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## Tidal Locking Question

One small thing I don't understand about tidal locking.

I'll use some round numbers as an example for my question.

Let's say there is a planet. 100 000km from the centre of that planet is the centre of a moon 200 km in diameter. So the near side of that moon is 99 900 from the centre of the planet and the far side is 100 100km from the centre of the planet.

If two golf balls were placed at those two distances, they would have different velocities for their orbits.

Why doesn't this differential of orbit velocities cause the moons, or any large satellite of any body to get torqued and rotate like a ball bearing?

I'm guessing the answer for our moon is that the mass is not distributed symmetrically, the heavy side is facing us and the forces are not enough to overcome the weight bias. But what if the satellite had a uniform density, would it still tidally lock?

2. Originally Posted by wiggy
I'm guessing the answer for our moon is that the mass is not distributed symmetrically, the heavy side is facing us and the forces are not enough to overcome the weight bias. But what if the satellite had a uniform density, would it still tidally lock?
I'm no expert, but from what I do know, astronomical objects are (generally?) elastic.
Even the moon has some elasticity. So; there will be a tidal drag in any system.

For the Earth and the moon, I think the asymmetry is a larger factor.

3. The other thing to consider is that your golf balls are able to move at different velocities because there are two objects with no fixed center of mass between them. With your moon, the gravity is centered 100,000 km from the planet's center. The diameter of the moon isn't really all that important as far as the orbit goes.

Now, if your golf balls were bound together with a fixed point, like a thin rod, you need to look at the gravitational pull for each individual mass, as well as the whole. Because of the inverse square law of gravity, the lower golf ball will have more pull on it than the upper one. As it tries to rotate due to torque, the energy needed to raise it up will be more than the energy pulling the other down. This will keep the low end always pointing at the planet.

At least, this is my understanding.
See below for any corrections.

4. Now if the moon is homogeneous all the golf balls cancel out if it is truly rigid but as in post 2 the two sides of the moon at any time are pulled toward the planet and half a rev later they are pulled back. This introduces shear forces reversing every half turn. The moon will be elastic and may also suffer non recoverable shear (creep or slip) which will cause heating and that heat is extracted form the rotating energy and radiated away. Until eventually it sits with one face to the planet like our moon.

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Originally Posted by wiggy
One small thing I don't understand about tidal locking.

I'll use some round numbers as an example for my question.

Let's say there is a planet. 100 000km from the centre of that planet is the centre of a moon 200 km in diameter. So the near side of that moon is 99 900 from the centre of the planet and the far side is 100 100km from the centre of the planet.

If two golf balls were placed at those two distances, they would have different velocities for their orbits.

Why doesn't this differential of orbit velocities cause the moons, or any large satellite of any body to get torqued and rotate like a ball bearing?
Because the tidal force doesn't produce a torque it produces a tension. To answer a question with a question, in your scenario where would the angular momentum come from?

Originally Posted by wiggy
But what if the satellite had a uniform density, would it still tidally lock?
Tidal locking is a consequence of dissipative processes that permit angular momentum to be transferred. The tidal force you mention slightly deforms the satellite so that its radial (i.e. along the line joining the centres) diameter is greater than its transverse diameter. If it's not rotating synchronously then the satellite is being continuously reshaped as it rotates. This leads to energy dissipation inside the satellite and a transfer of angular momentum from the satellite's rotation to its orbit.

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Put 2 golf balls on parallel orbits, but instead of putting them on circular orbits (which would have different angular velocities) make them have equal angular velocity.

If there is no bond between them, then they would diverge: the inner golf ball would be moving too slow to be on a circular orbit, so it would fall inwards from apogee, whereas the outer golf ball would be moving too fast, so it would be climbing outwards from perigee of its elliptical orbit.

Now, put a rigid stick connecting them. It would be in tension - hold both balls back against departing on an elliptical orbit.

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I realised where my error in thought was. None of the answers so far really nailed it, but helped me get there on my own.

I was only thinking of the extreme points, like the points of contact on a ball bearing with the inner and out race of the bearing.

If I now think of the moon as a flat disc perpendicular to the planet (only because it takes less brain power to model of circle instead of a sphere), if I go toward the centre of that disc, the orbit scribes an arc all the way through the body, not just point contact. <facepalm> This is why it doesn't generate a torque, its balanced left to right.

8. Hi Wiggy,
I don't find your explanation clear, it's because the moon is rotating that first order tidal effects occur, how do you see your flat disc rotating?

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