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I have done a lot of searching online and while I have been able to find out that theoretically a moon could exist in a near-synchronous/stationary orbit, I am wondering if it is possible for multiple moons to exist in this state.

I'm not sure if I've explained appropriately or not, so if this needs to be a little clearer, please let me know.

The purpose of this question is that I am writing a novel and I had this idea that the planet has 9 moons and that the area of land that the story takes place in the moons only travel across the sky over the course of many days. One moon might take 60 days to get from one horizon to the other, while another might take 15 days, and others would be varying times in between.

In my limited knowledge, I have surmised that a moon closer to the planet would take less time to cross the sky than a moon further away. Obviously, for this to work, the moons would have to be in a supersynchronous orbit, not fully synchronous. Would the range of distance for supersynchronous orbits allow multiple moons to exist in staggered distances and still be close enough to remain visible from one spot continuously for multiple days at a time?

Disclaimer: I am not sure that this is the appropriate place to ask this question, since it is mostly theoretical. I also want to apologize if my English is confusing. Finally, weird letters and symbols in math make my head hurt, so I am sorry I cannot follow complicated mathematical formulas, but feel free to post them if you believe it may help answer the question.

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You may want to try the Worldbuilding site https://worldbuilding.stackexchange.com/

Anyway, what you're describing is more or less possible, with some caveats. A major question is that of stability - how long those configurations remain in place.

There are several notions you need to think about:

Geostationary orbit: it's the orbit where satellites have an orbital period equal to the planet's rotational period, so they appear stationary in the sky.

Roche limit: the lowest orbit where natural satellites remain in one piece. Any lower than that and they break up into pieces due to tidal forces.

Hill sphere: is the region where the planet's attraction dominates and satellite orbits remain stable (as opposed to being stolen by the star, etc).

Usually Roche limit < Geostationary orbit < Hill sphere.

Satellites at the geostationary orbit appear fixed. Those close to the geostationary orbit would indeed appear to move extremely slowly across the sky. Orbits higher than geostationary would appear to move backwards.

With regards to the long-term stability of multiple moons in various orbits, they would be stable if the orbits are far enough from each other, or if they're sitting in each other's Lagrange points. Also see here https://worldbuilding.stackexchange.com/questions/36929/stability-of-multiple-moons

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  • $\begingroup$ I've already looked into Roche limit, I don't believe that will pertain to the moons, due to the fact that all of them will be farther out than geostationary. Hill sphere might come into play if the orbits are more eccentric. I will look at the World Building SE later, although I did read the specific post on multiple moons already. Thanks for the help! $\endgroup$ – Ernesto Jul 25 '18 at 19:13
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To add to the answer above, (and this is kind of a world building answer), but your scenario, at the very least, would be unusual and difficult but maybe not impossible. The answer is a little surprising, but the way to do it is to make the moons smaller and bring them in closer to the planet. They'd have less gravitational interaction with each other that way.

Long answer:

It's not difficult to have a moon with a 60 day orbital period. Our moon, for example has a 27.3 day period (sidereal) with an apparent 29.5 day synodic cycle, full moon to full moon, but the moon basically circles the sky in a little bit over 24 hours because of the Earth's rotation. Any relatively distant moon will orbit it's planet slowly.

But that's not really the issue. If the planet has normal days, similar to 24 hour days on Earth, and I'm guessing by your question that you don't want the day/night period on your planet to be huge, then any distant moon's apparent orbital period will be determined by the planet's rotation period, similar to our moon which appears to orbit the Earth about once a day (25 hours or so). If your planet has what we might consider regular days, 12 hours, 16 hours, 24 hours, what have you, then your 9 moons would need to crowd around the geostationary radius and crowding an orbit with 9 objects that would be visible from the planet's surface is never a good idea.

9 visible moons from the surface along is a lot. Jupiter has over 60 known moons and more waiting to be discovered, but most of those wouldn't be distinguishable as moons from the planet's surface. Only the big 4 would be clearly identifiable as moons. The rest are too small. 9 visible moons is a huge number and crowding those 9 moons around the geostationary orbital radius is nuts.

But there is a way to do it and it's straight forward math. Bring the geostationary orbit closer to the planet by making the planet less massive and by increasing it's rotation period, shortening it's days.

Take Earth as a starting point. Earth's geostationary orbit is about 35,786 km above the equator, and the equator's radius is 6,378 km, so for orbital purposes, it's 42,164 km from Earth's center of mass. Both numbers are relevant.

If you reduce the mass of your planet to 1/2 the mass of the Earth (orbital period formula is proportional to (r^3/m)^.5), r^3 needs to equal 1/2, so r is reduced to 79.3%.

And if you increase the rate of rotation of your planet from 24 hours to 16 hours. The period is now 2/3rds and, same formula, the ratio of the period to the radius the power of 3/2. 2/3rds the period equates to a 76.3% of the initial radius. Combined, with these factors, the new geostationary radius, from the center of mass is 60.6% of 41,164, or about 24,933 km from the planet's center, or about (assuming 5,100 km radius for the smaller planet). 19,833 km from the surface.

If you make the planet even smaller or the planet's rotation period even faster, you can bring the moons even closer. So, why does this help you?

As you bring the moons closer to the planet's surface you can make them smaller and they can still be visible. As you make a moon smaller, say you reduce it's radius by 50%. It's mass is reduced by a factor of 8 but it's angular diameter is only reduced by a factor of 2 and it's apparent brightness by a factor of 4. By shrinking your planet and by increasing it's rate of rotation you move the geostationary orbital radius closer in and you can make the moons smaller but they can still be visible. By making them smaller, they would have less gravitational interaction with each other and you could theoretically have 9 small moons in tight orbits, visible from the planet's surface, with relatively long rotation periods. You could explain the collection of small moons as the result of a collision between two moons. It's a stretch, but not impossible.

If you want astronomical accuracy though, moons that close to a planet would pass through the planet's shadow fairly often and given their size, they'd probably disappear from view. You could offset that somewhat by giving the planet a sizable axial tilt and the moons orbit the planet's equator, but they could still pass through the planet's shadow as the planet approached it's spring and fall equinox.

All that said, most of the Moons should still have a not that slow orbit, 1-2-3 days. Getting a 60 day orbit requires the moon be very near to the geostationary radius and another with 15 days, that's also quite close. You shouldn't have to many moons with long period orbits because there's no realistic way to do it, but you could have 2 maybe 3 in the 10-60 day range, and I'd push the others out into the 1-2-3-5 day range. You could even have a retrograde moon if you wanted. It wouldn't really be retrograde, it would just appear that way because it orbits the planet faster than the planet rotates.

If you wanted to get creative, you could have a Janus/Epimetheus dance. :-)

A final point. Your moons in this scenario shouldn't be round. They would be small enough to be lumpy potato like objects.

(too long?)

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