Re: Possible further elset developments

Phil Rogers (
Fri, 2 Apr 1999 23:02:40 -0500

On 1 Apr 99, Jim Varney wrote:
>On 1 Apr 99, Phil Rogers wrote:
>> NORAD's Special Perturbations model is nothing new and is indeed the
>> model which has for years been used to generate all NORAD elsets.
>The difference between the "special" elsets and the two-lines we all know 
>and love is much greater than just their longevity.
>I have an unclassified SPACECOM document that talks about this.  It says 
>the special perturbations element set is a "numerically derived 'XYZ' 
>vector."  It's a state vector.  It also says that the form of the elements 
>differ depending on whether the object is LEO or deep space.

Yes, I've read the manuals too... kind of difficult to avoid when the better
part of your working life has been spent doing just this kind of work.
All elsets begin as vectors and indeed, site data is fed to NORAD as
site relative smoothed vectors. The process of generating an elset is an
iterative least squares process in which an initial vector (either from
site data or from existing elsets) is integrated throughout the time span
of the data to be fitted. As in any least squares fit, errors are summed,
sigma determined, outlying points edited and the iterative process repeated
until the solution converges. The end result is a fitted, perturbed vector.
This vector is converted to a set of keplerian elements representing the
perturbed elset, then run through the perturbation model being used,
(whether SP or GP theory) to remove those perturbations and yield the
mean keplerian elset which NORAD publishes. The user then applies
whichever reverse perturbation model he has at his disposal, then
converts the resulting perturbed elset back to a vector at a given time
(all handled in one step by SGP4 et al).

I would certainly expect deep space orbits to be described by elements
of a different format, however, it should be noted that objects in high
geosync earth orbit are not in deep space at all. Once an object leaves
the earth far enough behind to no longer be influenced by the earth's
and moon's gravitational forces, it enters deep space where it is
influenced primarily by the sun (until it travels so far as to be beyond
even the sun's grip). As such, it would then be in a heliocentric orbit with
an entirely different set of parameters being used to describe such an
orbit. Earth relative elements would be meaningless in such a case.

>If this is correct, then there's no need for SPACECOM to distribute their 
>model.  Any numerical integration model can be used with varying success 
>depending on the sophistication of the atmospheric and gravitational 
>models.  The "increased longevity" does not come from the elsets 
>themselves; it comes from the numerical integration method, which can be 
>built to consider many more perturbation factors than SGP4 does.
>If SPACECOM started issuing state vectors accurate to a meter instead of 
>mean TLE's accurate to a kilometer, I would say hooray for them!  Despite 
>the short-term pain of some broken software, we should welcome this change 
>to higher accuracy in the long term with open arms.
> -- Jim

The difference in perturbation models is primarily in the number and
time period of the additional harmonic terms which are added with better
models. Having never seen the SP theory model personally, I can only
assume that this must also be the case for that model too. Therefore,
the net result of better perturbation models would be indeed be felt as
increased longevity of the elset. Since the distributed elements are
mean elements, the user's final pointing data can only be as good as his
error model used to massage that mean data. I might also add that all
integrators except the most basic Newtonian integrators have their own
perturbation models independent of the pertubative effects applied to
the elsets themselves via the particular SP or GP theory being used. I
believe that you are confusing the two.

Believe me, you would not want NORAD data to be published as vectors
regardless of how accurate they are at epoch. Elsets permit generation
of a valid vector at any given point in time with as much accuracy as at
any other given time (of course throughout the lifespan of the elset).
Vectors on the other hand must be integrated to the time desired and
with any integrator that is fast enough to be of practical use, the
numerical errors of integration accumulate to the point that the data is
useless one rev later. I have seen cases that were exceptions to this
rule such as a simple integrator putting a radar directly on a target
one rev later, but have extremely high doubts that the vector was not
recomputed at some time from the elset. The more typical case is a
better integrator which is several degrees off target by the next rev.

Indeed, NORAD does provide its sensors with vector pointing data,
primarily for tipsats where the orbits change too much within a given rev
for one elset to be good for all sites. Still, the ordinary NORAD elset reigns
supreme and I think that everyone here should be very thankful that they
release any of their data. Quite frankly, it surprised me greatly to
find out that elsets were actually released to the public at all or to anyone
other than NASA and other government agencies.

With SPACECOM, comes less, but I will reserve my comments on that topic.

Phil Rogers