tidal locking

[gusl]

I have always wondered why we only see one side of the moon.

http://en.wikipedia.org/wiki/Tidal_locking
http://en.wikipedia.org/wiki/Orbital_resonance

I like to think of this as being due to the tidal-lock configuration being lower-energy than other configurations... but it doesn't feel like a clean explanation, since I don't have a theorem explaining why things will tend to a lower-energy state. Does Lagrangian mechanics validate my intuition?
Fermat's principle is another example of the same sort of intuition that I can't justify rigorously.

Comments

[en-ki.livejournal.com]

Well, pretty much. Least action, not least energy.

Least action + symmetry = all of physics.

[(Anonymous)]

+ quantum mechanics, but yeah, I guess that there aren't too many celestial systems where qm is important!

But it's almost a tautology to say that the system is minimizing it's energy or extremizing it's action... As you say - that's all of physics...

That wikipedia page goes into the details though: the question is *why* that configuration is lower energy, and it's basically because the objects involved aren't completely rigid, and the deformation induced by gravitational forces makes for an effectively "inelastic" interaction where there is a net torque on the satellite, leading to the transference of angular momentum from on component (rotational - leading to tidal locking) to another (orbital - leading to the moon slowly drifting away).

[pbrane.livejournal.com]

whoops, that was me.

But yeah, the short form is also describable as: when they're not tidally locked, the tidal deformation of the moon leads to a net torque which only goes away when they become tidally locked.