Wednesday, November 15, 2023

[mzbgqocq] Moon vs geosynchronous orbit

the moon drifts away because tides cause earth's rotation to slow down (decreasing earth's rotational kinetic energy), and, by conservation of energy, the moon gains energy, becoming lifted to higher and higher orbits.  energy gets transferred from earth to moon as if by magic.  partial explanation of what's really happening: tides cause the shape of the earth to become oblate, and the tidal bulge is not perfectly aligned with the earth-moon axis, probably because position is the second integral of acceleration, not necessarily in phase with acceleration.  somehow, this ever changing shape of the central mass increases the moon's orbital speed so consequently raises the moon's orbit.  orbits around non-spherically symmetric non-rigid central masses are not intuitive.  I don't understand what is really happening.

(if the moon didn't orbit above the equator, stuff would be more complicated.)

why must energy be (mostly) conserved?  the deformation energy of tides could instead have become heat.  the answer is probably that tides are (mostly) elastic deformation, not too difficult to imagine with gradually moving (non-turbulent) water.

tides cause the earth's rotation to slow down because the moon orbits the earth with period more than one day.  that is, the moon is above geosynchronous orbit.  (future post ayhqopzh: geosynchronous altitude rises as earth slows down.)

if the moon were below geosynchronous orbit, then it would probably cause earth's rotation to speed up, and the moon world slowly drift toward the earth, eventually becoming ground into a ring by yet another manifestation of tidal forces.  this is the fate of Phobos, the inner moon of Mars.  it is surprising that Phobos can transfer its orbital energy to Mars despite Mars having no oceans to undergo elastic deformation.  on one hand every material can do some amount of elastic deformation, so that small bit is enough to do energy transfer.  on the other hand, maybe Phobos's orbital energy and orbital height is primarily being converted to heat by inelastic deformation.

how special do the circumstances of natural satellite formation need to be for a satellite to end up inside synchronous orbit?  perhaps not difficult if the planet rotates slowly (e.g., Venus, Mercury), but forming a slowly rotating planet is itself strange.  Venus and Mercury do not have moons. perhaps they've all been ground into rings which have since rained onto their surfaces: Venus and Mercury devouring their children.

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