Barton and Marilyn are the only characters we meet in the story, but the problem they come to face onboard the spaceship builds up from surrounding problems .
The main issue Marilyn deals with before stowing away on the ship is that she hasn't seen her brother Gerry for years, because his government job has moved him to a colony on another planet. Gerry has been supporting their family with his government job, and now Marilyn has secured a job on the planet Mimir so that she can earn money as well. But, while she is on the larger ship Stardust going to Mimir, she finds out a smaller ship is being dispatched from it to the planet Woden, where her brother is. She is naive to the laws and restraints of space travel, and she doesn't realize that her illegally boarding the smaller ship as a way to get to her brother has some dire consequences.
Before he discovers that Marilyn is aboard his ship, Barton's main problem is that people on the planet Woden are in need of a serum to cure "the fever carried by the green kala midges." His mission of delivering this serum is a highly important one—people will die without it.
But the major problem within the story for both characters is that the Emergency Dispatch Ship they're on is not large or sturdy enough to be powered by a nuclear converter, and it only has enough rocket fuel to carry the weight pre-calculated for this mission—which does not include the weight of stowed-away Marilyn. She only weighs 110 pounds, but that's enough to stop the ship from reaching its destination.
Protocol for a stowaway on an Emergency Dispatch Ship is to jettison the stowaway into space. Barton obviously feels extremely conflicted about this, because he realizes that Marilyn is young and didn't know what she was doing when she hid on the ship. Eventually, they both accept that Marilyn has to be sent out into space, where she will die, because if she is not, Barton and Marilyn will both die on a ship losing fuel, and the sick people on Woden will die as well.