Word has come that Wesley Crusher has been admitted into Starfleet Academy and will need to head to Earth to begin studies. Before Wes leaves, however, Captain Picard asks the young ensign if he will join him on a diplomatic mission to Pentarus V
As they are about to leave aboard a mining shuttle piloted by Captain Dirgo a distress call comes in from the leadership of Gamilon V. An unidentified vessel has entered their orbit and its presence has increased radiation across the planet to dangerous levels. The Enterprise speeds off to assist, and the shuttle heads to Pentarus V.
On the way disaster strikes as one of the shuttle's thrusters is blown off. Dirgo acts quickly and the trio crash land on an inhospitable moon. The shuttle is severely damaged, and will no longer fly, and the communications and food replicators are also smashed. Dirgo brags about being a great pilot, but is not very resourceful; he has no emergency supplies. Without any supplies at all, the three look for shelter from the boiling sun and yellow acidic air and eventually they stumble upon a cave.
The Enterprise arrives at Gamilon and discovers the ship in question is an abandoned garbage scow full of radioactive waste. Using remote modules the Enterprise crew work on towing the scow away from the planet and through an asteroid field to be dumped in a nearby sun.
Learning that the shuttle has gone missing, the Enterprise crew work more quickly, but have trouble with the remote modules. Riker orders shields extended around the scow to protect the planet from the radiation and they begin slowly towing the ship with a tractor beam through the asteroid belt.
Wes and the others locate a water fountain, but are not able to go near it as it is protected by a force field. Dirgo foolhardedly tries to phaser through the field, but a mysterious energy sentry appears, tosses away Dirgo's phaser, and causes a rockslide. Picard pushes Wes out of the way, but is bombarded in a hail of rocks.
Captain Picard is badly injured, and Dirgo believes Picard is done for, but Wes tearfully refuses to give up hope. Wes starts studying the energy readings, and concludes the sentry is sensitive to phaser energy. Dirgo arrogantly tells Wesley that he's "wrong", and bullies Wes into the idea that hitting the sentry with two phasers might work. However, the plan fails, and in the process Dirgo gets himself killed.
Meanwhile, the Enterprise finally manages to dispose of the scow and joins the search for the shuttle. In short order, the Enterprise crew locate the shuttle's destroyed thruster and are hot on the trail.
Wes manages to figure out a way to stop the sentry and gets to the water, which he then gives to Picard. The Enterprise arrives and Dr. Crusher and her medical team rescue the two. Dr. Crusher and her son, both in tears, hug. As Picard is carried out of the cave, he tells Wes that he will be missed.