Tide-Locked Planets and Moons

[Dollan]

Assuming an age of at least 500,000 years and above into the billions, is it a foregone conclusion that a planet tidally locked to its star would not be able to retain any satellites that might have formed with it?

Or could there be planets tidally locked to their stars with large moons?

...John...

[tony873004]

Here's my guess.

If the moon is large, the planet's tendency is going to be tidally locking with the moon, and not the star.

Tidally locking with both probably wouldn't be possible. Imagine if the Earth were tidally locked with the Sun. The Earth's rotation would be 365 days. But for the Moon to orbit in a period of 365 days it would be so far from Earth that it would be stripped away from the Earth by the Sun because it orbited outside the Earth's Hill Sphere.

[d.m.falk]

The Moon would probably come to rest at a Lagrange point if that happened.

d.m.f.

[tony873004]

The Moon would probably come to rest at a Lagrange point if that happened.

d.m.f.

Even scarier
There's no mechanism to lock the Moon into a Lagrange point. It's ultimate fate would be a collision with Earth.

[d.m.falk]

No, along the Earth's Lagrange points with the Sun, not the Earth-Moon Lagrange points.

Much like the Trojan asteroids at Jupiter.

d.m.f.

[ajtribick]

The moon is presumably going to have an orbital period shorter than the planet's year, and if the planet is tidelocked this is going to be sub-geostationary, which means tidal effects cause the moon to migrate inwards, until it gets ripped apart inside the Roche limit.

I take it you are asking about the timescale for this process... not entirely sure, but Phobos (which is in astronomical terms a pebble) is estimated to have about 50 million years left, and from what I've seen, more massive objects get shunted around by tidal effects faster.

This paper has some useful formulae for working out what can survive in a system, though you're going to have to find out the tidal dissipation factor and tidal Love number for Earthlike planets first... the paper gives numbers for Jovian planets, but they don't deal with ice giants or terrestrials. I've had a brief look on Google for these parameters, but they seem remarkably elusive (seems to be because they are pretty difficult to measure anyway)

[tony873004]

No, along the Earth's Lagrange points with the Sun, not the Earth-Moon Lagrange points.

Much like the Trojan asteroids at Jupiter.

d.m.f.

That is what I was referring to. Unless the Moon got locked in the Earth / Sun L4 or L5, it would almost certaintly make repeated close pass after close pass until it struck. But no mechanism exists to rob the Moon of a small amount of energy allowing it to be captured into a Lagrange point.

[d.m.falk]

Except that its slowly orbiting away from the Earth?

d.m.f.

[tony873004]

Except that its slowly orbiting away from the Earth?

d.m.f.

Yes, but this is in reference to the hypothetical situation that the Moon all of a sudden found itself outside Earth's Hill Sphere.

The Moon is slowly spiraling away from the Earth. As a consequence, the Earth's rotation is slowing down. This will continue until the Earth's rotation period and the Moon's orbital period are the same. The Earth will then become tidally locked to the Moon and the Moon will receed no further. Problem is that the timescale for this to happen is so long that the Sun will go red Giant first and destroy the Earth and the Moon.

[Dollan]

Thanks for the answers, folks. I've also gotten some hel with this on the Bad Astronomy forum, so I definitely have enough material to mull over for the next couple of days!

...John...

[Malenfant]

Yes, but this is in reference to the hypothetical situation that the Moon all of a sudden found itself outside Earth's Hill Sphere.

The Moon is slowly spiraling away from the Earth. As a consequence, the Earth's rotation is slowing down. This will continue until the Earth's rotation period and the Moon's orbital period are the same. The Earth will then become tidally locked to the Moon and the Moon will receed no further. Problem is that the timescale for this to happen is so long that the Sun will go red Giant first and destroy the Earth and the Moon.

But then the solar tides will suck out angular momentum from the system, and the moon will start spiralling back in. IIRC, once they're locked, earth starts to get slowed down to be tidally locked to the sun. This moves the synchronous orbit outwards, which means the moon is now in a prograde within that limit, which means that it starts spiralling in. Though to be honest, that means that there's tidal interaction between earth and moon again (does the earth's rotation speed up as this happens)? So I don't really know what happens next...

[bdm]

Yes, but this is in reference to the hypothetical situation that the Moon all of a sudden found itself outside Earth's Hill Sphere.

The Moon is slowly spiraling away from the Earth. As a consequence, the Earth's rotation is slowing down. This will continue until the Earth's rotation period and the Moon's orbital period are the same. The Earth will then become tidally locked to the Moon and the Moon will receed no further. Problem is that the timescale for this to happen is so long that the Sun will go red Giant first and destroy the Earth and the Moon.

But then the solar tides will suck out angular momentum from the system, and the moon will start spiralling back in. IIRC, once they're locked, earth starts to get slowed down to be tidally locked to the sun. This moves the synchronous orbit outwards, which means the moon is now in a prograde within that limit, which means that it starts spiralling in. Though to be honest, that means that there's tidal interaction between earth and moon again (does the earth's rotation speed up as this happens)? So I don't really know what happens next...

Let's consider the forces in the Earth/Moon system that drive tidal locking. Tidal locking happens because the tidal bulge of the Earth rotates ahead of the line connecting the Earth to the Moon. The moon's gravity pulls on this bulge, thus exerting a torque that slows the Earth's rotation. In turn, the tidal bulge exerts a pull on the moon that increases the radius of the Moon's orbit. This process will stop when the Earth and moon are locked to each other, like Pluto and Charon today.

The Sun complicates this picture because the Sun raises tides too. If Earth had no moon, the Earth would experience tides from the Sun 46% as great as the lunar tides. Thus the process does not actually stop.

Let's consider the case of Earth and Moon tidally locked to each other. The Sun raises a tide on Earth (and moon) that act like the lunar tide on the Earth. Like the lunar tide, this also serves to slow the Earth's rotation. When this happens, the tidal bulge of the moon on the Earth is now dragged so as to lag behind the line connecting the Earth to the moon. The moon's gravity will pull on this bulge, speeding up the Earth's rotation and dragging the moon in. The net effect would be to speed the Earth's rotation, drag the moon closer to the Earth, and widen the radius of the Earth's orbit. Eventually the moon would be dragged in so far that it would be disrupted.

PS: If any of this is wrong please post a correction.

[Malenfant]

Let's consider the case of Earth and Moon tidally locked to each other. The Sun raises a tide on Earth (and moon) that act like the lunar tide on the Earth. Like the lunar tide, this also serves to slow the Earth's rotation. When this happens, the tidal bulge of the moon on the Earth is now dragged so as to lag behind the line connecting the Earth to the moon. The moon's gravity will pull on this bulge, speeding up the Earth's rotation and dragging the moon in. The net effect would be to speed the Earth's rotation, drag the moon closer to the Earth, and widen the radius of the Earth's orbit. Eventually the moon would be dragged in so far that it would be disrupted.

It's rather hard to keep track of tidal forces when there's three bodies involved. Implicit in what I said was the assumption that basically solar tides don't really change the situation between the earth and moon, but only become important once the earth-moon system is tidelocked - just makes it easier to get one's head around. But of course, the solar tides ARE influencing the system all through that time.

IIRC the net effect of the solar tides has been to influence the system such that the moon is further out from the earth than it should be if we were just considering tides between the earth and moon.