World Without End

In March 1957, Commander Dr. Eldon Galbraithe (Nelson Leigh), engineer Henry Jaffe (Christopher Dark), radioman Herbert Ellis (Rod Taylor) and scientist John Borden (Hugh Marlowe), are returning to Earth from the first spaceflight, a reconnaissance trip around Mars. Suddenly, their spaceship is somehow accelerated to incredible velocities, and they are knocked unconscious. Their ship crash lands on a snow-covered mountain. When they venture out, they discover that they have become victims of time dilation and are now in Earth's future.
They theorize, from seeing time-worn gravestones and after their ship's instruments register heightened residual radiation, that a devastating atomic war had broken out in 2188, and that they are at least 200 years past that date. (They later learn that the year is 2508). Jaffe is particularly hard hit, as he realizes that his wife and children have long since died.
After surviving an ambush by giant, mutant spiders, they are attacked by one of two competing remnants of human society. The "mutates" (as the astronauts label them) are violent, primitive surface dwellers. They have mutated due to generations of exposure to heightened radioactivity. (However, the background radiation has decreased to tolerable levels, and the men later learn that normal humans are often born to the mutates. These, however, are enslaved.)
Seeking shelter from the attacking mutates in a cave, the four men discover the entrance to an underground city, whose residents are the descendants of those who fled there from the atomic war. These people live in a high-tech, sophisticated culture. They are a peaceful group led by Timmek (Everett Glass), the president of the ruling council. Underground, the men have grown less virile, and there are fewer and fewer children born each generation. In contrast, the women remain physically vital (and ready for romance). Elain (Shirley Patterson), admires a shirtless Herbert Ellis, commenting that the astronauts are "more muscular than our men". Deena (Lisa Montell), rescued from the surface as a child, falls in love with Ellis.
The astronauts try to persuade the underground people to arm themselves and reclaim the surface, but they are content with their comfortable existence.
When Timmek's daughter Garnet (Nancy Gates) shows she is attracted to John Borden, Mories (Booth Colman), an already hostile member of the council, becomes jealous. He retrieves the astronauts' confiscated pistols, but has to kill a man when he is caught in the act. Mories plants the guns in the astronauts' quarters. When Timmek is informed of the murder, he has his men search the newcomers' rooms. Finding the weapons, Timmek orders the astronauts expelled, but Deena testifies that she saw Mories hide the guns. Mories flees to the surface, where he is killed by the mutates.
With Timmek now cooperative, the astronauts manufacture a bazooka and head back to the surface. Fleeing the deadly bazooka fire, the mutates take shelter in the caves. Borden offers to fight their chief, Naga (Mickey Simpson), in single combat for leadership of the mutates in order to save the unmutated surface dwellers from Naga's threatened slaughter. Borden slays Naga and orders the remaining deformed mutates to leave. The astronauts then establish a thriving settlement, including members of both groups.

Question: Who do the astronauts try to persuade to arm themselves and reclaim the surface?
Answer: The underground people