In "The Cold Equations," why do you suppose Godwin chose the third person limited point of view instead of making Barton the first person narrator? How does third person limited point of view affect the story's tone, plot, and believability?

The classic science-fiction story "The Cold Equations" by Tom Godwin tells of a supply ship pilot named Barton carrying life-saving medicine to the colonists of a frontier planet. He discovers a stowaway aboard, a teenage girl who wants to visit her brother. The problem is that he does not have the fuel to land safely with the extra weight. He has no choice but to jettison his passenger before they are both killed and the medical supplies are lost. There is an emotional scene in which the girl speaks with her brother, and then she voluntarily walks into the airlock so that Barton can eject her into space.
In the first person point of view, the reader perceives the story solely from within the viewpoint of a single character. In a sense, the reader is looking out from the eyes of the first person point of view character and feeling all of their emotions. Third person limited point of view also focuses on a single character's viewpoint, but it moves back from within the character's mind so that the reader can see things from a more objective perspective.
The premise and plot of "The Cold Equations" rely on the irrefutable logic of scientific realities and how these realities have such a tremendous emotional impact on the characters. First person point of view would have been too immersive for this story. It would have had the reader focusing too much on Barton and not enough on the terrible cold logic that necessitates the killing of the girl. That's why Godwin chose to take a step back and use third person limited point of view instead: to get a more objective viewpoint, which makes the conclusion even more devastating.