What is some scientific evidence used in "The Cold Equations", by Tom Godwin?
I'm not sure what you mean by scientific evidence, but Godwin has his story turn on hard, scientific truths. The pilot of the spaceship has to decide what to do when he finds the young stowaway. His spaceship is carrying emergency medical supplies to a colony world. If it does not arrive safely, many people of the colony will die. The ship carries the exact amount of fuel necessary to transport the ship, supplies, and pilot to the colony world, and no more--it would not be economical to do otherwise. The young stowaway has no idea of this--she wants to see her brother, who she has not seen in ten years, and figures she will have to pay a fine. But the equations are exact, and the girl is jettisoned to her death. So the scientific evidence I think you want is that the amount of fuel can be calculated exactly, the flightpath calculated exactly, and that there is no room for extras.
The EDS has been fuelled only sufficiently to deliver the ship and its contents to the surface of the planet, with no margin for errror. It only has to follow the pre-programmed flight plan to get safely down to the surface, where the pilot will have to remain until the next scheduled contact. If a stowaway is not discovered, or allowed to remain on board, the pre-calculated fuel burn rate will not decelerate the ship sufficiently, and it will impact on the surface at high velocity, or, if the burn rate is increased to allow for the added mass of the stowaway, the ship will run out of fuel at some point above the surface, and it will crash, both scenario's spelling death for the pilot, the stowaway, and the colonists. The mass/energy equations admit no other outcome, and the stowaway must be jettisoned.