Below is just one of the application letters, written by a high-school student and notable if only for the postscript, in which the real reason for his application becomes clear.
Transcript follows. Image courtesy of the American Museum of Natural History. Found via Boing Boing.
I have just read in a Newspaper that you are reserving passage on the first spaceship that goes to Mars — for anyone who wants to go. At the present time I am a student attending High School, and I will be unable to go until I finish college... But from what I hear you won't be attempting the trip for quite a good many years to come.
My name is: Nordahl [Address redacted]
P.S. I would like to get out of this world before the H-Bomb blows it sky high.