Propagation Models

Rob Matson (
23 Aug 1996 14:01:38 -0800

Hi Jim,

Just wanted to chime in here on the propagation model issue.  Many people
refer to Spacetrack Report No. 3, which as you pointed out contains the
algorithms (and code) for SGP, SGP/SDP4 and SGP8.  However, I haven't seen
anybody mention Spacetrack Report No. 6 from July 1986, which discusses a
(then planned) switchover to a new, more accurate ephemeris prediction model
called HANDE.  As I understand it, they never made the switch, but here is an
excerpt from that report:

"New Users - 

A new user has the option of installing HANDE or SGP.  The SGP model is small,
fast, and an SGP element set is easily extracted from the HANDE element set. 
Some potential accuracy will be sacrificed but accuracy will still be greatly
improved over the present system.  The HANDE model will give the greatest
possible accuracy but will require storage of the 17-item HANDE element set. 
If the user has a need to predict deep space objects, then the HANDE model may
be necessary.

Current SGP Users - 

The majority of current users have either the SGP model or one closely related
to it.  These users must make only very minor changes to remain compatible. 
First, they must arrange to be able to accept the new HANDE element set
format.  Then the SGP element set can be easily extracted from the HANDE
element set.  The extracted elements can be stored exactly as the current SGP
elements are stored and the remaining HANDE elements can be discarded.  The
SGP user will obtain improved prediction accuracy when receiving HANDE element
sets.  If the greatest possible accuracy is desired, then the HANDE model can
be installed as discussed under New Users.

Current SGP4 users - 

For SGP4 users whose primary predictions are for drag-free deep space
satellites, software modifications will allow conversion to HANDE.  Required
modifications can be handled on a case-by-case basis by contacting the author.
 Prediction accuracies will be the same as currently but the software will be
smaller and run faster.

For SGP4 users whose primary predictions are for near Earth satellites, either
the SGP or HANDE model should be installed.  For either model, accuracies will
be greatly improved over SGP4."

Now, since they never made the switch to supplying HANDE element sets, most of
the foregoing is of no consequence.  However, the HANDE algorithm DOES contain
a different (more accurate?) force model for the atmosphere, and the HANDE
algorithm can be used with SGP-type two-line element sets.  The question is,
does HANDE do a better job than SGP or SGP4 for decaying objects?

SkyMap has implementations of SGP, SGP4 and HANDE, so it is possible to
compare the model accuracies against some recent decays.  For example, an
older element set could be propagated to the epoch of a more recent set (taken
as truth), and the various model offsets could then be compared.  HANDE should
do a better job.  SGP has zonal harmonics J2 and J3, and assumes the drag
effect on mean motion to be quadratic in time, resulting in a cubic variation
in mean anomaly w/time.  The drag effect on eccentricity is modeled in such a
way that perigee height remains constant.

HANDE, on the other hand, was developed by Hoots (1983) and includes zonal
harmonics J2, J3 and J4 for its gravitational model, and the dynamic
atmosphere of Jacchia (1970) for its atmospheric model.  It includes lunar and
solar effects as well as resonance terms for satellites with 1/2 day and 1 day
periods.  The reference for the Jacchia report is:

Jacchia, L.G., "New Static Models of the Thermosphere and Exosphere with
Empirical Temperature Profiles", SAO Report 313, May, 1970.

There is also a reference to a Hoots memorandum:

Hoots, F.R., et. al., "Improved General Perturbations Prediction Capability",
Air Force Space Command Astrodynamics Analysis Memorandum 86-3, July 1986.

If I can find some time, I'll run some comparisons using the recently decayed
Raduga 33 rocket body to see how the models compare.