Correct -
Travolta's is one of these 138B ex QF "short bodies" rocketship...
xxx
I checked on Travolta's FAA pilot license listings.
Appears that he has a CPL with a CE-500 rating, but no 707 rating yet.
Certainly has a crew to fly the airplane (rated captain, insurance reasons).
So he can get some practice in LH seat, sure will get a 707 rating soon.
Obvious, airplane must be on a FAR 125 certificate.
So anyone, any age, with a second class medical, and current 707 type is legal.
Might be a nice job for retired 707 guys.
I understand he is a nice guy, and more of a pilot than an actor...
I once had him aboard a 747, before his pilot days... asked 1,000 questions.
xxx

Happy contrails