FIND_ORB can take a set of observations of an asteroid or comet, given in MPC (Minor Planet Center) format, and find the corresponding orbit. (The MPC format is used because it is a "standard" used by most astrometry software, including Charon).
It can determine orbits of artificial Earth satellites and for satellites of other planets. It exists as both a 16-bit Windows program, and as a 32-bit Windows program (above the second). The only difference between the two is that the 32-bit version is considerably faster.
FIND_ORB is a user-friendly program that handles the initial determination of the orbit using the method of Herget. Given some more observations, it can find a "best fit" orbit using the method of least squares . It's sufficiently bright to include the perturbing effects of the planets and Earth's moon, and may eventually include effects of Jupiter's four largest satellites, Titan, and of the first four asteroids.