Most satellites are not perfect spheres, therefore you might see many different sides and perspectives as they travel through your sky.

Observe a rotating pencil from a distance. When you view the pencil from its side, you will be seeing the pencil along its entire length making it very easy to see. When you view the pencil from the front (tip) or back (eraser), you only see a very small area and the pencil is not as easy to see. This is called "cross-sectional area". When we see a satellite, we are not guaranteed the best orientation to see its maximum cross-sectional area.

The orientation of a satellite can represent anywhere from the minimum to the maximum cross-sectional area possible.

In order to see an Iridium satellite with the naked eye, its orientation must be such that its high gain antennae are reflecting sunlight directly to your location on Earth. Since Iridium satellites have well-known orientations, it is simple to predict when an "Iridium Flare" will occur at your location.

Many satellites are no longer active and are floating in space without any control. Many of these inactive satellites tumble which illustrates the orientation dependence of brightness even more. As the satellite tumbles, we can see many different sides of the satellite in a very short time, thereby showing us different reflectivity.

Imagine if several people, each located in a different location but at the same distance from an identical satellite, observed the satellite and recorded its brightness. There will a good probability that all will report a different brightness for eh object because they will be seeing different sides and possibly different cross-sectional areas.