Re: Mirror-ball satellite

Leigh Palmer (palmer@sfu.ca)
Tue, 27 Jan 1998 00:02:01 -0800

Rob Matson's calculation needs a bit of modification. He suggests
the satellite will reflect the Sun directly to an observer on Earth
sixty times per revolution. That turns out not to be the case; the
correct number is less than one tenth of that - nearer five times
than sixty. I understand where the error comes from; I made the
same error myself. If the equator of the ball is studded with
mirrors it will take sixty to go 'round. If the observer and the
Sun are in the equatorial plane then there will indeed be sixty
flashes per revolution. An observer half a degree outside the
equatorial plane, however, won't see any flashes.

Let's redo the calculation a bit. One thousand half-degree diameter
beams would cover 200 square degrees*. All of space covers 41,253
square degrees**, so only about half a percent of the surface of
the Earth is likely going to see a sun glint while observing the
illuminated satellite. Thus the average magnitude of a satellite
spinning with sufficient speed to have a flash period less than the
flicker time would have an apparent magnitude almost six magnitudes
down from the glint maximum. I didn't check that out, but it looks
about right. In any event this object will be about mag five on
time average, but as a much brighter glinter I expect it will be
naked eye visible, if sporadic.

Lageos, by the way, would not be bright except to an observer
approaching it for the direction of the Sun. It is not covered with
mirrors; those are retroreflectors.

Leigh

* 0.064 steradians
** 4 pi steradians