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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’

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    $\begingroup$ It cannot be a single shell because such a structure cannot be stable. (Hint: suppose a small perturbation gives it a tiny nudge; there is no force acting to restore it to the original position.) That's why savvy authors prefer to speak of Dyson swarms. $\endgroup$ – AlexP Jun 9 '18 at 13:24
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    $\begingroup$ @AlexP: there’s nothing stopping external thrusters on the outside of the sphere from performing station keeping, or a geodesically linked ‘sphere’ station keeping by thrusting. Of much larger concern is the material stress on the shell, which swarms avoid by having their individual drones orbiting in a variety of different orbits. If you’d like to, add an answer on minimising the impact of a Dyson swarm instead, as long as the end result can be thought of as a homogeneous mass distribution. $\endgroup$ – Joe Bloggs Jun 9 '18 at 13:33
  • $\begingroup$ Which was the central theme of Niven's The Ringworld Engineers. Denizens of the Ringworld were taking the orbital correction Bussard Ramjets to use for space ships. When a solar flare pushed the ringworld off center, there weren't enough ramjets left to automatically correct for position. This is a great question, because Joe's right. Once in place, the sphere's easy enough to keep in place. But during construction... that could throw the star itself off kilter. You'd almost need to build it in deep space and bring the "apple slices" together simultaneously. $\endgroup$ – JBH Jun 9 '18 at 13:56
  • $\begingroup$ Which just goes to show how impractical a Dyson Sphere (or, likely, any mega structure) really is. A civilization would expend a serious chunk (if not most) of the energy value of the star just building the darn thing. $\endgroup$ – JBH Jun 9 '18 at 13:58
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this answer is assuming that the structure is to (begin with anyway) a swarm (it can all be fused together once complete, though no real purpose is served by doing this.) it is also using a newtonian model of gravity.

Do it REALLY SLOWLY, this might sound like a complete joke but I am serious. there shouldn't be significant orbital disruption provided you don't move too much mass quickly but instead move it piece by piece. what mass you do move can then be moved with much lower reaction mass propulsion systems like ion thrusters for instance, this will reduce the total momentum you are imparting to the system taking more time also allows you to use more efficient orbits, which so far away from the sun will take upwards of two hundred years.

ideally you would take about million years to place orbital stations 50au from the sun. each station you place should be placed in such a way that the sum of all the stations is a reasonably close approximation of a sphere at all times. distributing them in orbits around the solar system evenly rather than placing them all at similar positions.

if it is the case that orbital disruption is occurring then its not actually a problem because you are doing this so slowly you can alter your routes based on computer simulations to try and "undo" any damage done. you can also place lagites near the planetary orbits to give them small gravitational tugs in the right direction over time or use sun screens (yes very literal) to change the photon pressure on planets.

its also worth noting that on a solar-system scale your Dyson-sphere is not horrendously heavy it weighs about a thirtieth of what jupiter weighs after all and the fact that its SO far out makes it not that much of a problem. for instance earth (the only planet you really need to worry about the orbital disruption of, given none of the others have complex, delicate ecosystems) currently experiences 3.3 * 10^22 N of force from the sun for comparison your dyson sphere if all its mass was at one point 49AU from earth would apply a force of 4.87 * 10^14 N less than six million times less perhaps a fair comparison is that of Jupiters gravitational influence on earth which is still on average four thousand times a worst case scenario for this sort of thing. Pluto might have some problems but if you can make a Dyson swarm/sphere you can straight up put Pluto where you want it.

to surmise the solar system is durable hence why it is still around despite natural gravitational variations and any wanna be K2 civilisation could make a dyson sphere around it without having to worry about orbital disruption much. it would only be concern if they where doing gravity assists or using propulsion systems with lots of reaction mass like conventional chemical rockets.

P.S.

to address JBH's concern that just building such a thing would require too much energy the suns power output is 3.83×10^26 watts meaning even using something like a photon drive (the least efficient possible thruster by energy.) you could accelerate this dyson spheres mass by 1m/s every two years. meaning in under one hundred thousand years all your required energy would be regained and then some. given the sun has four billion extra years remaining (more with 'maintenance') and energy can still be collected from an incomplete Dyson swarm it is still very much worth it.

if you think a million years is "just too long" then I am afraid you might not be cut out for being a K-2 civilisation but we do have a shortsighted race doomed to nuclear extinction package if you prefer.

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