A bright red ( round dot circle bubble luminous) UFO sphere splits into two, then travels in opposite directions after splitting

A friend and I were watching stars and night sky after an exciting night of fire works.  It was the day before my 16th birthday, and my friend was about the same age.   
I'm male, my friend was female.  I lost contact with her not too long after the encounter.  I am educated and a Science teacher now.  
As for the what we saw that night...  My friend and I were talking about teenage things when we both saw one bright red round dot - circle - bubble (words to describe it) which seemed very far above us.  It was not moving at all.  We discussed, was it a planet reflecting red?  A laser pointer?  Was it a satellite, because it did appear to be far away?  A plane?   Lastly,a UFO?  
Anyway, since it wasn't doing anything while we were talking about it, we continued socializing about other topics.  We would look back at the red luminous sphere every so often, but it wasn't moving.  After about 20-30 minutes, we started looking around the night sky again, and again the attention on the red brightness brought us back discussing the object.  
At some point, with our attention on it, the red dot split into two identical red round objects; like cell division division had taken place, the two bright red objects started traveling in opposite directions at a steady, medium speed.  
Freaked out, my friend and I became scared, and tears welted in my eyes, because I didn't understand what I was seeing.  
We both watched with tense anticipation watch the red spheres travel apart.  Within 2 minutes of the splitting, the separated red Unidentified Flying Objects disappeared.  I don't know what we saw that night, but it was something I cannot explain. 
From time to time, I think back to what I saw and it still makes my eyes welt with uneasiness.