Tidally-locked planet and moon

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mathmannix
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Tidally-locked planet and moon

Postby mathmannix » Fri Aug 16, 2013 1:17 pm UTC

So, most moons we have observed (including all the well-known / larger ones) are tidally locked to their planets. And in some cases, like Pluto and Charon (yes I know, Pluto is not a planet :(), the planet is also tidally locked to the moon. There are equations for how long this will take to happen. (My guess is that this is due to the system approaching a more stable state, although of course it could be thrown off by a rogue planet, or comet/asteroid collision.)

A few questions:

I would assume that planets can (and should eventually?) also be tidally locked to their suns, right? I would also assume that if a planet has only the one large moon (like earth!) then it will eventually become locked to the moon. Is this right? If the earth, moon, and sun were all tidally locked together, then would the moon end up either directly between the earth and sun, or directly opposite the sun, so that the three bodies are in a straight line? Also, come to think of it, would the inclination of the moon's orbit versus the earth's (which prevents solar and lunar eclipses from happening each once a month) disappear, leading to a permanent solar (or lunar) eclipse, based on which side of the earth the moon ends up?

Also, could you build a bridge (or run a cable) between two tidally-locked bodies, like Pluto and Charon? Or would that somehow collapse the system, like how if you built a true dysonsphere it would drift into the sun?
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davidstarlingm
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Re: Tidally-locked planet and moon

Postby davidstarlingm » Fri Aug 16, 2013 2:09 pm UTC

mathmannix wrote:I would assume that planets can (and should eventually?) also be tidally locked to their suns, right?

Mercury is locked in a 3:2 resonance with the Sun. Resonances are self-correcting and unlikely to change.

However, unless a satellite is very close and very small in comparison to the larger body, the time to migrate into a resonant or locked position is very high. It can be estimated using this equation.

I would also assume that if a planet has only the one large moon (like earth!) then it will eventually become locked to the moon. Is this right?

This is not necessarily correct. Because of Earth's oceans, tidal effects on Earth's rotation are muted; tides cause the moon's orbital radius to increase more quickly than they alter the rotation of the Earth. The moon will have left Earth's gravitational well before it has time to cause Earth to tidally lock.

If the earth, moon, and sun were all tidally locked together, then would the moon end up either directly between the earth and sun, or directly opposite the sun, so that the three bodies are in a straight line?

It would be more likely for the bodies to exhibit an orbital resonance of some kind, like the Galilean moons of Jupiter. But for the Sun-Earth-Moon system, that won't happen. The Sun is too far away; its tidal effects on the moon are enough to cause a precession of its orbital eccentricity, but not enough to induce locking. This also means that a permanent eclipse is all but impossible.

One neat possibility, though, would be a four-body scenario with three stars and one planet. Imagine a central binary orbited at a distance by the third star. Because the gravitational potential of the central binary would be constantly shifting, a planet near the L1 point of the third star would be pulled back and forth between the two in a jagged orbit, never moving out from between the stars and having permanent daylight on both sides.

Also, could you build a bridge (or run a cable) between two tidally-locked bodies, like Pluto and Charon? Or would that somehow collapse the system, like how if you built a true dysonsphere it would drift into the sun?

Unless the eccentricity of the bodies was exactly 0, the changing orbital radius would snap the cable/bridge like a twig.

Carnildo
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Re: Tidally-locked planet and moon

Postby Carnildo » Sat Aug 17, 2013 3:50 am UTC

mathmannix wrote:Also, could you build a bridge (or run a cable) between two tidally-locked bodies, like Pluto and Charon? Or would that somehow collapse the system, like how if you built a true dysonsphere it would drift into the sun?

A Dyson sphere will drift into the star it's around because there is no net force between a spherical shell and anything within the shell. If you could build the sphere with exactly zero net momentum relative to its star, it would stay in place, but even the slightest error or disturbance will eventually result in a collision.

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Sockmonkey
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Re: Tidally-locked planet and moon

Postby Sockmonkey » Sat Aug 17, 2013 3:21 pm UTC

Carnildo wrote:
mathmannix wrote:Also, could you build a bridge (or run a cable) between two tidally-locked bodies, like Pluto and Charon? Or would that somehow collapse the system, like how if you built a true dysonsphere it would drift into the sun?

A Dyson sphere will drift into the star it's around because there is no net force between a spherical shell and anything within the shell. If you could build the sphere with exactly zero net momentum relative to its star, it would stay in place, but even the slightest error or disturbance will eventually result in a collision.

What about the light pressure against the inside of the sphere?

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Copper Bezel
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Re: Tidally-locked planet and moon

Postby Copper Bezel » Sat Aug 17, 2013 6:58 pm UTC

It's been discussed here before, but the light pressure actually works the same way - it's repulsive instead of attractive, but the force on any one point scales with the same inverse square of the distance (assuming that both the inner surface albedo and the distribution of mass in the shell are perfectly uniform, because you can change them independently of one another, of course, though not in a way that helps.)
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