Decay of OSCAR 13

Lutz Schindler (
Thu, 12 Oct 1995 12:26:00 +0200

In the amateure-radio-network, I found the following article
about the decaying of OSCAR 13.
OSCAR stays for (O)rbital (S)atellite (C)arrying (A)mateur (R)adio.

Bye Lutz

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                    Oscar-13 Re-Entry Keplerian Elements

                             by James Miller G3RUH

                                 1995 Aug 09

Most amateur satellite operators are aware that AO-13 will re-enter during
December 1996.  At the time of writing, this gives us 16 months more operation.

Perigee height is reducing at a rate of 1 km/day due to luni-solar forces which
are increasing the orbit's eccentrity.  When the satellite begins to encounter
the atmosphere it will start losing energy in non-trivial amounts.  This will
be during the last quarter of 1996.

At that time, when the orbit is circularising and mean motion increasing
noticeably from its present value of 2.1 rev/day to 16 rev/day at re-entry, the
published NORAD elements are always going to be stale and virtually unusable.

In addition, since Mean Motion has a direct effect on rise and set times, and
if history repeats itself, we can expect the usual plethora of conflicting
"almost" Keplerian element sets lovingly massaged to perfection, that work for
no-one else but their creators!

Chaos Not
To try and bring some order out of chaos I have placed on the Internet a file
of some 200 2-line Keplerian element sets that represent Oscar-13 at 50 orbit
intervals until 1996 Oct 25, and then every orbit until re-entry.   The file,
which is about 10K bytes long is available via anonymous FTP as:


This enables you to look into the future, right to the last orbit, possibly
even to predict whether or not you will "see" burn up ...

This data has been derived by integrating the equations of motion, as described
in reference [1].  Forces modelled are Earth's gravity plus J2, J3, and J4 bulge
terms, Sun, Moon and atmospheric drag.

Fine Tuning
The uncertainty in re-entry analysis is caused by our not knowing the precise
magnitude of atmospheric drag.  This is because the upper atmosphere density
depends on so many variable factors, including  day/night, time of year, solar
activity, Sun's rotation, position in 11 year sun-spot cycle, as well as the
aerodynamic profile of the satellite.

Consequently it will be necessary for me to compare the predicted Keplerian
element sets with genuine NORAD sets regularly, and check for parity.  Then I
will create a new file of 200 elements and upload them.  This will happen at
approximately monthly until near the end of life, then with increasing

We do know that end-of-life perigees will occur during darkness, so that
hopefully conditions will be less unpredictable than otherwise.

Re-Entry Conditions
1. Nominal re-entry is around 1996 Dec 03-05, in darkness, between 0145 and 0245
   LOCAL time, at approximately latitude 50N.  The Moon is likely to be just
   rising due East.

2. If drag is lower than expected, the final orbits will be much more circular
   than for the nominal conditions, making accurate predictions impossible.
   We can expect re-entry to be in during darkness, but little else.

About the Element Sets
Typical satellite 2-line Keplerian element sets look like this:

1 30922U 88051B   96305.12146489  .00000000  00000-0  10000-4 0 08057
2 30922  57.1156  81.6242 7372121  54.7302 193.7462  2.23299095 64227
1 30923U 88051B   96305.57123433  .00000000  00000-0  10000-4 0 08051
2 30923  57.1160  81.5232 7368989  54.7750 195.6866  2.23741846 64231

1. These sets are syntactically correct as per the NORAD specification:


2. The Satellite Identifier, that usually appears as a title or menu entry
   in tracking programs, is AO13-xxxx where xxxx is the orbit number.

3. The Object Number for the real AO-13 is 19216.  The object number for
   these fictitious satellites is 24500+OrbitNumber, e.g. 30922, 30923 above.
   This number is much higher than any real satellite's, and enables you to
   construct a database (for example in InstantTrak) with each "Oscar-13"

4. The Element Set is   mmdd   where mm  is the month and  dd  the day the
   element set was created.  It's 0805 (August 05) in the example.

5. Decay is deliberately set to zero.  This means that ideally you should use a
   Keplerian element set fairly close to the orbit it represents.  When the
   true value of Decay is small you can be up to a month or so off, but at end-
   of-life when the true Decay is rising substantially every orbit, you MUST
   use the correct element set for the orbit or you'll suffer enormous
   tracking errors.  Successive sets coincide quite closely at perigee.

6. Each set represents the osculating ellipse computed from the satellite's
   position and velocity near apogee (MA=180 deg) in the orbit.

1. J R. Miller, "The Re-Entry of Oscar-13"
    - Proceedings of the 12th annual Amsat Space Symposium, Orlando, Florida,
       USA, 1994.  4 pages.
    - Oscar News (UK)  1994 Oct No. 109 p 16-20
    - Jamsat Newsletter (JA) No. 166, 1995 March 25. p1-4
    - Amsat-DL Journal (D), Jg. 22, No. 1, Mar/May 1995.
    - Amsat OZ Journal (OZ) No. 37, 1995 May
    - The Amsat Journal (USA) Vol 18 No.3, May/June 1995.

   The updated article and program listing is available via the Internet by
   anonymous FTP or WWW:

    FTP Site:
        File:   /amsat/articles/g3ruh/
    www  URL:   www://

James Miller G3RUH @ GB7DDX.#22.GBR.EU     1995 Aug 09 [Wed] 0939 utc

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