To teach children the two directions of force being exerted on a satellite, centrifugal and centripetal, children are given a string tied to something like a ball of paper, and told to swing it around. The ball of paper wants go straight, due to inertia, but the string, representing the pull of the earth, prevents this from happening.
Yes, you are right, the pull of the earth keeps the satellite from flying away - but only because the satellite is going at the proper velocity to maintain its orbit. If the satellite was going faster, it would fly away. If the satellite was going slower, it would fall to earth.
liftoff.msfc.nasa.gov
Further, earth does not rotate around its own center of gravity, both the earth and the moon orbit around their common "center of mass", which on average lies 4688 km from the center of the earth and 379712 km from the center of the moon. There are five points between the earth and the moon where a spacecraft would be in balance with the gravities of the earth and the moon and their orbital motion. These are called "Lagrange points" and are quite a bit further away than the orbit of a LEO.
Because the earth isn't exactly round, and isn't the only body in the solar system, satellites won't follow a nice Kepler orbit without a little help once in a while. I guess that's what you are suggesting, that once a satellite gets into a Kepler orbit, it will say there. |