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It is clear from the opening paragraph that the story opens in a space shuttle in the future:
He was not alone.
There was nothing to indicate the fact but the white hand of the tine gauge of the board before him. The control room was empty but for himself; there was no sound other than the murmur of the drives - but the white hand had moved. It had been on zero when the little ship was launched form the Stardust; now, an hour later, it had crept up. there was something in the supply closet across the room, it was saying, some kind of a body that radiated heat.
Thus Godwin very quickly establishes the setting in a future time where science and technology have developed so rapidly that space travel is far more common than it is today. Later on in the story we are told that the girl was born in 2160 which gives us some indication as to the year in which this story is set. However, what is most important to realise is the brutal reality of the desperate situation the stowaway finds herself in. As Barton explains to the girl,
"These little ships are always given barely enough fuel to reach their destination, and if you stay aboard, your added weight will cause it to use up all its fuel before it reaches the ground. It will crash then, and you and I will die and so will the six men waiting for the fever serum."
These, then, are the "Cold Equations" referred to in the title - the harsh, impersonal mathematical sums that make it impossible for the girl to stay on board and show that she has to be thrown out of the shuttle so that the pilot can reach his destination with the serum.
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