Sci-fi Radio (ep20/21) Houston, Houston, Do You Read by James Tiptree Jr.

Houston, Houston, Do You Read? by James Tiptree Jr. aka Alice Sheldon
The story portrays a crew of three male astronauts launched in the near future on a circumsolar mission in the spaceship Sunbird. A large solar flare damages their craft and leaves them drifting and lost in space. They make repeated attempts to contact NASA in Houston, to no avail. Soon, however, they begin to pick up strange radio communications.
They are puzzled that almost all of the voices are female, usually with a strong Australian accent. They overhear conversations about personal matters (including the birth of a cow) as well as unknown slang terms. Various theories are discussed by the perplexed astronauts: hallucinations? A hoax? A hostile power trying to trick them? They record and playback the conversations over and over, trying to figure out what is going on. Soon, they realize that these unknown people are aware of them and are offering to help.
At first, the Sunbird's commander refuses to communicate with them, suspicious of their motives. As they continue to plead with the astronauts to accept their rescue offer, the men are chilled to hear their mission referred to in historical terms. They come to realize that they were not only thrown off-course in space but in time as well and that their flight was lost centuries ago. They are given bare details of the current Earth: an undefined cataclysm has reduced the human population to a few million. Eventually, the Sunbird agrees to rendezvous with the spaceship Gloria to allow the astronauts to spacewalk to safety.
The Gloria is an enigma to them. Besides having an almost all-female crew, the ship is haphazard and cluttered with plants and animals on board. The technology used on the ship does not appear to them to be as advanced as they would have thought the world to be after such a long passage of time, and they think it odd that some of the ship's functions are powered by stationary bikes. Their culture shock is compounded by the cryptic and incomplete answers they are given concerning the Earth.
Little by little, the three gather clues from both observations and slips of the tongue. While crew members often refer to their "sisters," there is no mention of husbands, boyfriends, or families. There are twins on board (both named Judy), yet one seems older than the other. The one male, a teen, named Andy, seems strangely feminine. Technology, and science and culture in general, seems to be relatively unadvanced considering the centuries that passed.
Eventually, they learn the truth.