Under which conditions could a planet's massive moon's orbit get closer to the planet?

Question

The recent question How do we know the Moon was much closer than it is now? has piqued my interest. The answers are numerous and clear. But I started to wonder. The question includes the following fragments:

...is it an assumption based on the fact the moon is moving away right now, so it's a simple extrapolation backwards in time?

Could it possibly be the Moon distance oscillates?

I thought that there would also be a way to try to exclude the possibility of inwards motion based on the assumed composition of the Earth (core, mantle, crust, oceans) over billions of years to the extent that those assumptions might be true.

I'm no geologist, geophysicist, planetologist, planetary scientist nor astronomer, but I have some ability to write Stack Exchange questions, so I'd like to ask:

Question: Under which conditions could a planet's massive moon's orbit get closer to the planet?

Different but related:

• Where do we have it from that the Moon is migrating away from Earth?
• Why do Earth and moon move apart but binary black holes move closer?

For example, for certain combinations of planet/moon mass ratio, or their compositions and structures, or orbital altitude and plane (e.g. equatorial, inclined, polar, retrograde) or eccentricity, are there ways to obey conservation laws (energy and angular momentum) that can still get a moon to migrate inward?

Could adding a second moon that eventually escapes to infinity help?

I guess something vulgar¹ like a direct impact from a rogue moon or asteroid could do it, but that feels like cheating.

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¹"lacking sophistication or good taste. 'a vulgar check² suit'" (Oxford languages via google)

²cf. check suit from Walmart - https://i.sstatic.net/pGBw7.jpg

Answer 1

Yes, it is possible for a moon of a planet to move closer to the planet. If a moon moves close enough to the planet, the moon will eventually reach its Roche limit and shatter or else collide with the planet.

Tidal interactions between planets and moons usually push the moons outwards from the planets. A moon which forms in orbit around a planet will orbit the planet in the same direction as the planet rotates, the prograde direction. A moon captured by the planet can orbit the planet in either the prograde direction, or the direction opposite to the rotation of the planet, the retrograde direction.

A moon which orbits a planet in the prograde direction closer than the synchronous orbital distance, and thus circles the planet faster than the planet rotates, will be pulled closer to the planet by tidal interactions.

One example in our solar system is the inner moon of Mars, Phobos.

Tidal deceleration is gradually decreasing the orbital radius of Phobos by approximately two meters every 100 years,[11] and with decreasing orbital radius the likelihood of breakup due to tidal forces increases, estimated in approximately 30–50 million years,[11][54] with one study's estimate being about 43 million years.[56]

https://en.wikipedia.org/wiki/Phobos_(moon)

A moon which orbits a planet in the the retrograde direction will be pulled inward by tidal interactions regardless of whether it is below or above the geosynchronous orbital distance.

Many of the outer moons of the giant planets are believed to have been captured by those planets, originally being asteroids or other small solar system bodies. Some of those captured moons have prograde orbits and some have retrograde orbits.

Because those moons have low masses and orbit far from their planets their tidal interactions with their planets are very weak and move them inward or outward very slowly.

Except for Triton, the largest moon of Neptune, which is believed to have originally been a dwarf planet captured by Neptune. It is by far the largest and most massive captured moon, and orbits very close to Neptune in a retrograde orbit. Thus its tidal interactions with Neptune are very strong and pull it inward much faster than any other retrograde moon.

Tidal interactions also cause Triton's orbit, which is already closer to Neptune than the Moon is to Earth, to gradually decay further; predictions are that 3.6 billion years from now, Triton will pass within Neptune's Roche limit.[26] This will result in either a collision with Neptune's atmosphere or the breakup of Triton, forming a new ring system similar to that found around Saturn.[26]

https://en.wikipedia.org/wiki/Triton_(moon)#Orbit_and_rotation

Most massive moons of planets will be formed orbiting the planet in prograde directions above the synchronous orbital distance and so will slowly move away from the planet.

The example of Triton shows that sometimes a planet can capture a large dwarf planet and make it a moon with a retrograde orbit taking it closer to the planet.

See:

https://en.wikipedia.org/wiki/Tidal_acceleration#Tidal_deceleration

The Moon is continuing to slow the Earth's rotation and move outward from the Earth. But when Earth's rotation is slowed enough to match the Moon's orbital period the process will stop. The Moon will no longer slow the Earth's rotation or be forced outwards.

