# Question on the process of tidal locking



## Dennis E. Taylor (Sep 19, 2015)

Not sure if this is the right category. There's nothing obvious that screams "story research" in the forums. Disclaimer: I still have too much blood in my caffeine system, so I may have missed it.

Okay, picture a planet that's in a close orbit around a small K star. It's juuuuuuuuust about to go into tidal lock. Each rotation of the planet slows as the heavy end goes around the back side, then speeds up as it swings around towards the star. Just like a lopsided wheel.

Now, finally, the day comes when the last rotation just doesn't quite make it. The rotation stops, then slowly starts to reverse. The planet rotates around 355 degrees or so in the opposite direction, and comes to a stop again. Basically, now you have a pendulum. I've found a formula for calculating the period of a pendulum, but I don't think it would be based on the mass of the entire planet. I'm trying to visualize it, but a non-spherical non-homogenous planet would effectively be a bar shape for purposes of calculating periods. The length of the bar could be calculated by determining where the center of mass is compared to the center of geometry, but what would be the effective mass?

Sorry, meandering aside, I'm wondering what kinds of periods you could expect for this kind of cycle? Weeks? Months? Obviously it could be arbitrarily slow, but how fast at the upper end?


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## Venusian Broon (Sep 19, 2015)

Bizmuth said:


> Not sure if this is the right category. There's nothing obvious that screams "story research" in the forums. Disclaimer: I still have too much blood in my caffeine system, so I may have missed it.
> 
> Okay, picture a planet that's in a close orbit around a small K star. It's juuuuuuuuust about to go into tidal lock. Each rotation of the planet slows as the heavy end goes around the back side, then speeds up as it swings around towards the star. Just like a lopsided wheel.
> 
> ...



Don't quite understand the pendulum part of this - do you mean: the planet rotates one way, till it reaches a certain point (the end of the day) then it just reverses its spin and goes the other way...gets to the other extreme, then reverses again. Does this ad infinitum.

ah wait a minute - this planet you have - it's not spherical for some reason. That wasn't clear  (Why? is it pretty small. Asteroid small? Dwarf planets can be oblate or weird, but they are sort of defined so that they are in 'gravitational relaxation' and so will generally form spherical objects - basically anything with a diameter of 800km or more should be spherical - quick rule of thumb, although I'm sure it does depend on quite a few factors)

However, even if it were a lumpy shape - what force is causing it reverse it's spin every day? This is not obvious to me what that force is. The pendulum comes to a stop and then reverses it's movement because it's constrained by gravity, the string and the energy of the system. What's doing that for the rotation of the planet?

With regards to your bar planet calcs, again I may be missing something, but it should rotate around its centre of mass. The effective mass? Well essentially for the purposes of gravitational calculations when you are reasonably far away from it the effective mass is just the mass of the whole thing (just that because it's a weird shape, doesn't change the total mass of the planet.)

If however you are going for a cool 'fantasy' world and anything can be done, possibly the easiest thing to do is just calculate the period of the orbit (Kepler 3 for a rough idea, Newton and differential equations if you have a strong ellipse!) Then as it's tidally locked the number of days will fit into the orbital period. Hence 'fully' tidally locked will have the day 1:1 with the period of the orbit. Mercury was thought to be tidally locked but has a 3:2 spin–orbit resonance - or three days = two of its years.

So I guess you can play about with that and put anything you like in!


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## Dennis E. Taylor (Sep 19, 2015)

My understanding of tidal locking is that it is dependant on the planet not being a perfectly homogenous, perfectly shaped sphere. Gravity needs something to "grab onto." The moon, for instance is tidally locked because it has inconsistencies in mass. Yes, a rotating planet will rotate around the center of mass, but if there are mass concentrations "off-center", they will cause tidal locking.

A good example is a simple method used by satellites to maintain orientation. The satellite has a long boom with a weight at the end of it. The boom always ends up pointing towards the Earth because of orbital mechanics. It's essentially a form of tidal locking.

Given all of the above, I think there would be a point in the evolution of the planet where it goes from a rotating body to a body that isn't rotating. It wouldn't just immediately stop, because that would require some kind of braking. So there must be a period of time when it's swinging back and forth. During this time, the sun would alternately rise in the east and set in the west, then rise in the west and set in the east, for most of the planet.

I'm really looking for two things:
1) Am I totally out to lunch on this? Is there some other process that results in a tidally locked planet, that doesn't have this as an intermediate step?
2) What, intuitively, might be the minimum period of swing?

I'm not looking for rigorous calculations. This is for a SF story, so it just has to be plausible.


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## chrispenycate (Sep 19, 2015)

Obviously, if the centre of gravity and the centre of the planet were one and the same, there would be no such effect - the  rotation would be damped only by ffiction with the solar wind (which would take a *long time*). And when you're creating a planet, the tendency is towards homogeneity - and the rate of the simple harmonic motion is totally dependent on the distance between the centre of rotation and that of gravity. So, unless you embed a very big meteorite in it or something to seriously destabilise it, I suspect very slowly - walking pace, at maximum.


