Pulsating sphere interaction with a moving object

5:00 AM - woke up, when to bathroom.  Looked out window - saw a 'star'.  Normally I don't see stars in the city, too much city lights.
5:00 - 5:30 - back in bed, but can't sleep.  I have a head congestion - sinuses are all stuffy.
5:30 went to bathroom to blow nose, looked out window.  The 'star' is still in the same location about looking about South or SSE.  I can barley see the 'star' but it is there, in view, out of view, in view, out of view...  not moving.  Same size, not changing other than I can see it, then not see it...  I think it is a shimmering star, but at 5:30 AM I should not be able to see a star in the city .
About, say, 5:31, this star started pulsating - yellow, and orange - over and over and becoming fully in focus - like it was rotating.  Size never changed.  I thought can this be a weird angle on a plane, it kinda looked like that, but it was in the same position as a half a half hour ago.  It was rotating/shimmering, but never moved in location.
Then - a tiny second light appears - it was very small, just a bright yellow dot, ... like a meteorite, this little light shot right into or close by the big light.  This was an interaction.  The little light moved like 1-2 inches in my perception direct at the big pulsating light, it went right by it then disappeared.
Then immediately, the big pulsating light moved west - a few feet from my perspective,  - my view was then blocked my a neighbors roof.
Size - the pulsating light stayed the same in size, circular, rotating/pulsating.  When it moved, it moved like, the velocity of a plane, not crazy fast.