I'm not a physicist, but my master's thesis was on numerical ODEs preserving physical (symplectic structure).
I think the best way of looking at these problems is thinking of space already equipped with a vector field (like streamline plots with little arrows) and objects just being carried by them, as if laying down small rocks on a busy river. Of course, this vector field is not constant and the object's mass alters it, but this will be small in the spaceship vs. planets setting.
This is more of a mathematical intuition than history-of-the-universe answer, but I think it should help.
Ed: This is very simple to reason about when talking about independent particles in one dimension; the phase space arises out of a simple variational problem. It's also easy to reason about in 3 dimensions, but the problem is that the "river" in one dimension has two coordinates, momentum and position. So to think of two dimensional space you have to imagine four dimensions, etc. But thanks to Darboux's theorem these dimensions are "coupled in pairs" (this is what symplectic means), and it's not that difficult to visualize four dimensions. Cf. this illustration of the "symplectic camel theorem":
I think the best way of looking at these problems is thinking of space already equipped with a vector field (like streamline plots with little arrows) and objects just being carried by them, as if laying down small rocks on a busy river. Of course, this vector field is not constant and the object's mass alters it, but this will be small in the spaceship vs. planets setting.
This is more of a mathematical intuition than history-of-the-universe answer, but I think it should help.
Ed: This is very simple to reason about when talking about independent particles in one dimension; the phase space arises out of a simple variational problem. It's also easy to reason about in 3 dimensions, but the problem is that the "river" in one dimension has two coordinates, momentum and position. So to think of two dimensional space you have to imagine four dimensions, etc. But thanks to Darboux's theorem these dimensions are "coupled in pairs" (this is what symplectic means), and it's not that difficult to visualize four dimensions. Cf. this illustration of the "symplectic camel theorem":
https://encrypted-tbn0.gstatic.com/images?q=tbn%3AANd9GcRtOK...