Have you ever seen an Iridium flare? It’s amazing how many people have never even heard of them, but they are amongst the easiest and most impressive man-made celestial phenomena. And anyone can see them with the information on this site.

http://www.heavens-above.com/

To quote from the help:

The Iridium satellites are relatively small telecommunications satellites in a low Earth orbit. They are part of a world-wide system for mobile communications operated by the Iridium LLC Corporation. When complete, there will be a total of 66 satellites in 6 orbit planes, at an altitude of around 780km.

As can be seen from the diagram (see site), each satellite has three main mission antennas (MMAs), which are flat, highly reflective surfaces, that can reflect the Sun’s rays to an observer on the ground when the geometry is correct. The satellite’s attitude is controlled so that the long axis remains vertical, with one MMA always pointing forwards. Given this knowledge of the attitude, together with the orbital position of the satellite and the Sun and observer’s location, it is possible to calculate the angle between the direction to the observer from the satellite and the line of a perfect reflection of the Sun. This is the so-called “mirror angle” and determines the magnitude of the flare.