Phobos, Tides and Resistance to Motion
Use this equation to calculate the KE "lost" / transfer from our Moon and phobos to their mother planets ...
Oops. Phobos is not losing kinetic energy, it is gaining kinetic energy, and will eventually slam into Mars at full tilt. Unlike our moon, which is currently moving away from Earth at about 3.82±0.07 cm/year (
Dickey, et al., 1994), Phobos approaches Mars at about 18.3 cm/year (e.g.,
Sharma, 2008). By applying straightforward dynamics, we arrive at Phobos arriving at Mars in roughly 11,000,000 years (somewhat faster than the previously estimated 50,000,000 years, at least according to Sharma).
Kinetic energy is not lost but converted , ...
There is a transfer of energy between a moon and its primary as a result of tidal forces, but this transfer is a direct result of the fact that both satellites and primaries in the real universe are both deformable and physically extended objects (i.e., they are not geometric points). See my short discussion of the topic for the Earth-Moon system here:
The Recession of the Moon and the Age of the Earth-Moon System, 1999 or see
Solar System Dynamics by Murray & Dermott (Cambridge University Press, 1999 & 2001 for a more detailed mathematical & physical analysis).
Earth spins on its axis faster than the moon orbits Earth. As a result, Earth pulls the moon from in front, whipping it so that it would go faster if it remained at a fixed distance from Earth. But the moon is not so constrained, and as a result of the transfer of energy from Earth to the moon, it moves into a higher orbit with a lower velocity, and therefore less
kinetic energy, but rather more
potential energy, with an overall gain in energy.
But Phobos is the only moon in the solar system (as far as I know) which is so close to its primary that it orbits Mars with a period that is less than the spin period of Mars on its axis; i.e., a "month" for Phobos (7.65 hours) is less than a "day" on Mars (24.63 hours). Hence, Mars pulls Phobos from behind, not in front, and so tends to slow it down. The transfer of energy is from Phobos to Mars, opposite from the transfer of energy from Earth to the moon. So Phobos would slow down if it remained at a fixed distance. But Phobos is not so constrained and drops into a lower energy orbit closer to Mars, where it must move faster. So Phobos gains
kinetic energy but loses
potential energy, with an overall loss of energy.
The idea that there could be any natural resistance to motion, in the absence of friction, was disposed of by Isaac Newton several hundred years ago, which I assume has already been mentioned more than once in a thread this long. Anyone who wants to argue that Isaac Newton was wrong is welcome to give it a shot. But Newton has a pretty good track record for brains, and while he might be wrong here and there, don't count on anything quite that obvious. After all, it took 218 years
and Albert Einstein to make the rather small correction from Newtonian gravity to special relativity. And we are definitely not dealing with Albert Einstein on this thread.