Synodic effects w/GEO flashers

Matson, Robert (
Mon, 10 May 1999 17:59:42 -0700

Hi Mike & Bjoern,

Thanks for cc'ing me on the synodic effects as they relate to
day-to-day correlations of satellite period.  Mike's example for
a prograde-rotating GEO satellite is approximately correct;
however his example is a very specialized case in which the
satellite spin axis is perpendicular to the equatorial plane, and
the sun itself is in the equatorial plane (which of course it isn't).
Because of the tilt of the earth's axis relative to the ecliptic,
the synodic effect will vary sinusoidally over the course of
the day.

However, if the satellite happens to be spinning around an
axis perpendicular to the earth's axis (as Superbird A is),
then the synodic effect is going to be much smaller because
the apparent motion of the sun (as seen by the satellite) is
primarily in a direction perpendicular to the spin plane.

So the precise flash period measured for a GEO satellite
depends both on the time of day and the day of the year it
is measured.  Add to that the complication of the inclination
of the satellite's orbit, and you've got a messy problem
backing out the true inertial spin rate.  One thing I've
wondered about is if it is possible to tell which direction
(prograde or retrograde) that a satellite is spinning based
on measurements made on consecutive nights.  With
Superbird I don't think you can do it, but for Gorizont 23
it just might be possible.

Of course, if you can get enough longitude separation between
two observers who both time Gorizont 23's flashes at the same
time, that would be a more direct approach.  For a satellite at
GEO with a 90-second rotational period (like Gorizont 23), the
reflection sweeps across the entire earth in less than 2.2
seconds.  Assuming each observer can guarantee his absolute
times are accurate to +/- 0.1 seconds, a flash time difference
of a tenth of the 2.2 secs would be sufficient to determine the
rotation direction.

For a satellite at zenith (and observers on the equator), they
would need to be separated by at least 1100 km, or roughly 10
degrees of longitude.  At midlatitudes, the longitude separation
will have to be even greater -- probably at least 20 degrees.
Lisbon and Vienna, for example, may be sufficiently far apart.
Or Moscow and any point in western Europe.

If it's too late to try this experiment in Europe, perhaps we
can get some U.S. observers to try it when Gorizont 23 swings
our way.  Texas and the east coast would be far enough apart,
and we have plenty of Seesat observers in both locations.
(Getting the weather to cooperate at both locations will be
the hard part!)