SDP4 failure example

ROB MATSON (ROBERT.D.MATSON@cpmx.saic.com)
28 Mar 1997 12:14:57 -0800

Okay, folks, for all those who've been following the SDP4 discussion, here is
an example that I believe will fail on all existing implementations of the
SDP4 model.  It exploits the coding bug in the Lyddane modification section of
DPPER that I mentioned, which occurs when the right ascension of ascending
node makes a transition between quadrants 1 and 4:

 (e.g.  359 --> 359.5 --> 0 --> 0.5 )

Try your code with object #23243, 1992-021N, using the following elements
(from a recent ALLSAT.DAT):

1992-021N
1 23243U 92021N   95016.23792613 +.00000374 +00000-0 +34706-2 0 00450
2 23243 003.2770 358.1095 7290859 272.4086 014.1114 02.14568415009855

Plot the track of the above object on January 10, 1995, from 21:33 UTC to
21:53 UTC.  With SGP you'll have no problems; with SDP4 the object will jump
when its instantaneous RAAN passes through 0 degrees.

This is a mild example of the failure.  The position error is much greater
with higher inclination satellites.  The Lyddane cutoff is 11.459 degrees --
any inclination less than this will exhibit the error.  The magnitude of the
error is approximately equal to 2*Pi*(1 - COS(Inclination)).  For the above
example,
inclination is only 3.277, so the error is only about 0.59 degrees. For an
inclination of 11 degrees, the error increases to 6.6 degrees!  When I find a
worse example, I'll post it here.

--Rob