But the weaker tidal interactions between the Earth and the Sun will slow the Earth's rotation. Thus making the Moon's orbit be below the synchronous orbit and causing the Moon to move closer and closer to the Earth, eventually reaching the Roche limit and breaking up. Of course that process will take tens of billions of years.

This tidal drag makes the rotation of the Earth and the orbital period of the Moon very slowly match. This matching first results in tidally locking the lighter body of the orbital system, as is already the case with the Moon. Theoretically, in 50 billion years,[176] the Earth's rotation will have slowed to the point of matching the Moon's orbital period, causing the Earth to always present the same side to the Moon. However, the Sun will become a red giant, engulfing the Earth-Moon system, long before then.[177][178]

https://en.wikipedia.org/wiki/Moon#Earth%E2%80%93Moon_system

The Sun should become a red giant in "only" about five billion years. That will probably destroy the Earth and the Moon. If they survive they should come to a standstill in about 50 billion years, and then the process of the Moon spiraling inward toward Earth will begin, no doubt lasting tens of billions of years.

A hypothetical double planet where the two objects have similar masses should hve much stronger tidal effects between the two objects and so they might both become tidally locked to the other in just a few billion years - like Pluto and Charon, for example. And then tidal interactions with their star should start making the two objects more closer and closer to each other.

A red dwarf star would remain on the main sequence for many times longer than the Sun, so it might be possible for a double planet orbiting a red dwarf to move apart, become tidally locked, and then move closer and closer and eventually collide before the star becomes a red giant and swallows them both.

Since the universe is believed to be "only" 13 to 14 billion years old, I doubt whether than has ever happened yet anywhere in the universe. But I will leave it to astrophysicists to calculate the minimum time for such a process.

Answer 2

Under which conditions could a planet's massive moon's orbit get closer to the planet?

I'll give the most straightforward condition:

The tidal interaction tends to accelerate the orbiting moon in the direction that would bring its orbit into synchronization with the planet's spin. Since the Earth spins $\sim 30$ times faster than the Moon orbits (in terms of orbital frequency), the tidal interaction tends to speed up the Moon along its orbit. This increases the Moon's orbital energy, making it move away from the Earth into higher orbits.

(Note that the Moon doesn't speed up in the end; it actually slows down because orbital speeds are lower for higher orbits.)

However, if the Moon were orbiting more rapidly than the Earth's rotation (in terms of orbital frequency), then the tidal acceleration would go in the opposite direction. The same would be true if the Moon were orbiting retrograde at any rate. In these cases, the tidal interaction would act to decelerate the Moon, reducing its energy and sending it into lower (and even faster) orbits. So this is one condition under which a moon's orbit would get closer to the planet over time.

For the same reason, a moon's orbit can also decay over time if its own spin is slower than, or in the opposite direction from, its orbit. But if the moon is much smaller than the planet, this consideration would be subdominant to the impact of the planet's spin.

Answer 3

Both Sten and M.A.Golding have provided good answers, so I shall only add some details.

(1) The tides exerted in the planet by the moon are pushing the moon away when its semimajor axis' exceeds the synchronous value, and are pulling the moon downwards otherwise.

The tides exerted by the planet in the moon are working to push the moon away if its spin is faster than the its mean motion around the planet, and are working to pull the moon down if the moon's rotation is synchronised with its orbital motion (i.e., if it is showing the same face to the planet).

This entails two conclusions:

• If a nascent moon accreted only slightly below synchronism, and is spinning sufficiently swiftly, the tides in the moon may, in principle, beat the tides in the planet, and enable the moon to "jump out" of the synchronous radius. This option is, of course, of a theoretical nature, because the angular momentum of the moon's rotation is very small compared to the orbital angular momentum. Accordingly, small will be the rise of the orbit.

• If a moon residing above synchronism is synchronised and has a substantial eccentricity, the tides in the moon may well take over the tides in the planet and enable the moon to fall down through the synchronous radius. This is a very realistic situation, and computations demonstrate that, in all likelihood, this is how Phobos found itself on its present orbit.

(2) Just as a tidally receding prograde moon slows down the rotation of the planet, a tidally descending prograde moon accelerates the planet's rotation. In the former case, the planet's synchronous radius is expanding and may catch up with the moon before it leaves the reduced Hill sphere. In the latter case, the synchronous radius shrinks and may catch up with the moon before it enters the Roche lobe. In both cases then, a mutually synchronous configuration will be attained.