Firstly, good on you for brainstorming this kind of idea, we need much more of that kind of out-of-the box thinking.
I absolutely agree solar is the only sustainable solution.
All energy came from that one single source.
If we take it from the planet in any way, then we are obtaining energy very inefficiently whilst reducing the energy of the planet in some way or another, there is no getting round that.
So we have to plug directly into the sun, there is no alternative.
In my opinion, wind and wave power are a dangerous distraction, since they harvest the kinetic energy of our planet.
That might seem insignificant, but in truth what we are doing is putting a very small, persistent, increasing brake on the rotation of our planet. This has a corresponding knock-on effect which could eventually affect the equilibrium of our orbit around the sun, that very same, precious, single source of energy which we depend on. We could one day find ourselves on a trajectory diverging irreversibly from it, spiralling outwards.
Asking how much accumulated energy it would take to do that is a little like asking how many times can we get away with pulling the trigger in solo russian roulette.
We should also note that there are already frictional forces acting to slow down the planetary rotation. The length of a day is already 24 seconds or so longer than it was in the seventies, since we began using nuclear clocks and GPS time references, that is the number of leap seconds we’ve had to insert.
Best not to pull the trigger at all, if we can help it, I think.
As an Engineer myself of almost thirty years in big programs including space, I am sure a real analysis will quickly reveal it is perfectly possible, and more practical to just create a broad ring around Earth’s equator with solar cells, than to tackle the challenge of a moon based solution.
The likely effects of such a ring of solar cells around Earth on orbital rotation, are again very interesting.
Cells entering the sunlight in the morning would be heavily loaded, connected to largely discharged batteries, in an efficient system. As such, those cells would absorb more photons than the lightly loaded cells exiting the sunlight in the evening, connected to fully charged batteries.
So there would be a persistent differential solar pressure on the ring, acting as a very small rotational force, in the same direction as our rotation.
This would work to accelerate our rotation, like a very weak electric motor, tightening our orbit around the sun, offsetting the frictional effects we see slowing us down.
An equatorial ring would also provide us with more than enough energy.
We already know that the Sahara desert alone has more area than needed by itself.
We have the technology to do that right now.
But it would require collaboration of all of the countries of the world, which still seems a tall order as yet.