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> has to keep walking west to stay in the sunlight so she doesn't freeze to death.

Reminds me of the opposite problem we can see in "The Chronicles of Riddick" (2004). Keep running to stay in the night side of the planet to survive the sunrise.

With great music "The Chronicles of Riddick | Outrunning the Sun" https://www.youtube.com/watch?v=sGihB0gxgko

One of the earliest Star Wars novels (now part of the noncanonical “extended universe”) featured a walking mining colony that walked across a planet to stay in its night side.

The story: https://www.baen.com/Chapters/0671878522/0671878522___1.htm

Futurama writers must have read that:

https://en.wikipedia.org/wiki/The_Series_Has_Landed?wprov=sf...

A slightly smarter protagonist would have headed slantwise for the nearest pole. 200 miles/day is a pretty hard slog, but close enough to a pole, you might get along on just one. Being at the crash site so rescuers can find you, besides, would be hard to calibrate.