All I know is that it's basically about a little girl who sneaks onto a spaceship. The ship can't land because its too heavy, all automated or something. But she is found and they try to shoot a bunch of junk out into space to get the weight right, no joy, so at the end she calls up her parents that are on another ship, says goodbye, and I guess she gets shot out into space.
That's about the gist of it. Not sure if it's from The Outer Limits or The Twilight Zone.
This is "The Cold Equations", an episode of The Twilight Zone that was the 16th episode of the 3rd season of the 1980s incarnation of the series. The episode is an adaptation of a rather famous 1954 short story of the same name by Tom Godwin.
Thomas Barton is an astronaut who must deliver a vital cargo of vaccine to a plague-stricken colony world. However, a young girl named Marilyn has stowed away on his vessel with hopes of reuniting with her brother Gerry at the colony. Now the entire mission is in jeopardy as her presence on board was not calculated into the flight plan, which goes strictly "by the numbers" and there will be no way for the pilot to compensate for her added weight. They also discover that there are no other ships which can pick her up prior to arrival at their destination.
The promo can be viewed here:
