I've read a bit about space-based solar power. It would be sent to earth by either laser or microwave. Could it not also be reversed and have energy sent from earth to satelites in LEO, where they use that power to transfer to GSO and other places in the solar system. It seems to me to be a hell of a lot cheaper than carrying all that fuel with them
It's not enough to just have power, you also need reaction mass to move a spacecraft (see, for instance, ion engine). The spacecraft would still need to carry the gas (or other propellant with it); the only exception is if you use a solar sail and shine a laser from Earth onto it.
Beaming power to a spacecraft could work (the Wikipedia article goes into some detail), but there are a number of practical problems which remain unsolved. Among them:
- The Earth is permanently rotating; you would need a number of "beaming" stations around the planet to constantly power a spacecraft.
- The machinery on board the spacecraft to convert the beamed power into electricity weighs; the question is, does it weigh less than solar panels?
- Beamed power attenuates fairly strongly through the atmosphere, and diffuses with distance. So you lose a fair chunk of power by beaming it through the atmosphere, and the further the spacecraft is away, the less power it will receive.
So: in theory it's possible, but there are a number of obstacles to be overcome first, and given our current level of technology it's not worth doing.