A CLOSE ENCOUNTER! Yes, I had one... but this one wasn't with strange visitors from another planet, the pilots were 100% earthling. I paid a visit to Heavens Above just to confirm, and within seconds my suspicions were validated. Observe:
You can use Heavens Above to schedule your own close encounter with the ISS, which is easily visible as it passes over - it's very bright - or maybe one evening you'll be lucky enough to have a surprise encounter like I did.
So if you see a really bright star-like point moving at a breakneck pace (and it usually fades in brightness as it passes over, so it could appear to fade in and fade out, very myterious and UFO-like) take a peek at Heavens Above before you go calling in the team from Area 51. There are plenty of man-made satellites in orbit that will catch the sun's light just as the moon and planets do, and many of them shine brightly enough to be frequently mistaken for little green men.
More math coming soon, I promise! It's a crazy vacation weekend and I've had barely any time to calculate anything that isn't my bank balance, and that's far more intimidating than trig. Yeesh.