I just observed a satellite almost directly above me travel for a few minutes while constantly dimming and then getting brighter. It did this for about 3 minutes until it faded out. I also observed a satellite with similar behavior on July 4th. I was thinking the satellite might be rotating, but I do not know of any satellites that rotate. Then I thought it could be a piece of space junk, but I don't think they get big enough to be visible from the ground. Does anyone know why the brightness of some satellites change while others remain constant? I am in the Northwest of the US. (Northern hemisphere)
I do not know for sure, but you are viewing the satellites by the reflection of sunlight. As the satellite moves across the sky, the Sun-satellite-you angle changes, therefore there is no reason to expect that the brightness should stay the same.
As for why it should fade and brighten again - if you imagine the satellite to consist of a number of surfaces, these surfaces may essentially cast a beam of light onto the Earth, which move across the Earth's surface. The satellite will brighten as one of these beams crosses you. I suppose this could happen several times for the same satellite.
The extreme examples of this are the Iridium satellite that "flare up" to magnitude -8, before fading in a matter of seconds.
It is exactly the rotation of a space object (satellite or space debris) combined with unequal light reflection ability of its surface parts which makes its brightness rapidly vary over time no matter how short it is while observed either visually or with a camera. Rotation periods can be even smaller than a second, and there is a plenty of rotating objects, especially defunct satellites out of control do rotate. Rather constant brightness speaks either for non-rotating objects or for objects with homogeneous surface in terms of light reflection or simply due to low amplitude of brightness fluctuation unperceivable by the detector (your eye in this case).
The phase angle (Sun-object-observer angle) effect mentioned by Rob Jeffries causes only a gradual raise or fall of brightness which takes place within a rather longer period of time depending on the apparent angular velocity which again depends on object's height. The greater the angle the fainter the object. Thus, even apparently non-rotating objects would at least demonstrate this effect.
And bright flashes are caused only at times of particular geometric orientation, when a certain highly reflective surface part reflects sunlight more or less exactly along the line of your sight.