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...