Re: Determining orbits from a single location?

B Magnus B{ckstr|m (b@eta.chalmers.se)
Wed, 26 Aug 1998 16:06:26 +0200 (MET DST)

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