Tom Godwin's story "The Cold Equations" has very few characters—just Barton the pilot, Marilyn Cross the stowaway, Gerry her brother, Commander Delhart, and an unnamed records officer. These characters are factors within the equation of the plot: Barton, Delhart, and the records officer represent the known quantities, while Marilyn and Gerry are unknowns which the plot must "solve for" to determine how they will influence the result.
Every character is subject to the titular "cold equations" that rule life on the galactic frontier, but perhaps none more so than Barton himself, for he is the one who must choose whether to submit to those equations or try somehow to find a way around them. When Barton finds Marilyn hidden on his supply ship, her presence throws Barton's personal equation out of balance. The appearance of this unknown quantity changes the calculation used to determine how far Barton's ship...
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can safely travel, and logic dictates that Barton must jettison Marilyn, or her weight will cause the ship to run out of fuel before it reaches its destination.
Barton accepts the fact that he must execute the stowaway as an uncomfortable but necessary duty:
"There could be no alternative [...] What he must do would be unpleasant for both of them; the sooner it was over, the better."
He is not prepared for Marilyn's childlike innocence, however, and finds it difficult to justify killing her on the basis of mathematics. Marilyn appeals to Barton's humanity, pleading to be spared and insisting that there must be some way to complete the journey without ending her life. By telling the story from Barton's third-person-limited point of view, Godwin forces the reader to go through all of Barton's calculations as he tries to find an alternative solution to his dilemma. Barton slows the ship down to conserve fuel,and radios Commander Delhart to explain the situation, hoping against hope that the commander will be able to suggest something:
"The call would be futile, but he could not, until he had exhausted that one vain hope, seize her and thrust her into the air lock as he would an animal — or a man."
The commander, however, enforces the rules:
"'I’m sorry — I can do nothing. This cruiser must maintain its schedule; the life of not one person but the lives of many depend on it. I know how you feel but I’m powerless to help you. You’ll have to go through with it.'"
Marilyn is anguished and argues desperately against this sentence. The reader, tied to Barton's third-person viewpoint, must continually reassess Barton's available options, and continually return to the conclusion that Marilyn must be jettisoned—the one sacrificed to save the many who are depending on the ship's supplies. And yet Barton still tries to spare Marilyn her fate for as long as possible:
"She would have to go when deceleration began; it could be no other way. When would that be—how long could he let her stay?"
Because the reader is limited to what Barton knows, feels, and understands, there is still some hope right up to the final paragraphs that Barton will somehow be able to save Marilyn. Likewise, because the reader is limited to what Barton knows, feels, and understands, they are left with Barton's doubts about the rightness of his actions, and haunted by the consequences of his decision.
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.