That's an interesting idea, but I have two further questions/doubts:
1. Wouldn't all of the parts of the mass be affected to a more or less similar degree? Surely the parts closer to the big planet would be subjected to a bit more gravitation, but the difference would seem small, especially since the smaller object is usually some kind of solid rock. I don't think that's enough of a difference to cause a core to melt or whatever. The bigger body would even make the smaller one stop rotating like how the earth made the moon stop rotating. Additionally, earth went from really hot to a cold shell instead of getting heated up by the sun's gravitation somehow. The moon's gravitation affects some processes on earth (tides and possibly also in the core), but less so the other way around. Especially since the moon does not rotate around its own axis anymore.
2. The acceleration would not only depend on the size of the body that the small mass orbits, but also on the distance and the shape of the orbit. A low and less circular orbit should cause higher acceleration than a very high and very circle-shaped orbit around the same object, no?
The planet size would then be a more secondary factor. I'd expect the acceleration to be relatively low either way though, since a high acceleration would probably require a much stronger force than gravity, the weakest elementary force we know.
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