RE: Positional requirements

Robert H. McNaught, Anglo-Australian Observatory (
Thu, 30 May 1996 15:09:19 +1000 (EST)

>>>It is possible to get elements from observations without a
>>>previous element set ?

>>Yes.  In theory, it takes six independent numbers to geometrically
>>define an orbit.  Three positional observations at
>>three different times fit this criteria.  Then it's a matter of
>>doing a lot of math to get an orbit that fits through these three
>>points in time and space.

>But for low earth orbits, this method doesn't work unless your
>observations are accurate to better than arc-seconds.
>For an object with an unknown orbit, it is best to use two widely
>separated observations to come up with a preliminary circular solution
>and then apply the differential corrections method as used
>by elcor and fitelem, including your other observations, to calculate 
>an accurate elliptical orbit.

The idea that you require ARC-SECOND accuracy to calculate a low earth
orbit is simply not true.  Certainly, to REPRESENT an identified orbit,
the higher the accuracy the better, but to calculate an orbit, there is
(as far as I know) no limitation.  If the observations are sufficiently bad,
you will produce physically meaningless orbits (eg eccentricity approaches
infinity or topocentric distance approaches zero).  If your program doesn't
derive an initial orbit from three reasonable representative positions,
then I can only assume it is a limitation of the method used or its coding.

Note that for a satellite moving at 1 deg/sec, a timing accuracy of +/-0.1 sec
will represent an along-track error of +/- 360 arcseconds.

Cheers, Rob McNaught