Space Equilibrium

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 co

So far we have determined: Producing 1 kg of rocket fuel a day on Earth requires 38.1 square meters of solar panels and 1 kilogram of water. 77,466,483.6 kg of people and seats to launch into space every day. To launch 1 kg into low earth orbit requires 27.0 kg of rocket fuel. Putting this together means every day we need to generate 2,091,595,057.2 kg of rocket fuel a day which requires 79,689,771,679.3 square meters (79,690 square kilometers) of solar panels. It's about the size of one of the smaller states in the USA: South Carolina or the Czech Republic.

A rocket moves forward by pushing propellant out in the opposite direction. It can't pull its way through the air like an airplane can do with its propellers. It can't push its way along like a car does with its tires. By pushing propellant out at a high velocity, a rocket accelerates. The velocity of the propellant is a measure of the efficiency of the engine and is called the Specific Impulse or the Effective Exhaust Velocity. We can calculate the ratio of fuel to payload using the Tsiolkovsky rocket equation. initial mass / final mass = mass ratio = exp (delta-v / exhaust-velocity) To reach low earth orbit from Earth, it requires a change in velocity of about 10 kilometers per second. The effective exhaust velocity of Hydrogen-Oxygen engines can be up to 3 kilometers per second. Applying the rocket equation, yields a mass ratio of 28.0. Bottom line: To launch 1 kg into low earth orbit requires 27.0 kg of rocket fuel.

Rocket fuel is easy to make: Water + Electricity = Rocket Fuel. More specifically, electrolysis of water to break it down into hydrogen and oxygen. When it burns, it just makes water again which falls as rain; it just might be the cleanest fuel on the planet. In industrial setups, takes about 80 kilowatt hours of electricity to separate a kilogram of water producing a kilogram of fuel. The theoretical limit is less than half that at 39.4 kilowatt hours. Maybe some advances can be made to get closer to the theoretical limit, but for these calculations, we will use 80 kilowatt hours. Solar is a good option for power. We're going to be needing a lot of rocket fuel, and solar scales well -- you just need to build the panels and have the space somewhere sunny and near the water. Also, we're going to eventually need to be making rocket fuel in space . There is a lot of sunlight in space. There is not very much wind or rain. Solar cell technology is up to 44% efficient