On Wed, 26 Aug 1998, Marco Hahn wrote: > What is necessary to determine an orbit of a single satellite? In particular, > is the following enough: >... Enough, at least in theory, is: Two observations and their times, of position, angular velocity, and angular acceleration (position in the sky, how many degrees per second, and how much is it apparently speeding up/slowing down) OR Three observations and their times, of position and angular velocity. and in both cases, knowledge of your own location. With this sort of data, there are closed-form mathematical expressions for the orbital elements. Beware, that's Theory, and it depends on some simplifying assumptions: that the earth is a sphere with uniform density and has no atmosphere, for example. Much more useful are statistical methods which use several observations from any number of passes to derive approximate values of the orbital elements; the Space Command most probably uses such methods. The more observations you have, the better your estimate of the orbit gets. It's possible to build such a method around a _propagation_ model and have it derive orbital elements by iteratively fitting the propagated orbit to the observations. (There is indirect evidence that this is actually how the Space Command does it) There are programs out there which use multiple observations and lets you interactively estimate the orbital elements. Look for "firstorb" and "elcor" -- I've never had opportunity to try them, but I beleive they are used in updating the TLEs for the classified satellites. Also, there are some good books on the subject. I bought David A. Vallado's "Fundamentals of Astrodynamics" a while back, and I like the practical angle at which it describes the rather complex theories involved. Victor R. Bond & Mark C. Allman's "Modern Astrodynamics" is also said to be good. ISBNs: Bond 0-691-04459-7, Vallado 0-07-066829-9. Good luck, Magnus