Could you be thinking of the 1960 film, Beyond the Time Barrier? It's the future, and involves a single test pilot, but has a similar premise:
Experimental pilot testing a new rocket powered craft (actually a Convair F-102 interceptor) manages to fly into the future and land at the now deserted airbase he left. He ends up in a city with people who are suspicious he is a spy and who want to keep him to procreate with the rulers daughter because the majority of the inhabitants are sterile. He manages to escape and return to his own time but "with consequences".
Said consequences, as best I can tell from a plot summary, are that:
The pilot is shown at the end of the film to have rapidly aged to decrepitude as a result of his time travel.
It's also in black-and-white, which you did not mention, but would fit with the era you believe the film to be in.
Found with search terms of 1950s film "experimental jet" lands on a different planet