Hey, you can leave the ship by interacting with the star map.
If you are using an older save, there is a high chance that you haven't correctly unlocked the star map due to the previous switches, I can fix your save file though if you send it to us on our e-mail.
Normally, after you did Tripteen, the star map is unlocked forever, if you are trying to get to the first planet for the first time, make sure you have your space suit equipped over the outfitter. (you might need to pick it up from your room first)