Dyson spheres are a staple of science fiction. Solar system spanning megastructures, they represent a significant effort by whatever species chose to build them, and a significant mass moved into the orbit of the star they engulf.
Now, shell theorem shows (assuming a homogeneous mass distribution on the Dyson sphere) that the planets, moons and other objects orbiting the star feel no gravitational effects from the sphere and spin on unaffected.
But what about while the sphere is under construction? As the various components are manoeuvred into position they will represent a non-negligible amount of mass being added to the star system, and they won’t suddenly pop into existence in place, implying they can effect a change in the trajectories of the various orbiting bodies.
The question is how best can this disruption be minimised?
Assumptions: The sphere is being constructed around our star (though generalised answers are very acceptable). The sphere is being constructe by a race way beyond our current tech in terms of material science and propulsion, but who don’t use FTL/gravity manipulation tech. The sphere will eventually be a single homogeneous shell constructed outside the orbit of Pluto (50AU from the sun). Any bodies outside can be assumed to have been removed by said aliens. The mass for the shell is being shipped in from outside the solar system.
Based on a very conservative estimate of shell density the shell is 7x1025 kg in total.
EDIT based on very valid concerns raised by AlexP: if the shell is constructed of a dense swarm of drones or series of spinning rings that’s fine, as long as the end result approximates a homogeneous mass distribution closely enough that the Sphere won’t have a gravitational effect on the planets within, and provides total coverage of the star (ie every bit of light hits a part of the ‘sphere’