Such a vast inter-planetary settlement requires sending lots (read LOTS) of material to those worlds. Establishing even a small permanent outpost on Mars would require sending hundreds to thousands of tons of material to its surface. This has to be done in the form of multiple launches, of the order of dozens to hundreds.

The core problem of rocket science

The more the payload a spacecraft has to carry, more the fuel required in the rocket to launch it. Since the inclusion of more fuel increases the weight of the rocket itself too, we need more fuel to carry that fuel. Rocket science.

As you add more weight to the spacecraft, the fuel requirements thus increase exponentially. This requirement is called the delta-v budget. The more the delta-v required, more the cost & technological complexity of a mission since more energy is needed to get out of the Earth’s gravitational influence/gravity well.

Delta-v increases exponentially with added mass. Source: Wikipedia

Sending hundreds of tons of payload per rocket to other worlds requires a really high delta-v from Earth. The engineering cost to achieve such an aspirational vision is going to be quite off the charts. This is where the Moon can help.

The Moon as a rocket platform

The following chart shows the delta-v (and thus energy) required to reach various points from the Earth and the Moon.

Delta-v required to reach various points from the Earth and the Moon, calculated using vis-viva equation. Not to scale. Source: Me.

Going from the Earth to Low Earth Orbit (LEO) requires a delta-v of 9.4 km/s . A further delta-v of 3.2 km/s is required if the spacecraft has to free itself of the Earth’s gravity well. Notice that the Moon exists in the outer part of the Earth’s gravity well.

Combined with the Moon’s low gravity, the delta-v required to escape the Earth’s gravity well from the lunar surface is just 2.64 km/s , which is even less than what is required from LEO.

The gravity wells of the Earth and the Moon visualized. Source: xkcd

The lower delta-v required to launch stuff from the Moon has multiple advantages:

1. Accelerated growth

Lower delta-v means launching the same amount of payload from the Moon takes less fuel compared to Earth. Large rockets like Space X’s Falcon Heavy or the BFR can launch far more payload from the Moon than from Earth.