Think of a Dyson Swarm ("Sphere") as the water droplets in a fog. Collectively they absorb the light going through but the water droplets (and the orbitals) are relatively sparse. So a billion orbitals around our Sun at a distance Venus and Mars would still have a mean distance between them of over 100,000km.
So how much material do you need? One estimate I've seen for a billion such orbitals is less than 1% of the mass of Mercury. Why Mercury? Because it's metal-rich and its proximity to the Sun means energy is incredibly abundant and cheap.
That's to build billions of O'Neil Cylinders.
Even if you don't need that much living room, here's something else you can build: statites. That's a portmanteau of "static satellite". Instead of orbiting the star, they are so light that the solar wind is sufficient to counterbalance the gravity. These things would simply collect energy and/or just reduce the amount of solar energy hitting something like a planet (eg to cool the EArth).
The real problem is that Dyson spheres are wasteful because stellar fusion is thermodynamically inefficient. If you harvest the material of the star and fuse it yourself, you can keep the lights on for trillions of years.
If I understood correctly, you suggest to turn the heat from fusion into a usable form of energy. On earth we'd do that using steam turbines. Harvesting only the hydrogen from the star to bring it on a planet and fuse it in a reactor seems silly, as the hydrogen is already at sufficient temperature to fuse on its own. So we could send water and steam turbines close to the sun where the turbines charge some sort of battery? Perhaps on some super elliptic orbit, where we switch the full batteries with empty batteries at the apihelion.
Or did you have something else in mind?
We discovered half the planets by doing the math to predict the orbits based on the known distribution of math in the solar system.
General Relativity was initially validated by predicting mercury's orbit accurately.
And mass as well :)
Mercury is not similar mass to the sun, so this is not the three body problem
The point is that a very small difference in starting conditions yield wildly different results.
https://www.google.com/url?sa=t&source=web&rct=j&opi=8997844...
1) Much less material required
2) Much longer star lifespan (trillions of years rather than a handful of billions)
However, what's interesting is that those spheres all seem to be around red dwarf stars, which are much more active and shorter-lived than white dwarfs. They're just not as stable.
Our nearest neighbor, Proxima Centauri, is a violently active flare star -- and it's also a red dwarf with an estimated lifespan of ~4 trillion years.
I was under the impression that red dwarfs are the longest-lived stars.
But white dwarfs -- which are technically stellar remnants -- are indefinitely stable. They just keep cooling. It's surmised that they'll still be quite a lot warmer than the universe's background temperature in 10^15 years.
This has yet to be observed, but red dwarf stars, when they reach the end of their lifespan, should contract and become white dwarfs. It's said that our sun will also eventually end up as a white dwarf.
White dwarfs are superlatively stable, long-lived, and quite hot. And there are already quite a lot of them. If you're going to build a Dyson sphere/swarm, they're a very good choice. Though red dwarfs aren't bad...
In contrast, a Dyson Swarm is easier for my uneducated mind to understand.