The U.S.S. Enterprise takes aboard Troi's eccentric mother Lwaxana and Dr. Timicin of Kaelon II. Timicin has been brought aboard to conduct an experiment which he hopes will save his threatened home planet. The lives of the people of Kaelon II are in jeopardy as the sun their planet orbits is in a state of near-collapse. The Federation has enlisted the Enterprise to take Timicin to a sun in a similar state of decay to conduct experiments which may yield a method for saving the Kaelon system from destruction, a peril which will certainly occur if its sun fails.
Upon arrival at their destination, the crew assists Timicin in modifying a photon torpedo to be fired into the proxy sun in the hopes that it will repair the damaged star and prove that the technique can be safely applied to the Kaelon sun. The torpedo is fired and, although the experiment seems initially to rectify the damage, the effect is short-lived and the experiment is declared a failure. The Enterprise returns to Kaelon II and Timicin is crushed. After some questioning by Lwaxana, Timicin reveals that experiment's failure is not the only fact troubling him. Indeed, Timicin is about to turn 60, and on Kaelon II, everyone who reaches the age of 60 kills him or herself in what is known to their people as "the Resolution," a means of ridding their culture of the need to care for the elderly. Lwaxana is outraged by this fact, and when Picard makes it clear that he will not interfere in the planet's local affairs, Lwaxana tries to beam herself down to the planet to halt the process. When she is thwarted, she goes into hysterics until Deanna comforts her.
After Lwaxana and Timicin end up spending an evening together, he tries to explain the custom of the Resolution to her, stating that they should never expect to be repaid for the care they show their children, and a fixed age had to be selected because just randomly choosing a time to die would be heartless. However, she still considers the custom barbaric, and refuses to accept their tradition, listing an example in Betazed history of a woman who went against the tradition of wearing a ridiculous wig and changed their civilization for the better. When Timicin's analysis of the failed test turns up some promising options, he suddenly realizes that no one else has the knowledge to carry on his work to save his world, and requests asylum on the Enterprise.
B'Tardat, the Science Minister on Kaelon II, is outraged, and sends up two warships to ensure that the Enterprise does not leave the system with Timicin on board. As Picard orders the bridge crew to analyze the offensive capabilities of the Kaelonian ships, Timicin realizes that his situation is not as simple as he had hoped, for the planet below will not accept any further reports from him. Indeed, he's informed that even if he finds a solution they will not accept it. The final straw comes when his daughter Dara (Michelle Forbes) beams on board to insist that he return. She cannot bear the thought, she says, of him being laid to rest anywhere but next to her mother and, although she loves him, she is ashamed of him.
Timicin realizes that he is not the man to forge a cultural revolution, and agrees to return to Kaelon II. Lwaxana, despite her disagreement, realizes that Timicin's decision is his to make and, as it is the custom for loved ones to be present at the Resolution, beams down with him to be at his side as he dies.