Glints from nadir-pointing

9 Mar 1998 16:23:50 -0800

Regarding a satellite with a nadir facing surface, Bjoern Gimle wrote:

> I haven't checked the references, nor the reasoning in the mails that
> followed Russell's, but to me it seems it wouldn't flare:

> Looking from the satellite, the Sun would have to have a zenith angle
> greater than 90, but still above the true horizon.
> The reflection from the nadir-normal surface will proceed in the same
> azimuth, with the same zenith angle, i.e. it will pass above the
> horizon, as did the incoming sun rays, and not hit Earth.

Technically, Bjoern is correct.  If the surface in question is truly =
at nadir, then you can never see a perfect specular reflection of the sun
from this surface.  All you have to do is consider the symmetry of the
situation -- put yourself on the satellite.  For there to be a specular
reflection, the sun must be above the horizon.  But since the
reflecting surface is pointed at nadir, the reflection direction is =
above the horizon -- by the same amount as the sun.  In other words,
the reflection just misses the earth.

Now there are some additional factors that still make a glint

1.  the earth isn't exactly spherical,
2.  the satellite surface may not be pointed exactly at nadir,

but most importantly,

3.  satellite surface imperfections will scatter light in a cone
     centered on the specular direction axis.  (i.e. you can
     probably be at least 3 degrees off the specular axis
     and still see some obvious brightening.)

For a satellite in low-earth orbit, being 3-degrees off the specular
axis still doesn't buy you much.  For example, if the satellite altitude
is 400 km, and the sun is setting (or rising) as seen by the satellite,
then the satellite altitude angle corresponding to the 3-degree
off-axis direction is only 11.5 degrees.  So at your ground site, if
the satellite in question was at the same azimuth as the sun, the
sun was about 31 degrees below your horizon, and the satellite
was no more than 11.5 degrees above your horizon, you could
expect to see a glint.  The lower the satellite altitude angle, the
brighter the glint.

But things improve dramatically for satellites at geosynch.  Assuming
an altitude of 35,900 km, the nadir-angle of the earth limb (from the
satellite's perspective) is only about 8.7 degrees.  Thus, if the sun
were rising or setting at the satellite, the specular direction would
be on the opposite side of the world from the sun.  If you then relax
that angle by 3 degrees (the angle off-specular), then you're looking
for the ground altitude angle that corresponds to a satellite nadir
angle of 5.7 degrees.  That angle is about 49 degrees!  In other words,
when a geosynch satellite is approaching eclipse, if it is at nearly the
same azimuth as the sun (as seen from the ground), it will glint if it
is less than 50 degrees above your horizon.  The lower the altitude
angle, the brighter.  For comparison, if your requirement is to be within
1-degree of the specular axis, then the satellite altitude angle needs
to be less than 28 degrees above the horizon.

Of course, for the geosynch case, the solar elevation angle is critical.
You have to be watching the satellite just before eclipse entry, or just
after eclipse exit.  Every degree that the sun is above the earth limb
(as seen from the satellite) is 1 more degree off the specular axis.
Thus, two limited geographical areas would be in position to see such
a glint each night.  (One area just before eclipse entry, another just
after eclipse exit).

The northern hemisphere would be favored in February, March,
October and early November; the southern hemisphere would be
favored in April, early May, August and September.  The best
ground longitudes would be 60 to 80 degrees east or west of
the geosynchronous satellite's longitude.

Apologies all for the long post!   --Rob