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At the end of Interstellar, Murph tells Coop to

go find Brand instead of staying to watch her die

and her closing monologue suggests she knows that Brand is

setting up the colony on Edmunds' planet.

How did she know anything about Brand's whereabouts or survival?

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3 Answers 3

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When Coop first arrives at the station, he asks about Murph, and the doctor says "She'll be here in a couple weeks." So at some point during those two weeks it's reasonable to speculate Coop had been interviewed/debriefed about his experiences, and Murph had learned what he said before they finally saw each other. If this is the case, she would know that Coop had helped Brand escape falling into Gargantua just before he fell in himself, and that she was headed for Edmunds' planet--as mentioned earlier after the disaster caused by Dr. Mann, they had been planning to do a gravitational slingshot around Gargantua in order to get there:

COOPER The navigation mainframe's destroyed and we don't have enough life support to make it back to Earth. But we might scrape to Edmunds' planet.

BRAND What about fuel?

COOPER Not enough. But I've got a plan — let Gargantua suck us right to her horizon — then a powered slingshot around to launch us at Edmunds.

So based on this, Murph could infer that Brand was on her way to Edmunds' planet, and perhaps had had enough time to get there (for some discussion of why Brand arriving at Edmunds' planet probably happened at roughly the same time Cooper arrived at the station, see this answer). And Murph's use of the word "maybe" in her comments suggests she was just making some reasoned speculations on what was going on with Brand at that moment, not that she knew for sure:

She's out there ... setting up camp...alone in a strange galaxy...maybe, right now, she's settling in for the long nap...by the light of our new sun...in our new home.

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Murphy shouldn't have known anything about Brand's circumstances, notwithstanding Cooper's assumed de-briefing. Edmund's planet was comparatively near a black hole (Gargantua), and so moving at a tremendous speed compared to our solar system, located far from the center of the Milky Way's black hole (Sagittarius A) Therefore, Cooper's time back in our solar system (2 weeks) would amount to perhaps just minutes or hours on Edmund's planet, as demonstrated on the watery world (Millar's planet). So there was not enough time for anyone to know if Brand made it to Edmund's planet alive, or if the conditions there were survivable. The filmakers want you to understand however, that Brand did survive and that Edmund had died and was therefore "available" for Cooper. Cooper couldn't know this though. "Brand" is an awesome name for her character, as she will now be the "brand" of first humans on our species' new home. Cooper means barrel maker, but could be slang for a Rooster?

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Well she knew, because that's they wrote in the script. You could presume one of two things. She knew, because she knew Brand was on the mission, and in amongst the data transmitted there was some how information pertaining to the ship, or coordinates, etc, that lead her to the conclusion that Brand was with or near when he went into the black hole, and she used intellect and intuition and guess that she made it. Not hard for a woman who solved gravity.
Or. She was able to figure out that Cooper was her ghost, read binary in book spaces.. it's possible the future us-is some how gave her a glimpse insight. Or she could see it in her dad's face somehow. I mean really she wouldn't know. But as smart as she is maybe she just figured it out.

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