What is the description of the gravitational interaction in the philosophy of Plato? Are there some drastic differences from Aristotle's physics?
I don't think he discussed anything like gravity. This does not mean he lacked interest in physics. For example, his elemental atoms were platonic solids whose sides were broken down into triangles. So in a basic way, he was saying the world was geometric. And this a long time before Minkowski.
The key difference between him and Aristotle is that Plato is an atomist whereas Aristotle is a thinker on the continuum. According to Rene Thom, the topologist, Aristotle was more or less the only thinker on the continuum for two millenia.
Whereas a key similarity is that both were Pythagoreans. For Plato, mathematics was the first step on a dialectic where one progressively understands the nature of the One or the monad in Pythagorean language and which derives from the word monas (alone). Aristotle, does something similar via his notion of cause tracing the All back to a unitary first cause and mover but which is unmoved itself.