Re:SDP4 Algorithm

Bruno Tilgner (
Thu, 27 Mar 1997 18:33:33 -0500

R.Kracht wrote:

>This causes an error of about 4 deg in the predictions, because
>XNODES and ACTAN(ALFDP,BETDP) are taken from different quadrants!

>XNODES is derived from the RAAN of the elset (331.8258), which is
>in the range of 0 to 360 deg. The ACTAN-function yields angles in
>the range of -180 to 180 deg.

>If we take both angles from the same quadrant, the change of OMGASM
>is COS(8.2812)*(-28.1742) - COS(8.2637)*(-28.1842) = +0.0111 deg!

>to the same quadrant as ACTAN(ALFDP,BETDP). The new code is:

A more fundamental fix to this problem, which might occur in more places
of the code, is to replace the ACTAN function by the function ATN2 which,
if it doesn't already exist in the programming language used, can be written
in such a way as to always yield a result in the range 0... 2*pi. That's what
I have done about 5 years ago.

>Rob Matson has pointed out to me that this is only a partial fix,
>we have to dig up the original paper(s):

>Hujsak, R.S. "A Restricted Four Body Solution for Resonating
>Satellites with an Oblate Earth", AIAA Paper No. 79-136, June 1979


>Hujsak, R.S. and Hoots, F.R., "Deep Space Perturbations Ephemeris
>Generation", Aerospace Defense Command Space Computational Center
>Program Documentation, DCD 8, Section 3, 82-104, September 1977.

>Perhaps someone can provide the URL's of these documents?

I doubt that these papers can be found on-line. The first one should be
relatively easy to locate in a library and I am pretty sure I could find

I have also made a database search which came up with this result which has
the title of the first paper but the publication source of the second, plus
a slightly different publication date:

Quest Accession Number : 80021224
  AD-A081 263/6 NTIS Issue: 8000

  A  Restricted Four Body Solution for Resonating Satellites
Without Drag. (Scientific rept.,)

  Notes: Report on Project Space Track.
  Author(s): Hujsak,  Richard S.
  Corp.   Source:   (065158001   411617)  Aerospace  Defense
Command, Peterson AFB, CO. Office of Astrodynamics.
  NTIS   Prices:   PC  A04/MF  A01.   Journal  Announcement:
  Number of Report:  ASTRODYNAMIC-1.
  Publication Year: Nov 1979.  Pagination: 71p
  Language: English.  Country of Publication: United States

  A  generalized  method  of  averaging is used to study two
general problems for drag free motion of an artificial Earth
satellite.  The first development includes perturbations due
to  the  point  masses of the Earth, Moon and Sun as well as
zonal  variations.  The second development extends the first
to  include  tesseral  and  sectoral  harmonics as resonance
perturbations for two specific classes of orbits. (Author)

22C Space Technology-Spacecraft trajectories and reentry
84D   Space   Technology-Spacecraft  trajectories  &  flight

  Controlled  Terms:  *Equations  of  motion  /  *  Orbits /
Gravitational fields /  Perturbations /  Harmonic analysis /
 Legendre functions /  Transformations Mathematics
  *Four  body  problem  /   Tesseral  harmonics /  Spherical


I will try to obtain the full text of the paper.

Bruno Tilgner
Paris, France