It is the not-too-distant future in an alternate timeline, and humanity has tripled-down on solar power.
We built a network of solar focusing satellites that orbit Sol at close range (so they can capture more sunlight). "Close range" means somewhere between the orbit of Mercury and the solar corona. So, not as close as the Parker probe, but still pretty close. The details of how they focus the light without being incinerated are outside the scope of this question; assume handwavium.
These satellites focus light at a variety of targets distributed throughout the solar system to provide power, all of which have super-advanced solar-conversion tech aboard. The targets that get the most love are, in priority order:
- Electric-powered "solar trains" on their way to and from Earth's space facilities. Each must be powered continuously for the bulk of its climb and descent. We have five or six of these at present.
- Large permanent space stations near Jupiter, Ceres, and Saturn, whose batteries need to be recharged every month or so. (The colonies are primarily robotic, hence their outsized consumption.)
- A giant solar-collection station in orbit around Earth, which charges massive batteries that we then carefully land on Earth. It demands power continuously, and can handle the light from 2 satellites simultaneously. It does not provide all the power Earth needs, but we want it to do more; the limiting factor is the number of batteries we have, and we're building more (subject to material scarcity).
These satellites must be very hardy to survive so close to Sol, so building them is expensive and consumes scarce resources. Thus, we haven't built a bajillion of them; more in the neighborhood of two or three dozen. (Though that number is up for grabs.)
We obviously want each satellite to have line-of-sight on as much of the solar system as possible for as much time as possible. Each satellite has a "firing arc" of 50° from its Solar radius (apologies if I've expressed that weirdly).
So: what kinds of orbits are best-suited for these satellites?
Here are a couple of obvious ideas, which (for starters) I'd appreciate help evaluating:
- one evenly-spaced ring around the sun, in the plane of Earth's orbit
- evenly spaced around the entire surface area of the sun, with orbits calculated to avoid collisions
The biggest objection I can think of to the ring is that many targets will frequently be obscured by planets, leading to blackouts.
The biggest objection to the second pattern is that the limited firing arc means that many satellites would have line-of-sight on nothing for a long time, which means we'd need to build a gazillion satellites (which we haven't), which once again leads to power blackouts.
You might think that Earth can take a blackout because we have other sources of power, but the environment is near the breaking point, and the Terrarium Laws are absolute and totally merciless: anyone who tried to turn on a coal plant for even a few minutes would be summarily executed. If that means a hospital full of babies dies, that is what happens.
The stations and the space trains really can't take a blackout either: the few people on them will die without heat and recycled atmosphere, and if station-keeping goes untended for too long, the station itself could be lost.
If the solution requires a minimum number of satellites higher than what I've proposed, feel free to add them, but then I want some kind of demonstration showing that nothing lower than your number will suffice. Assume my number is 36.
If the firing arc is unworkable, you can change that, too, subject to similar requirements about proof.
Edit to add: there are no mirrors or lenses anywhere in this system. At least, nothing anybody would recognize as such. I said "handwavium," and that's all you're going to get (in this question). I think this would not evade the problem of etendue, but it should short-circuit a host of other concerns that answerers might get tripped-up by.