An unnamed world physically identical to Earth, where a failed life-prolongation experiment three centuries earlier killed every adult and left only slowly ageing children.
Miri's planet is the setting of the original series episode Miri. The Enterprise answers an old-style distress call and finds a world that matches Earth exactly, down to its continents, with towns resembling the mid-twentieth century.
About three hundred years earlier, scientists there created a virus meant to extend life. It killed the adults, the grups, in madness and disfigurement. Children age only a month per century, but the disease takes them when they reach puberty. The survivors, who call themselves Onlies, are led by the boy Jahn.
Kirk's landing party is infected and has days to live. With help from Miri, a girl on the edge of adulthood, they win back their stolen communicators and McCoy tests a vaccine on himself.