|MadSci Network: Astronomy|
When astronomers talk about manifolds, what they're referring to is a mathematical way of describing the shape of space itself. Einstein's theory of general relativity showed us that gravity can be described by matter, such as planets and stars, curving space in its vicinity. This introduced the concept that space (or, more accurately, spacetime) has a geometric shape which we can describe with mathematical equations.
So, the manifolds don't exist as seperate entities inbetween the planets. It's more like a manifold can be used to describe the shape, or geometry, of space around a planet. This then determines, for example, the shapes of the orbits of any moons that planet may have.
For moreinformation about relativity and spacetime, you should take a look at Ned Wright's Cosmology Tutorial, and the links that it contains.
Try the links in the MadSci Library for more information on Astronomy.