In the story, the cold equation is explained simply:
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.
Basically, Marilyn represents x, the "unwanted factor" in the cold equation that will doom her to death. Since Marilyn's weight adds too much to the mass of the EDS ( Emergency Dispatch Ships), she must be expelled from the craft. To keep her on board will doom the rest of the crew as well as those who await emergency supplies of a fever serum on Woden, a frontier station.
The author further makes the point that scientific laws are "irrevocable and immutable" and that such order is a necessity in terms of human existence.
The circumference of a circle was always pi times the diameter, and no science of man would ever make it otherwise. The combination of chemical A with chemical B under condition C invariably produced reaction D. The law of gravitation was a rigid equation, and it made no distinction between the fall of a leaf and the ponderous circling of a binary star system.
Since each EDS can only carry a limited amount of rocket fuel, the computers must calculate the exact amount of fuel needed by taking into account the course coordinates as well as the masses of the EDS, pilot, and cargo. Unfortunately, because the computers have not been programmed to take into account the added mass of a stowaway, Marilyn will end up being sacrificed to the dictates of the "cold equation."