Someone who saw my previous message asked if it's surprising that you
can see a reflection from a satellite that's hundreds of miles away.
I'll answer here, just in case someone else might find it interesting.
Think of it this way:
Human night vision can detect a tiny number of photons, and the sun
provides a _huge_ number of photons (trillions of times more than you
get from the dimmest naked-eye stars), so a person on the night side of
the Earth who's looking at an object that's in full sunlight can easily
see a reflected beam, even if it's a billion times weaker than the
sunlight that a spacewalker next to the satellite would see.
I can see Polaris from the campus observatory, even though it's in a
badly light-polluted location near the Reitz Union. If the predictions
are correct, the 5:49 PM flare will be about 3,000 times brighter, and
the 7:26 PM flare will be about 4,000 times brighter, than Polaris.
(To do the math, raise Pogson's ratio (the fifth root of 100) to the
power of the difference between Polaris's apparent magnitude (2) and the
magnitude in the prediction (called "Brightness" on
heavens-above.com).)
I expect it to look like when you see an airplane's landing light being
turned on, but more gradual. (But I've never been right at the center
of the beam path, so I might be wrong about how it will look.)
-- Robert