(Geo) satellite flash geometry

From: Björn Gimle (b_gimle@algonet.se)
Date: Sat Nov 23 2002 - 05:16:44 EST

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    > Just a quick follow-up question about TDF 2.  When I ran
    > predictions, it seems never to go as far south as -18
    > declination (which is what you wrote).  So I'm not sure
    The flashing surface's normal traces a circle on the sky globe.
    Since the Sun can be far from the circle, the reflections can trace a very
    large, contorted (?) circle over the sky.
    > what to make of that.  Maybe it's due to me still not
    > really being able to visualize these things.  I need to
    > make a satellite model and use it with a globe -- and
    > something else in the room be the Sun.
    For the geos, it is "never" so complicated that a satellite model is required -
    just use a mirror mounted at some fixed angle to an axis. The orbit is small
    compared to the Sun's distance, and the solar panel is small compared to the
    observer range.
    So the rays are two narrow 1/4 degree radius cones (ideally).
    The one from Sun to satellite changes direction slowly during the year.
    Because the satellite rotates like a gyro, its axis moves very slowly, usually
    at a constant declination, a few hours of RA per year for a geo.
    The panel's normal sweeps quickly over a (usually) wide cone (circle) as the
    satellite rotates.
    The reflection traces a wider "cone" in space (two "cones" counting the back
    side). (I have not yet worked out if this double width cone actually traces a
    circle on the celestial sphere)
    The directions of these reflections in space are totally independent of where
    Earth and its geographical features are "below" it - but the direction of the
    flashes determine where (in RA+dec) the reflections can be seen from Earth.
    If the satellite spin axis were parallell to the Earth axis (decl=90) and the
    cone angle equal to 90 degrees, the reflections would trace the celestial
    equator at solstices, and be contained between +- 24 degrees declination the
    rest of the year - even then there would be long periods when no Earthbound
    observer could see reflections since the satellite moves at almost constant
    declination within +- 9 degrees (if the orbital inclination is zero).
    If the axis declination, cone angle or inclination is different, the range of
    flash directions extends even more. The values above seem to be dynamically
    "ideal", but if the satellite suffered a collision or a control jet malfunction,
    the axis may be altered. Superbird A has an axis declination of 6-9 degrees
    only, and the ones I analyzed were between 60 and 89 degrees. The cone angle can
    be off if there was a control malfunction, or if the mass distribution of the
    satellite is unsymmetric. The ones I have found were 60-90 degrees.
    I realize that this description may be over-ambitious and difficult to follow
    (return to the simple mirror model!). It could be better with an image, even a
    3D-pair or a movie, but these would take me even more time to produce.
    > Quoting Björn Gimle <b_gimle@algonet.se>:
    > >
    > > TDF2 ... its entire flash path
    > > (except in daylight) appears to be below -18 decl.
    > > [ Flashes will reach -9 deg when it rises for me, end of
    > > Dec., but TDF 2 stays N of -7    (8-(>   ]
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