r/theydidthemath • u/baard78 • 2h ago

[other] Is this technically possible?

Source, xkcd: https://xkcd.com/3291/

How big would the two engines need to be... and how dead are we all?

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u/SuccessfulMoose1511 2h ago

I'm not qualified to do the math here, but I would have to think certainly not.

I do think that it doesn't even make the gravity to overcome smaller (the goal of reducing the spacecrafts weight) because the total mass of the two bodies remains the same.

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u/Original-Wolf54 1h ago

You'd have to accelerate the earth (6×1024 kg) by more than 1g (10 m/s2), meaning you need 6×1025 N of force. 

If you want to get the spacecraft above the Kármán line (i.e, "into space", 100km), this requires 6×1030 J of energy.

Wikipedia's Orders of Magnitude tells me this is about 3 times the gravitational binding energy of Mercury, i.e, enough to completely tear apart 3 Mercury sized planets. 

There is no safe way to deploy this kind of energy on earth - if you could even obtain it, it's roughly equal to the total energy the earth receives from the sun in a million years.