While a passenger aboard the U.S.S. Enterprise, Troi's overly-amorous mother Lwaxana becomes infatuated with Dr. Timicin of the planet Kaelon II. The rather reserved Timicin, a leading scientist who has enlisted the Federation's aid in saving his planet, is equally smitten with Lwaxana, and the two begin spending time together.
Timicin has boarded the Starship Enterprise to test an experiment that he hopes will revitalize the dying sun of Kaelon II. The U.S.S. Enterprise assists him by transporting him to a similar sun in a remote region of the galaxy where the scientist can test his theories. With the help of the crew, Timicin fires photon torpedoes into the surrogate sun in an effort to elevate and stabilize the temperature. At first, the experiment seems successful, but the sun's temperature continues to rise to dangerous levels, forcing the starship to evacuate the region and return to Kaelon II. Later, when even the charming Lwaxana is unable to comfort the defeated Timicin, he confides to her that he is returning home to die.
Soon afterward, Lwaxana marches into Picard's office, outraged by Timicin's revelation that he will soon participate in a ritual suicide known as The Resolution. The ritual calls on all citizens of Kaelon II to kill themselves upon reaching the age of 60 in order to eliminate the society's responsibility of caring for the elderly. Lwaxana likens the ritual to murder but Picard refuses to intervene since the problem is out of his jurisdiction.
Unable to sway Picard, Lwaxana focuses on Timicin, urging to stand up to the arbitrary Resolution. She begs him to take the first step toward changing the policy by publicly rejecting the ritual. Timicin initially refuses her request, but reconsiders when he discovers how close his research has brought him toward saving his planet's sun. With this in mind, he asks Picard to grant him asylum aboard the U.S.S. Enterprise.
Picard agrees, nearly launching the U.S.S. Enterprise into war by incurring the outrage of the people of Kaelon II. The planet's science minister insists that Timicin return at once, dispatching warships and ordering them to fire on the U.S.S. Enterprise if the ship attempts to leave the area with Timicin. Timicin remains firm, however, until his daughter Dara transports aboard and pleads with him to accept his heritage — the heritage he taught her. The request touches Timicin and he agrees to return home to die among his loved ones. Since Lwaxana is now a loved one, she swallows her pain and disappointment and transports down to the planet with him, to witness his final Resolution and give her support to his decision.