SDP4 remarks

ROB MATSON (ROBERT.D.MATSON@cpmx.saic.com)
28 Oct 1997 13:14:24 -0800

Hello all,

Bruno Tilgner inquired about the comparative accuracies of propagation
models when applied to geostationary satellites -- in particular the failure
of said model(s) to reproduce the observed relative and absolute motions
of satellites in the ASTRA cluster located at 19.2 E longitude.

He went on to say, "Since I suppose virtually all software uses the
same NORAD model as the prediction engine, I begin to have serious
doubts about the applicability of the SDP4 model to geostationary
satellites."

As Bruno knows, very few programs actually have SDP4 coded.  And
any programs that have coded SDP4 using the source code in the
widely available Spacetrack Report #3 are flawed.  Note that the
equations there are not flawed -- just the coding.  I corrected these
coding mistakes back in March of this year, incorporating them in
SkyMap 5.11.  At that time, SkyMap became the first publically
available program with SDP4 coded as originally intended by the
designer.

In March and April I exchanged hundreds of messages with a number
of individuals explaining how to "fix" SDP4.  As far as I know, only Ed
Wright of JPL had sufficient perseverance to make all the necessary
changes, and his results are now compatible with those of SkyMap.
My notes also indicate that Bruno, Rainer Kracht, Jim Varney and
Curtis Haase made, at the very least, partial fixes that eliminated a
rarely-occurring discontinuity caused by a modulo-2 pi problem -- a
problem which we've referred to as the "Lyddane bug".  (As an
historical footprint, I'd like to mention that it was Rainer who discovered
this discontinuity and traced it to the Lyddane modification section of
SDP4.) 

But unless the solar-lunar offsets are handled correctly, SDP4 will not
work as the author originally intended.  If anyone wants to know how
to fix the SDP4 source code, let me know.  The Lyddane fix is easy;
the solar-lunar offset problem is a bit more involved, but it is the more
important fix of the two since it affects the results of all high-altitude
satellites.

Finally, as a side note I'd like to mention that at least one other
organization created its own corrected version of SDP4 -- Goddard
Space Flight Center.  Their Lyddane correction is essentially identical
to my own, and their S-L offset correction solution produces the same
results as mine.  David Irwin did a great bit of sleuthing back in
April and located Goddard's source code on the web:

http://seawifs.gsfc.nasa.gov/SEAWIFS/SOFTWARE/src/bobdays/sgp4sub.f

I haven't confirmed that this link is still accurate; if it isn't, I still
have this
file on my computer somewhere.  --Rob