Near Earth Objects

In some ways "space" is actually very close. A low Earth orbit is typically about 100 km above the surface. That's a distance you can drive in about an hour. Getting up that high isn't the hard part. It takes a delta vee of 1.4 km/s to get up to 100 km. It takes the additional 8.6 km/s to be going fast enough to orbit the Earth.
Asteroids are very far away - the asteroid belt is hundreds of millions of kilometers away and close approaches are millions of kilometers away. However, because many of them orbit in the same direction as Earth at about the same distance from the sun, the delta vee required can be as low as five kilometers per second.
Half the delta-v doens't mean half the fuel required. The trade-off is exponential. Accelerating 1 kg to 5 kilometers per second takes 4.3 kg of fuel. Compare this to 27.0 kg of fuel to reach 10 kilometers per second, and it's less than a sixth the cost.
After making it to an asteroid, you might want to come back. The return trip is also about 5 kilometers per second, and it's going to take fuel. You need to bring this fuel with you to the asteroid. Imagine that we send a robot to an asteroid. It cuts off a piece that's 100 times as big as the robot itself and brings it back. For every 1 kg of robot, it's going to bring back 100 kg of asteroid. For every kg of robot, we need to return with 101 kg of robot and asteroid which requires 434.3 kg of fuel. That means we need to arrive at the asteroid with 434.3 kg of fuel plus the 1 kg of robot - 435.3 kg of payload to get there. That means to bring this there, we need 1,871.8 kg of fuel at the start to bring back 100 kg of material from the asteroid.
The fact that we need to spend fuel to move fuel is why the rocket equation is exponential. It's known as "the tyranny of the rocket equation."
If we want to launch the same 100 kg of material from Earth, it takes 2,700 kg of fuel. It's a substantial savings because we only need to carry the fuel for the first 5 km/s and the materials for the second 5 km/s.
Bottom line: Moving material from asteroids to orbit around Earth is 70% the cost of launching it from Earth.

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