Bright light crossing the sky, circles the full moon, and crosses back across the sky.

I as a young boy was staying with a group at a friends house.  We were in the yard sitting around a fire.  The moon was full and was to the right of my field of vision while observing the sky.
I observed a bright round light moving left to right on the left side of my field of view.  If the moon was the size of a small dinner plate, the object was about the size of a dime.
It took several minutes for it to cross the sky and reach the center of the moon.  It crossed the surface and circled around behind it and came back from the other side and proceeded to move right to left back across the sky.  The whole event lasted maybe 10-15 minutes.  The object disappeared from view off to the left.
Witness indicates that the date of the event is approximate.  PD