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Literature: The Cold Equations

"The Cold Equations" is a short story by Tom Godwin, first published in 1954, which has been done as a radio play for the X Minus One radio drama of the 1950s, a 1988 episode of The Twilight Zone, and a 1996 made-for-TV movie for the Sci Fi Channel.

Barton, the pilot of an Emergency Dispatch Ship (EDS) dropped from a Hyperspace cruiser, discovers there's a stowaway on board, a young girl named Marilyn. His ship is taking a load of vaccines to the planet Woden, it has just enough fuel to make the deceleration and landing with no reserve, and if they don't get there, 8 colonists will die. Also, there is no way to reduce the weight of the ship to compensate for Marylyn's mass. Typical practice as required by regulations is to jettison stowaways, as these vessels do not have any reserve fuel to allow a safe landing with the extra weight. However, the situation is complicated because Marilyn is an innocent who just wanted to see her brother (who is stationed on Woden) and didn't know that stowing away on an EDS would carry a penalty worse than a stiff fine.

The primary ship informs Barton there is no way the primary ship can retrieve Marilyn (Other lives depend on their strict timetable as well), that there's no other ships in the area, and he knows there's no planetary launch available, either. He must reduce the ship's mass, but he lacks the appropriate means to, for example, seriously strip the ship of unnecessary components. (There's nothing on the ship that isn't necessary.) She can't land the ship either as it's not computer-piloted, so Barton can't sacrifice himself. Barton doesn't like the only choice available, and realises that he's going to have to live with the thought of what he's going to have to do for the rest of his life.

Failing to reduce the ship's mass — by spacing Marilyn — will mean the ship will crash, and Barton, Marilyn and the colonists will die. Marilyn eventually accepts that there is no alternative, so after being able to reach her brother over the radio to say goodbye, Marilyn walks into the airlock, and Barton ejects her into space.

The point of the story is that in space, sometimes the cold equations leave no alternative, and balancing the equation means someone dies.

This story supplies examples of

Always Save the Girl: The whole point of the story is to avert this trope.
Cold Equation: The Trope Namer.
Downer Ending: There's no solution to the problem that does not result in Marilyn having to be executed.
Executive Veto: Ironically, it was Campbell himself, the Trope Namer for Campbellian Hero, who refused to publish the story until the author wrote an ending in which the girl died.
I Did What I Had to Do
Missing White Woman Syndrome: Barton notes that "On Earth [Marilyn's] plight would have filled the newscasts...Everyone, everywhere, would have known of Marilyn Lee Cross and no effort would have been spared to save her life." In space, however, there's no room for that kind of emotion.
Mohs Scale of Science Fiction Hardness: Very Hard, with the exception of hyperspace aircraft carriers, as the fuel dilemma is based around the application of the Rocket Equation, which can be simplified to: In space, you need fuel to lift the fuel, and more fuel to lift that fuel, so every gram counts.
Science Hero: Also a deliberate aversion — no-one pulls a technological Ass Pull to save the girl.
Swiss Cheese Security: The whole situation could have been avoided by a 30-second pre-launch check.
Take a Third Option: The fact that there isn't one is the entire point. The story was originally a much-needed subversion of early 1950s Science Fiction and its omnipotent men of SCIENCE!.
Thrown Out The Airlock