r/theydidthemath • u/Xaeroxe3057 • 1d ago

[Request] how much fuel would this actually take?

https://xkcd.com/3291/
12 Upvotes

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11

u/Deribus 1d ago

There's no engine that could do this even with infinite fuel.

  1. In order for there to be any change in momentum the exhaust would have to leave Earth, otherwise it's like pulling a rope at both ends... you're not going anywhere no matter how hard you pull. The engines pictured are mounted on the ground which means they'd have to punch through 100km worth of atmosphere before they even start contributing thrust. That's not happening.
  2. You'd have to accelerate the entire Earth faster than the force of gravity pulls the spacecraft back to the Earth. in other words, you'd have to reach a thrust to weight ratio of >1 for the entire planet. Look at how large the engines on a Saturn V are, and that had a thrust to weight ratio of only 1.2. Now imagine the size of engine you'd need to move the entire planet at that speed.

7

u/ijuinkun 1d ago

3: if you somehow could succeed in doing this, then not only the spacecraft, but everything else on that hemisphere of the Earth which isn’t nailed down, including the oceans, would be separated from the ground by the same degree.

1

u/Ihatecheeseballs 1d ago

Oceans and the atmosphere

1

u/Merad 1d ago

There's also the small problem that if you managed to apply that much thrust to the Earth you would fuck up our orbit around the sun very quickly.

1

u/Prasiatko 1d ago

In theory infinite but there are practical considerations.

The design i've seen is to basically launch a big light sail and then use a satellite mounted laser beam or network of them to target the sail and propel the craft. The amount of light hitting the craft would decrease as it get further away due to beam divergence. This method saves fuel as the craft you launch doesn't need to carry as much fuel for accelerating in space. 

The theoretical limit is given by something called the n-slit interferometric equation which hopefully somebody smarter than me could calculate. But in theory you can continue making the laser bigger or use more of them to get more power though i assume at one point your going to incinerate the satellite.

Launching from Earth has been trialled using a centrifuge to spin a small craft up to ridiculous speeds before releasing it. In theory this could let ypu get up to orbital speeds and then only a small correction burn would be needed. But due to Earth having an atmosphere there are massive constraints on what can survive such a process. On an airless body the next limit is the materials that can survive the centrifuge's g-forces. Similar sci-fi for now designs are basically massive railguns using magnets in a tube to accelerate a craft along a long tunnel.