State Vectors

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 orbital information.

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.

Download VEC2TLE

VEC2TLE is flexible in input state vector format:

  • Earth-Centered Inertial (ECI), True Equator and Equinox of Date
  • ECI, Mean Equator and Equinox of 1950 (M50)
  • Earth-Fixed Greenwich (EFG) - aka True of Day Rotating (TDR)
  • Position - km; Velocity km/sec
  • Position - ft; Velocity ft/sec
  • Position - nm; Velocity nm/sec
  • Coordinated Universal Time (UTC)
  • Mission Elapsed Time (MET)

VEC2TLE can automatically extract a formatted state vector embedded in an ordinary text file. Thus, NASA Spacelink STSTLE E-mail Messages may be copied directly to an text file and then read by VEC2TLE to compute the Keplerian elements. VEC2TLE can also be set up to add or replace a satellite's Keplerian elements (as appropriate) in the user's text files. This makes VEC2TLE a very efficient mode of maintaining Keplerian elements for the Space Shuttle, when used in conjunction with the STSTLE mailing list. Instructions for subscribing to the STSTLE mailing list are available on the Space Shuttle page.


State Vectors and Keplerian elements both completely describe a satellite's orbit

Orbit propagators (like NORAD SGP / SGP4) compute state vectors from Keplerian elements

VEC2TLE computes NORAD - compatible mean Keplerian elements from State Vectors

VEC2TLE supports a variety of vector formats and measurement units

VEC2TLE can update Keplerian elements text files