Satgen320  In Orbit Pt4  Kepler Problems  by GM4IHJ              13 May 95

There is a natural human tendency to regard anything printed on a computer
screen , as absolute truth. This can be very misleading. Indeed , users of
satellite tracking software sho
ld never regard what they see on their
screens , as absolute. The tracking data you get from a computer is only
as good as the Keplerian elements you put into the computer, and there is
a further consideration that the actual computer calculation itself may
not be very accurate.

Consider two practical examples of Keplerian orbital elements :-
MIR     Epoch 95114.23599939  Mean Motion 15.58427
KVANT 1 Epoch 95114.10777901  Mean Motion 15.58405
We are asked to believe that on the same day Mir travelled roughly 0.00022
more orbits than Kvant 1 . That is 2 * PI * 6771 * .00022 = 10 kms

When in fact Kvant 1 is fiymly docked on Mir

Please therefore be aware that NASA make no claim for any great accuracy
for these Keplerian Elements. Users are warned not to use them in
situations where accuracy is required. The reason for this apparent mix up
, is that the military trackers of these vehicles , start a separate set
of tracking data for each vehicle when it is launched . They then revise
this data individually from then onwards. Mir launched some time before
Kvant 1, and the separate elements sets for the two vehicles have not been
combined although Kvant has been hard docked on Mir for years.

Equally at risk of being taken too much for granted is the accuracy of the
actual computer calculation. This is particularly noteworthy in regard to
calculations for satellite slant range and radio signal doppler shift. 
Calculated every 2 minutes in a single precision calculation , the doppler
shift of a satellite at long range ( not near closest approach ) was
reported as +200   +200   0   -100   -400 Hz over an 8 minute sequence. In
fact the doppler shift was not as irregular as this. The irregularity
occured in the calculation whereby very small changes in range every two
minutes were causing changes in the lower end of a binary number which
were not big enough to give a smooth sequence. 

The solution in the case of irregular binary fluctuations as above, is to
improve the precision of the calculation by telling the computer to use
double precision mathematics. But not all software can do this , and few
users are aware of this complication. Please note however that no amount
of double precision mathematics can improve the accuracy of the final
calculation when the Keplerian elements used have no great accuracy , as
in the case of Mir and Kvant reported above, or , in the case of Keplerian
elements which are out of date 

At Sunspot minimum as now , you need new Mir ( altitude 400 km) elements
every month , and you need new elements for RS12 ( altitude 1000 kms)
every three months. Because upper atmosphere drag gradually changes the
orbit in a manner which is very difficult to predict.