Why do you think Godwin chose third person?

I would argue Godwin uses third person in his classic science fiction short story to provide emotional distance.

As the title indicates, much of the theme of the story revolves around Barton (the pilot) thinking coldly. He and the stowaway are living in a universe determined by these equations. All actions are determined by mathematical formulae, which are fundamentally third person and objective. There is (ideally) no subjective element to math. In the same sense, a third-person perspective allows Godwin to maintain emotional distance and objectivity. A first-person perspective would permit too much intimacy.

A second, related reason is to maintain tension. Readers must wait for Barton to reach his decision. They have no access to his internal processes. They don't know what he is thinking or feeling, and must wait for the decision to emerge, waiting along with Marilyn (the stowaway) to learn her fate.