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I read this answer and thought “that’s not right”. But thinking that the moon would continue to receed and the Earth torqued in the same direction (speeding up) doesn’t balance kinetic energy. I realized that the common explanation of the “bulge lags behind” doesn’t separate effects due to rotation of the Earth, advancement of the Moon along its orbit, and general hysteresis of piling up the water.

So, if the moon and the primary rotated in opposite directions, what would tides do to the system?

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The answer is correct. It's only objects that orbit prograde and do so above the planet's geosynchronous altitude that spiral outwards. Objects orbiting prograde below geosynchronous attitude and all objects orbiting retrograde spiral inward. Phobos, for example, orbits prograde but does so below areosynchronous altitude. It is spiraling in toward Mars as a result and is predicted to either be pulled apart tidally or to collide with Mars somewhere between ten to fifty million years from now.

If you want to look at things from the perspective of the tidal bulge (which doesn't exist), the planet's rotation makes the bulge lead (not lag) an object that orbits prograde above geosynchronous altitude (in other words, the object's orbital period is larger than the length of the planet's sidereal day). The closer leading tidal bulge gives the object an along-track acceleration, The bulge on the opposite side of the planet is behind the object, but because it is further away, the force it exerts is less than that exerted by the closer leading bulge. End result: The object spirals outward.

For an object orbiting prograde below geosynchronous altitude, or for an object in a retrograde orbit the bulge lags behind the orbiting object. End result: The object spirals inward, which is exactly what Phobos is doing right now, even though Mars has no water.

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