On 1 December Alphonse Pouplier wrote: >Hi all! >There are a lot of programs giving previsions and using TLEs. >But does a program exist which would give the TLEs using >observations? Since nobody has answered yet, it appears there are not many of such programs, perhaps none at all. Hence I would like to submit the following suggestion: Dan Boulet's book "Methods of Orbit Determination" contains algorithms to compute the state vector (position and velocity in cartesian coordinates) from observations. A computer program (in BASIC) is given as well as another program to improve initial state vectors by further observations. It is a relatively straightforward job to compute classical Keplerian elements from these vectors, except in some pathological cases. Ken Ernandes' program VEC2TLE allows to perform the next step, calculation of TLE's from the state vectors, due consideration being given to the reference system and units of measure. This will still give a first approximation only because drag effects are not taken into account. Mike McCants' program FITELEM allows refinement of initial TLE's either by manually changing parameters or by inputting the time delay between computed and observed positions. His program is not terribly user-friendly because everything has to be entered through a batch file in classical mainframe style. I have not tried this approach myself, but that's the way I would go about it if I couldn't find a program that does the job. Needless to say that this is a classical problem of positional astronomy, treated thoroughly in the 18th and 19th centuries by Laplace, Gauss and Olbers, were it not for non-gravitational forces. A word of caution is in order, however. The Spacetrack Report No.3, "Models for Propagation of NORAD Element Sets", warns that NORAD element sets are mean values obtained by removing periodic variations in a particular way (not explained further) which must be re-introduced before using the elements. Using NORAD TLE's in a different model will result in degraded predictions even if the model is intrinsically more accurate. Conversely, it could be argued that using TLE's, constructed in the way outlined above, with a NORAD model such as SGP4 could lead to erroneous results. Comments are welcome! Bruno Tilgner 100533.2016@compuserve.com Fax +33 1 557 0042