There are several reasons why you want to study the orbits of satellites:
There are 8 elements that you need to define an orbit. These elements are also called Keplerian Elements after the German astronomer Johannes Kepler (1571-1630). Kepler discovered that planets moved in elliptical orbits rather than circular orbits. The following are Keplerian Elements:
as the satellite gets closer to the Earth, its velocity increases. If we know how fast the satellite is going, we also know the altitude of the satellite.
http://www.amsat.org/amsat/keps/kepmodel.html
http://www-leland.stanford.edu/~iburrell/sat/kepler.html
To learn about types of orbits, click here.
There are several satellite tracking programs that people can download free of charge: