This is a classic science fiction story. A teenage girl stows away on a space ship headed to a colony on a far away planet, in order to see her brother. The ship is carrying medications necessary for the survival of the colony. It also has only the bare minimum fuel needed to carry the bare-bones ship to the colony. The equation of the title is the one that relates the weight of the ship to the weight of the ship plus the girl--there is nothing to jettison in place of the girl, and the captain has to tell her she must be sacrificed so that the medications reach the colony.
Tom Godwin's "The Cold Equations" is a very utilitarian science fiction short story. Utilitarianism is a moral theory that bases right and wrong on the number of people the action benefits or brings pleasure to. The story is utilitarian because the pilot is forced to act for the sake of the greater good by saving multiple lives rather than just one.
In the science fiction story, outer space is being colonized, an action that leads to its own set of moral obligations and consequences. One consequence is that the colonists do not have the easiest method of delivering emergency supplies. As the narrator, who is the pilot, named Barton, explains, "huge hyperspace cruisers" transported colonists and made routine visits to the colonies; however, since they were very expensive to operate, they could not make unscheduled emergency stops. As a solution, small, lightweight Emergency Dispatch Ships (EDS) were created, but their size necessitated being engineered in such a way they could only carry as much rocket fuel as was needed to make it to their destination. Fuel was calculated based on the "mass of pilot and cargo"; any extra weight on the ship would lead to a shortage of fuel and an inability for the emergency vessel to make it to its destination. The danger of emergency mission failure led the authorities to devise the interstellar regulation stating, "Any stowaway discovered on an EDS shall be jettisoned immediately following discovery."
Barton knows instantly he has a stowaway on the ship due to a heat gauge on his control panel. He expects the stowaway to be a "man with some ulterior motive" and is very surprised to see a young curly-haired, blue-eyed, perfumed girl emerge, named Marilyn Lee Cross. As their conversation progresses, Barton learns Marilyn stowed away to travel to see her brother, being completely naive of the dangers the frontier poses and of the consequences for stowing away. Barton becomes faced with the moral dilemma of choosing between empathizing with and protecting Marilyn due to her naivete or protecting the lives of the colonists by succeeding in delivering the medical supplies. However, Barton knows protecting her will lead to the loss of many lives rather than just her own life, leaving him to make a utilitarian decision.
Barton does all he can for Marilyn, including trying to get the commander to bring the Stardust to rescue her, calculating how much time she can remain on the ship, asking permission to remain at that speed for as long as the computer allows him to, allowing her to write letters to her family, and even getting in contact with her brother, Gerry Cross, so she can say goodbye. However, Barton knows it is his moral duty to eject her from the ship in order to spare the lives of many, even though, as she says, she "didn't do anything to die for."
Beyond raising questions about the rightfulness of utilitarianism, it also raises the ethical question concerning whether or not a person should pay consequences for wrongful acts committed simply out of ignorance. The resounding answer the story gives is "Yes"—a person must pay consequences regardless of innocent ignorance.