"Mudd's Women" is a first-season episode of Star Trek: The Original Series. The episode first aired on October 13, 1966 on the NBC Network. Teleplay by Stephen Kandel, Story by Gene Roddenberry. Directed by Harvey Hart
In Mudd's Women, The USS Enterprise chases an unregistered starship, a small class J cargo vessel. Fleeing, the ship approaches an asteroid belt. Scotty manages to beam the ship's master who identifies himself as Leo Francis Walsh and three women off just before an asteroid destroys the vessel with a dead-center hit. Captain Kirk's discussion with the ship's master trader is not productive. The trader has unusual cargo: three stupendously seductive women he says are to be wives for lonely men on frontier planets. Leo Walsh is revealed to be intergalactic criminal Harcourt Fenton Mudd. As the ship damaged all its dilithium power crystals chasing Mudd's vessel, he feels himself empowered to force Kirk to make a deal. Mudd overhears Kirk's orders to contact the miners on Rigel XII, he begins to plan how the situation can work to his advantage. Using their allure, the women learn about the miners and intend on beaming down once the Enterprise arrives at the planet Rigel XII to acquire replacement lithium crystals.
The lesson of the story
In the odd science fiction version of the universe where this melodrama takes place, a ship on "impulse power" from its batteries is in danger of "spiraling in" to the planet. This is obvious nonsense to any physics student or mathematician, because a spiral is not one of the possible orbits.
Nonetheless, the story contains a potent lesson: "You either believe in yourself, or you don't." When one of the women stops taking the Venus Drug, she reverts to homeliness but upon taking a placebo given by Kirk, she regains her attractiveness.