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Considering the movie Interstellar, I just did not understand how solving the equation saved the earth from the Blight. As I understood, the equation had to do with gravity. What was the relation of gravity with a massive infestation of a microorganism?

  • hmm, a bit of a different angle, but your question is answered in the linked question. – Möoz Aug 3 '15 at 22:47
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There's no indication that the equation saved the Earth from the Blight. The final scenes are based on a space station; Cooper Station and there's evidence from the novelisation that they're building and populating a series of stations by evacuating the Earth (presumably the equation somehow reduced the cost of attaining orbit, making this mass-exodus a realistic possibility).

Edmunds’ world didn’t have the same length day-and-night cycles as Earth, and since the eventual goal was to live there, Cooper Station — and her sister stations — were gradually modifying the length of each day. The human circadian rhythm had been the same for millions of years, and asking a body to change too quickly was generally considered to be a bad idea.
- Interstellar: Novelisation

Frankly, the strong implication is that (non-blight) life on Earth is doomed and nothing that Cooper did, nor their possession of the gravity equation has changed that fact.

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  • Indeed. I believe the equation was the beginning of humanity's space-faring civilization that eventually leads to us becoming the bulk beings. We left Earth behind, and it was when we started our journey to leave our bodies behind. – user31178 Aug 3 '15 at 20:33
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The point of solving the gravity equation was to lower the Earth's gravity enough to make it possible to launch the really massive space colonies they had built, which were presumably large enough to carry some significant fraction (or all?) of the Earth's remaining population. See this answer for details. Meanwhile, for some reasonable speculations about how they could avoid taking the Blight with them on the space colonies (I don't think they ever cured it, just left it behind on Earth), see this answer.

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    A slight nit-pick, but the gravity equation didn't lower Earth's gravity, it made it possible to build anti-grav engines. – Valorum Aug 3 '15 at 17:41
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    @Richard - If you look at the quote from Kip Thorne in my answer to the other question, he says "Murph must have figured out how to reduce Newton's gravitational constant G inside the Earth ... In my interpretation, with Newton's G reduced inside the Earth to, say, a thousandth of its normal value for, say, an hour, rocket engines could lift the enormous colonies into space." – Hypnosifl Aug 3 '15 at 18:19
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    ...and Thorne also says "As a byproduct, in my interpretation the Earth's core—no longer compressed by the enormous weight of the planet above—must have sprung outward, pushing the Earth's surface upward. Gigantic earthquakes and tsunamis must have followed, wreaking havoc on Earth as the colonies soared into space, a terrible price for the Earth to pay on top of its blight-driven catastrophe. When Newton's G was restored to its normal strength, the Earth must have shrunk back to its normal size, wreaking more earthquake and tsunami havoc." – Hypnosifl Aug 3 '15 at 18:20
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    @Richard But on the plus-side, at least it actually mentions 'gravity' (as opposed to, for example, your answer which still doesn't) and why a gravity equation was relevant to the eventual solution. I think both answers could benefit from further edits.. – Andrew Thompson Aug 3 '15 at 18:22
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    Also, note that Thorne wanted to avoid explicitly contradicting real physics theories (while allowing for new phenomena owing to a fictional theory of quantum gravity), and antigravity engines would actually contradict Einstein's theory of general relativity--the equivalence principle says any experiment you do in a small room on a planet's surface should give the same results as if the room were accelerating in deep space far from any gravity, but an antigravity engine would move upward in the 1st case but not the 2nd. – Hypnosifl Aug 3 '15 at 18:32

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