object following an earth-orbiting satellite in the night sky.

First, I can't remember the date, even the year, but I was a teenager, about 14 which would make it around 1966. As a boy, I used to love to look at the night sky through my binoculars. Occasionally I would spot a satellite just after dark. Satellites were easily recognized by their steady, fast paced bright light. On this occasion, I spotted a satellite moving south to north in the eastern sky. When I trained my binoculars on the light, the magnification revealed that instead of one light, there were two, one following another. I watched for about ten to fifteen seconds as the two lights moved along the same path. Then, suddenly the rear light instantaneously changed direction and speed and faded to black as it zoomed off in an abrupt turn.  Through my binoculars looking toward the northeast, the two objects were moving from a two o'clock position toward an eight o'clock position. The rear obect then turned toward a one o'clock position. It seemed to do so without any hesitation whatsoever. It was many years later that I realized that what I had seen might be a UFO following a terrestrial satellite.
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Date is approximate.  We have assigned an arbitrary date in 1965