| MadSci Network: Astronomy |
Good question!
Take a look at this graph of circular motion. This is an object in perfect circular motion. Notice that its velocity is always exactly tangent to its path---there is no component perpendicular to the path.
Now, take a look at the elliptical orbits near the bottom of this document on circular motion principles for satellites. The force, or equivalently the curvature of space, is the same as when the motion is circular. What is different is that the velocity now does have a component perpendicular to its path. The force, and space-time, are spherically symmetric; the motion is not. Indeed, one plausible path that an object can take in a gravitational field is straight towards the center (just drop something to see this path demonstrated), which is as far from a circle as you can get!
Finding a satellite or planet in a perfectly circular orbit is extremely rare, rather like balancing a pencil on its point. The eccentricity of the orbit (zero if a circle, 1 if a line directly into the sun or planet) depends on how the object got into its orbit in the first place, and what interactions (collisions, near misses) it has suffered since.
The lesson? The symmetry of the forces, or equivalently of space-time, does not completely determine the paths of objects---their initial velocities matter as well.
Finally, if you want to play with eccentricities, visit the Demonstration of Satellite in Orbit site. You can adjust the eccentricity of the orbit all the way from zero to one, and see what happens.
Try the links in the MadSci Library for more information on Astronomy.