Propellant-less spacecraft acceleration using split design and gravity assist
First, let us look at regular orbit in 2D of a spacecraft orbiting a planet. It has a orbital line(corresponding to plane in 3D).
(1) Spacecraft orbiting a planet in 2d
Now let us introduce a spacecraft that consists of two equal mass parts, has an energy source(e.g. photovoltaic, nuclear etc.) and mechanism for ejecting both parts in opposite directions(e.g. electromagnetic, centrifugal etc).
As in (1) spacecraft would accelerate due to gravity while approaching planet, however reaching a certain proximity to planet both sides of spacecraft would be accelerated and ejected in opposite directions. After ejection gravitational force affecting spacecraft parts would consist of two parts - one that is parallel to orbital line and one that is perpendicular. The parallel force now is smaller compared to case if spacecraft had continued movement as one as each part is now further from planet, so the distance of apogee will be increased. The part that is perpendicular will at some point bring both spacecraft parts together again (of course if the ejection acceleration didn't escape the planet).
After reaching apogee and rendezvous of both halves spacecraft would accelerate towards planet so utilizing the gravity of planet. Upon reaching the planet separation can be repeated again.
(2) Split-type spacecraft ejecting both parts in separate directions in proximity of planet, rejoining after passing(click to rerun the simulation)
Alternatively both spacecraft parts can be tethered together. This would allow to actually keep the spacecraft adjoined and adjust the dynamics of trajectory.
(3) Split-type tethered spacecraft ejecting both parts in separate directions in proximity of planet, then rejoining at apogee
This technique can also be utilized to improve regular gravity assist maneuver when after accelerating during approach towards planet, spacecraft experiences deceleration due to the planet's gravity pull. This gravitational deceleration effect can be reduced by separating the spacecraft in halves and then making a rendezvous in some distance from planet where gravitational effect is smaller.