Dont feel too bad. I watched a light head towards me once then off to my left one night when I was stargazing. Long story short through the 20 x 50s I could see an onion shaped plume as though I was now looking up the tail pipe of a rocket. Nothing on radar no recent launches wasnt a satellite either. Was moving faster than the speed of an aircraft based on my calculations about 150k away as that is the maximum distance I can see an aircraft light at night.
I think all sorts of Military exercises and tests take place all time at night.
I would put what you seen down to aircraft operating from an Aircraft Carrier.