The Cold Equations (1996)

Lt. John Barton is sent on a special mission to deliver a special vaccine to a distant mining colony. He is infuriated to find Lee, a stowaway aboard his spacecraft. Barton has only enough fuel to carry himself and his precious cargo, and Lee's added weight insures that they will crash if she stays on board. They have gone too far to turn back, and Barton's superiors make it clear: the mission takes precedence and Lee has to be dumped into space. But she won't go quietly.