Maybe slightly off-topic, but still related to satellite, I just came inside from watching the ISS (International Space Station) fly over New Orleans. The sky was clear and cold, which makes for a perfect view. The ISS is probably the brightest object in the night sky (other than the Moon, of course).
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Heavens-Above Home Page is a good sight to help with ISS sightings, as well as others.
Even brighter than the ISS, and if I remember right, even brighter than the moon, are the Iridium Flares. Those things are really neat.
Basically, the Irridium sats are communications satellites, and they have a mirror surface that will reflect the sun to a very narrow spot on earth, and when you are near the spot it is reflecting to, it is VERY BRIGHT. You can google Irridium flares for more info, but the above Heavens above site has a link for predicting when to see the flares. You need to set up your latitude/longitude AND time zone (on a couple occasions, I organized sort of a party to watch a flare, only to find out that I had used the wrong time zone, and we were watching at the wrong time).
If you see one predicted to be near you, it might be worth the drive to go a few miles to get directly under the path of the flare, because even 5 or 6 miles will make a big difference in the intensity of the observed flare.
If you are near the path of a flare, and look at the right time, what you'll generally see, is a very dim satellite going across the sky, then, at the predicted time, that dim satellite will suddenly get very bright for just a couple seconds. It takes a lot of planning to be looking at the right time, but it's worth the effort to see one at least once.
Another neat thing to do with any satellite, particularly the ISS, is to get a prediction program (or one of the web pages) that will not only show the predictions for where and when the sat will be in the sky, but also show whether it is illuminated or not. What is neat, is when a sat like the ISS goes from sunlight into the shadow of the earth, that very bright sat just suddenly dissappears, (or appears, if it's going from shadow into light). If you have a telescope, you can also do the same thing with the moons of Jupiter. Ie there are charts in the various astronomy magazines' web pages that will show you at which times the moons of Jupiter will go into the shadow of Jupiter. Again, if you have the time correct, you can be watching Jupiter's several moons, and suddenly one of them will dissappear or appear. Pretty neat.
EDIT: I just checked, and the Irridium flares are NOT as bright as a full moon at least.
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Also, as the ISS gets bigger and bigger, it's been getting brighter and brighter, so references to it's magnitude are constantly changing.