lunar month--as in, it takes them each thirty days to complete their cycle.

With their specified masses, this is not possible. If Thoth was a lot smaller, at most a thirtieth of Selenara's mass, but preferably rather less, then Thoth could be in the L4 or L5 point of Selenara's orbit and would be stable there. As it is, their masses are too similar, and Lagrange stability will not apply. Their orbits would be chaotic and unpredictable; the likeliest outcome is that they collide and end up forming a single moon. The fragments thrown off in the collision would do a lot of damage to the planet's surface.

Putting Thoth at Selenara's L1, L2 or L3 points will not make a significant difference, and a collision is, again, the likeliest outcome. Those points are unstable no matter how tiny Thoth's mass is; satellites in Earth's L1 and L2 points need to use thrusters to stay there.

Making Thoth low enough mass for it to be stable in L4 or L5, while retaining its apparent size and visibility, requires that it be a balloon. Earth's moon's density is only 3.3g/cm3; cutting its mass enough requires a density of 0.1g/cm3 or less, and there's no solid natural material with such a low density. Of course, a pressurised balloon will be punctured by meteoroids very soon on an astronomical timescale.

Having the two moons in different elliptical orbits with the same 30-day period won't work either: they're too close together and will perturb each other, leading to a collision.

The nearest thing to a workable solution is to have Thoth in a circular orbit quite close to the planet, not far outside the Roche limit, and Selenara in a distant circular orbit, not far inside the planet's Hill Sphere. This is not stable either, but you'll probably get a few million years before they collide.

I would prefer for both moons to be visible in the sky simultaneously at some points of the month

You'll get that with this solution, but the time of the month when they're both visible will change from month to month.

I also wanted them to be in different points in their phases, which I suspect isn't possible.

They will be at different points in their phases most of the time, but what the phases are when they're both visible will change from day to day.

If it is impossible, I want them at opposite orbits to each other(as in, while one is on the sun facing side of the planet, the other is on the night side).

That's the really impossible one, if you're using anything like real astrophysics. To make that stable, you need a magical universe, or super-advanced science that can push large moons around without any kind of drive flame.

• Yikes, I knew Thoth was too heavy for a Lagrange Orbit, I didn't realise by how much.
– Ash
Commented Jun 1 at 21:11
• Thank you, this was very helpful. I know how to proceed now. Commented Jun 2 at 2:57
• Isn't there moons in Co-orbital orbits(sharing the same orbit) around Saturn? Or does that just work since the orbital radius is a lot bigger? I don't see why the moons cant have the same dynamic as Epidemus or Janus. Commented Jun 3 at 15:56
• @bubbles: Bigger orbital radius, and moons both tiny compared to Saturn. May well not be stable forever, too. We're still learning the history of ring systems. Commented Jun 3 at 21:58

The only places I think you could put Thoth with stability is Selenara's L4 or L5 Lagrange Point, these are the attractive Lagrange points, they tend to accumulate mass in the form of Trojans. I'm pretty sure this would also lead to the phase inconsistency you're interested in as Thoth would be 60° ahead of, or behind, Selenara. Both bodies would, by default, be visible in the sky at certain times of the day and night, assuming one can see more than 60° of sky arc, since they share an orbital track. However, I'm pretty sure that as written Thoth is simply too massive to be a Trojan without creating orbital instability. You could play with the density, have Thoth look half the size but be a primarily icy body that has a very low mass for it's apparent size but that's a different question.

• Lagrange points do not work for objects of comparable mass. One must be very much lighter than the other. Commented Jun 1 at 13:58
• L3 is off the table? I would have assumed the distance would balance out the orbit. Is it because Selenara is three times as massive as Thoth? Commented Jun 1 at 17:26
• @AlexP Yes that's why I said "I'm pretty sure that as written Thoth is simply too massive to be a Trojan without creating orbital instability".
– Ash
Commented Jun 1 at 21:07
• @Danvad Yes, nothing to do with mass balance, Thoth is probably degrees of magnitude too heavy, but L3 is of the table due to orbital mechanics even if it were light enough.
– Ash
Commented Jun 1 at 21:09