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## Ray McCarthy (Sep 19, 2015)

no swing. just a gradual reduction in rotational speed.

The large amount seawater may have aided the lock on our moon. The energy in the tides have to come from somewhere. Now perhaps the tide affects the lunar period?


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## Venusian Broon (Sep 19, 2015)

Bizmuth said:


> My understanding of tidal locking is that it is dependant on the planet not being a perfectly homogenous, perfectly shaped sphere. Gravity needs something to "grab onto." The moon, for instance is tidally locked because it has inconsistencies in mass. Yes, a rotating planet will rotate around the center of mass, but if there are mass concentrations "off-center", they will cause tidal locking.



Ok a brief foray into the interweb does not mention this requirement. A definition I stumbled across says:  The change in rotation rate necessary to tidally lock a body B to a larger body A is caused by the torque applied by A's gravity on bulges it has induced on B by tidal forces.

No mention at all of the object having to be non-homogeneous or not being a perfectly shaped sphere. In a sense the large object will always deform the smaller object by the mere presence of its gravity and this causes the smaller object to eventually tidally lock. Hence any 'homogeneous spherical object' should, under the correct conditions, be able to quite easily be tidally locked.

However you may have some references for your original premise? I'd honestly be very interested 

The effect on the tether and the satellite is there because it is exploiting the change in gravitational gradient and so, yes, is a tidal mechanism and because the satellite is vastly tiny compared to the Earth it very quickly arranges itself to fall along its axis of moment of inertia. However the geometry of this situation is not what you should take from it.

EDIT: Thinking about the last paragraph, what I mean is that: On it's own a tiny little satellite is not effected by any gravitational gradient - so it needs to release a tether so it can then mechanically exploit the gravitational gradient. A planet being a much, much bigger thing will automatically 'exploit' this gravitational gradient no matter what it does


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## Dennis E. Taylor (Sep 19, 2015)

hmm, it looks like these are completely different effects. Tidal friction will operate on any sphere that can be deformed, however homogenous. However, even the Earth is not homogenous, although the differences are small. There's a web page with a graphic of the Earth with gravitational anomalies exaggerated, and it's almost a rough cube.

OTOH, as I said, _small_. If I want to have my Klown Kar planet, I'm going to have to introduce a large inhomogeneity. In such a case, tidal friction would gradually slow the rotation down until it slowed below the natural pendulum swing period based on the inhomogeneity, then it would start the back-and-forth thing. Also, tidal friction would continue to operate, so the swing would get gradually smaller and smaller. But the slower the swing, the lower the effect of tidal friction, and the longer this state would last.


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## Mirannan (Sep 27, 2015)

AFAIK the rotation-slowing effect of tides does not depend on inhomogeneity; it merely needs a rotating object (an extreme case being the satellite previously mentioned) which is not spherical.

Bearing in mind that any planet close to being tide-locked would be much closer to its star than Earth is, a good approximation to the shape of such a planet might be a prolate spheroid with the axis pointing towards the star.

Incidentally, I think it likely that a planet not quite tide locked would be rather volcanic. Why? Because it would be regularly squeezed out of shape, a situation similar to that of Io although probably not quite as drastic - at least at the stage you describe.


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## Kylara (Sep 27, 2015)

No science help to provide, definitely not my area of expertise, but although I like the concept of pendulum planet, I'm not sure it would ever happen? I thought tidal locking just slowed the thing down until it stopped? I had a SF short about that - the planet stopping. But never finished it as I was never certain of how slow it would have been turning before the stop and if very slow would have ruined my plot as the long day/night cycle would be similar. 

With the rising/setting sun issue, are you expecting almost full spin on each swing of pendulum? 

Also random thought. Would gravity get all weird at the change of direction during each swing? 

As I said, not my area of expertise, but I do like the concept of pendulum planets, although I would think about it a lot, so your theory and reasoning about it would have to be extremely plausible for me to stay on board. 

Very interested to hear the rest of the discussion!


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## Phyrebrat (Sep 27, 2015)

My brain hurts but I feel I'm learning lots here. Great thread! 

pH


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## Vertigo (Sep 28, 2015)

I think to get that swing effect your planet would have to be massively inconsistent in it's composition. And I do mean massively. Also the pendulum effect you are looking for would only occur if you overshoot the stable tidal locked state, however, the approach to a tidal locked state would be so slow - taking hundreds of thousands (or even millions) of years - that any overshoot would be very unlikely. I'm pretty sure the planet would simply very slowly settle into the stable tidal locked state.


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## chrispenycate (Sep 28, 2015)

How about starting with a tidally locked planet then clobbering it with a small retrograde nickle/iron asteroid, startin a tendency to rotate, but without enough energy to do a complete cycle?


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## Ray McCarthy (Sep 28, 2015)

I think a pendulum effect isn't possible. Because any planet will rotate on centre of gravity and a pendulum needs the point of rotation to be off centred from the centre of gravity, hence bob on rod or string or wire.


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## Vertigo (Sep 28, 2015)

Precisely this.


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