I've been thinking about this since I saw the movie a few weeks ago and I haven't been able to put my finger on a definitive answer so I figured I'd ask here.
At the end of Interstellar
Coop leaves the Tesseract around 80 years after the mission started in our universe. He's spit out by Cooper Station which was by Saturn which was where the wormhole was located if I'm not mistaken. When he meets with the elderly Murph she tells him to go find Brand who is apparently alone on Edmund's planet just trying to do the whole plan B thing. This leads me to believe that no humans had made it to Edmund's planet yet.
Why hadn't humans made it to this planet yet? It seems like
As soon as the gravity equation was solved they'd begin their voyage as a species to this new galaxy and their new home
Am I missing some sort of time dilation effect that has stopped humanity from going there? Like word of this planet not reaching our galaxy yet?
Answer
I think the answer is simple: at the time Cooper was dropped off at Cooper station by the tesseract, Brand had only just arrived at Edmund's world, or was still making the trip there. I picked up the screenplay on Kindle, after Cooper and Brand did the gravitational slingshot around Gargantua to get Brand to Edmund's world Cooper said "That little maneuver cost us fifty-one years", so Murph would have already been an old lady before Cooper dropped into the black hole's event horizon. And as explained by Kip Thorne in chapter 30 of The Science of Interstellar, one of the rules Christopher Nolan had decided on for the film was that only gravitational waves could travel backwards in time, but physical objects including Cooper himself could not return to their own past (which is why Cooper in the tesseract was limited to viewing scenes passively or pushing things with gravitational waves the tesseract would send whenever he banged on the "world tubes" of objects like books and the watch).
So, the tesseract could not have returned Cooper to our ordinary 3D space any earlier than 51+ years after the last message he got from Murph, made just after Professor Brand died. It seems reasonable to speculate that it dropped him off as early as it could, which would mean the from the perspective of the outside universe, Cooper would have reappeared at Cooper Station only a short time after Brand had seen him drop into the black hole's event horizon (in relativistic terms I would imagine he was dropped at Cooper Station at a point in its history just slightly outside the past light cone of the point in spacetime where Cooper was scooped up by the tesseract). In Murph's speech to him at the end, she speculated that Amelia Brand was just now arriving at Edmund's world, saying "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."
edited to add: I just realized that although this would explain why no one had yet come to rescue Amilia Brand, it wouldn't explain why there weren't already lots of other settlers on Edmund's world waiting to welcome her. But Keen's answer may be a reasonable explanation for this: mounting an expedition to the wormhole could have been a major logistical challenge and they might have wanted to focus all their resources on the space colonies (also, although their control of the gravitational constant allowed them to launch the colonies into space, getting such massive objects from Earth to Saturn would still probably take many years, since in that case the obstacle to moving the colonies would be inertia, not gravity). There is also the possibility that Murph discouraged space agencies from mounting another expedition to the Gargantua system until after the events that led Cooper into the tesseract had played out, out of fear of what might happen if anyone interfered with events she knew were necessary to their own history, although she did say that no one believed her about Cooper being her "ghost", and she probably wouldn't have known when he plunged into the black hole, whether it was in her past or her future. But Murph's last lines which I quoted above suggest they were planning to make Edmund's world their new home, for whatever reason they just hadn't made the journey yet.
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