UFO Sighting in Sandy, Utah on October 7th 2015 – Sphere of light brighter then all stars that would brighten and disappear slowly then very fast. This object moved and stopped directly overhead

My Wife, Son, and I were walking home after a short walk through our neighborhood. My wife exclaimed, "did you see that?". I said "no", but began to fixate my eyes in the direction she had mentioned. Suddenly a sphere of light brighter then all stars appeared and disappeared. This object would brighten and disappear slowly and on separate occasions very fast, brighten and disappear. Also, this object would reappear in different locations giving the impression that it had moved. We hurried home and I asked my father and step son to try to observe what we saw. They only had to wait a few minutes to observe the exact same thing. All four of us saw the light do what I explained above. The last time I saw it that night, the light appeared directly over head at least 3 times and did not move while appearing and disappearing. I was a physics major at the University near my home. I have a good understanding of acceleration (pertaining to change in direction and velocity) and a good general understanding of how satellites and meteorites behave. Stopping and changing direction does not happen and would be catastrophic for a satellite though this could be a highly reflective science experiment I suppose. In my opinion this was not farther away then the moon but did not seem to be within our atmosphere either. Also I found a video on MFOON's Last 20 Sighting Reports page that matched exactly what I experienced. The case number is for that observation is 71265.