There are two "cold" equations used and referred to in Tom Godwin's short story "The Cold Equations." The first is the equation used to calculate the exact amount of fuel needed for an Emergency Dispatch Ship (EDS) to reach its destination; the second is the equation used to determine how long Marilyn can safely stay on-board the EDS at a decreased deceleration speed. Both equations are governed by the laws of nature, and these laws determine the longevity of Marilyn's life, just as they determine the longevity of the lives of all men on the frontier, meaning the men who are colonizing outer space:
The men of the frontier knew—but how was a girl from Earth to fully understand? h amount of fuel will not power an EDS with a mass of m plus x safely to its destination. To him and her brother and parents she was a sweet-faced girl in her teens; to the laws of nature she was x, the unwanted factor in a cold equation.
The first equation is the one computers use to determine the precise amount of fuel needed for an EDS to reach its destination in order to fulfill its emergency rescue mission. Since EDSs must be fast and, therefore, lightweight, they can only carry a limited amount of fuel. Fuel is calculated based on mass and distance. The amount of time and energy it takes to reduce the ship's deceleration speed must also be factored because EDSs have to be traveling very slowly to be able to enter the atmosphere of the new planet without burning up. Deceleration requires a great deal of energy, which consumes fuel faster; the girl's additional weight would increase the "gravities of deceleration" to the extent that the ship would run out of fuel before reaching its destination.
The second equation is the one the computers use, upon Barton's request, to calculate how long Marilyn can safely stay on-board the ship traveling at a reduced deceleration speed of .10 gravities. Commander Delhart agrees to feed the data of Marilyn's weight, the speed of deceleration, and distance into the computers in order to keep Marilyn on-board and alive as long as possible and returns with the answer that Barton can remain at the deceleration speed of .10 gravity until 19:10, exactly 57 minutes.