In "The Cold Equations" by Tom Godwin, does the girl understand why she cannot stay on the ship?

In this story, a girl stows away on a space ship in hopes of seeing her brother. Unfortunately, there is only enough fuel on the ship for the captain, and the captain has no choice but to "jettison" her from the ship in order to complete his mission. 
At first, the girl cannot comprehend that the captain would do this to her because it would lead to her certain death. When the captain tells her of her fate, she says, "No! You're joking-- you're insane! You can't mean it!" However, the narrator makes it quite clear that she does come to an understanding of why she has to die. When she asks if he really means it-- that is, if he is certain that she will have to be thrown off the ship-- the narrator writes that she "sagged back against the wall, small and limp like a rag doll, and all the protesting and disbelief gone." This detail suggests that, even though she does not want to die, she understands why it has to be. She still has questions, and based on those questions it seems she might hold out a small hope that something could change, but ultimately she understands the predicament and the "cold equation" of the amount of fuel in the ship after the captain explains why she has to die. She fully understands that her options are to "go alone" or to "take seven others" with her. The girl continues to ask questions of the captain, such as whether someone can come help her, but they all lead to same conclusion, which she seems to accept. She even tells the captain at one point that she understands. Though she doesn't want to die, she understands why she has to.