"Failsafe" ?
Yes. Excellent guess verner!!! I forgot to check my imdb voting history and found it also there.
Cast with Walter Matthau as the Professor and Henry Fonda as the President.
http://www.imdb.com/title/tt0058083/Interesting i find also this here listed under Trivia for the movie:
The view of the satellite zooming into a closer shot is actually film taken from a camera mounted on a captured German V2 rocket launched from White Sands, New Mexico. The film is run backwards to show the illusion of zooming closer to the ground.