Satellite tracking software routinely computes satellite positions and velocities from Keplerian elements. Since the six components of a position
velocity state vector and the associated time are independent, these also provide a complete description of a satellite's orbit. Thus, the six osculating Keplerian elements may be computed from a state vector.
You can estimate an Earth-fixed state vector for a new satellite launch, given the launch location, orbital parameters, and booster ascent profile
using the satellite orbital injection spreadsheet.
The conversion of state vectors to Keplerian elements is a useful process since there are times when a position and velocity is the only available
The Keplerian elements used by most satellite tracking software are the mean rather than the osculating parameters. The difference between the two is a somewhat complex topic involving orbital perturbations and long and short term periodic variations. Because of computational expediency, the Keplerian elements produced by US Space Command and released by NASA are the mean values. This has resulted in most tracking programs using the Space Command Simplified General Perturbations (SGP/SGP4) orbit propagation algorithms in order to maintain compatibility with the Keplerian elements.
The computation of the mean Keplerian elements from the state vectors or the osculating elements is a nontrivial process. This led to the development of of the
Vector to Two-Line Elements (VEC2TLE)
software. VEC2TLE is an MS-DOS based program that computes Keplerian elements from a variety of state vector formats. The Keplerian data computed by VEC2TLE are mean elements, fully compatible with the SGP/SGP4 orbit propagators. You can download the latest version of VEC2TLE for personal use or evaluation.