very close encounter in 1976, in arizona, with extremely large craft,seen clearly

I am a college graduate,artist,mother,was secondary educator. at the time I was driving on a secondary highway, heading home with my daughter (sleeping) from an appointment with specialist in tucson.it was warm and my windows were down,had the radio on low. saw a "falling star" was ready to make a wish, when the falling star matched my speed(60mph)and contiued by me for about 4 min. it was aprox.100 ft. from ground, same distance to my left.Icould see it clearly. it was silent (turned down radio-it did not go off.) I watched it and it watched me.it was very large-at least two football fields and organic looking black,with what appeared to be windows down the sides. it was quite beautiful. my thought was: this is someone important! suddenly it ignited from rear and shot off into the distance out of site in approx 1 sec. I had seen the stealth just previously-no comparison. my husband then worked for the local radio station so I had access to various military bases and had seen some of the latest military and experimental aircraft up close and being tested(flown.) have been to many current airshows so I feel I have enough exposure to what we have developed on earth. this was not of this earth,it came from the stars. it did have some kind of lights but they were indescribable. no one believed me-but I don't care. I saw it and I believe they wanted me to see them. maybe they liked the little volvo sports car I was driving. at any rate I know we have extraterestrial visitors and they want us to know . remember this happened in 1976! can anyone explain this away? I keep looking for the same description and experience.anyone else see a craft like this ?