I have a vague memory a movie with a scene like that being shown in school for some reason. I think it was called "E=mc2", but I have not been able to find it online. It was a family on a space exploration mission.
I remember a girl saying "There's a blue planet up ahead," and her brother replying that it just looks blue because of the Doppler effect, and when they pass it the planet will appear to turn red. This happens, and the girl calls him a know-it-all.
I remember also that as they're trying unsuccessfully to escape the black hole's gravitational field, they detect that the black hole is rotating, and that theoretically a rotating black hole is a gateway to another universe. They end up going through, and the stars in the other universe look they were filmed with a different lens to give them points.
EDIT: Bobby Newmark has it right. I thought it was called "E=mc2" because according to the Wikipedia page on Into Infinity,
In his script, Byrne proposed that E=mc2, the Einsteinian
formula that relates mass to energy, should appear on-screen at
intervals.