Positional requirements

Robert H. McNaught, Anglo-Australian Observatory (RMN@aaocbn2.aao.gov.au)
Mon, 27 May 1996 17:06:30 +1000 (EST)

>Also in theory, an orbit can be deduced from two positional
>observations at two different times.  This method generates two
>possible orbits that pass through the two points.  One of the two
>orbits is obviously "wrong" and is discarded.

Actually, there are an infinite number of orbits that pass thru two
points/times.  However one can limit the possibilities by certain
physical constraints.  Firstly, the perigee should be above, say, 6600 km,
so that it doesn't re-enter in one orbit.  Also, an eccentricity of less
than 1.0 is reasonable, but the perigee constraint will usually limit
the eccentricity.

About a decade ago, I played around with two position orbit determination
of satellites.  The simplest solution is for e=0 and is easy to compute.
It is also pretty close to reality for many satellites and the derived
node, inclination and mean motion can be sufficient to suggest an
identification.  There are some criterea used in meteor work for comparing
orbital similarity and these could be used to suggest an identification,
but the strict validity of these methods may not apply to satellites.

I use two position/time orbit solutions in asteroid work.  Dealing with
photographic discoveries, this is the only information I have to work with.
By fitting a range or orbits using varying geocentric distances and angles of
motion relative to the observer, one can derive "the best of all possible
orbits" by suitably weighting each orbit according to the probability of
the various orbital parameters.  It is all a bit iffy and as a result I call
the program PANGLOSS after the character in Voltaire's novel.  However it
can give me an indication if the orbit is in any way exotic and also suggests
which direction the asteroid is likely to be moving if exotic orbits are
suggested.  The general principle would also apply to the geocentric orbits
of satellites.

I believe there is always at least one formal solution to three
positions/times.  In general, it is advisable to have redundancy in an orbit
calculation by having four or more sets of data.  Note that the data can come
from observers at different locations so long as you are sure the same object
is being observed.  Techniques to utilise partial data from different orbits
also work but are more esoteric.

So, what are the requirements?  The higher the accuracy the better and four
times/positions should be aimed for as minimum.  What can be determined
accurately should be.  This is basically the geographic location and the
setting of the watch.  Crude observed positions of satellites (+/- 1 degree)
can still produce useable orbits but it is easy to achieve much higher accuracy.

Cheers, Rob McNaught