Jupiter's Gravity: How Many Ships in the Queue?

[proteo]

Imagine you are in the universe of the Expanse book. First of all, you want to speed up your spaceship to reach the alien gate. And you will use Jupiter's gravity. But there is a queue of spaceship wanting to go to the gate, and they all use Jupiter's gravity to accelerate. Suddenly Jupiter comes out of orbit and travels alone in space. How many ships are there using Jupiter's gravity at the same time?

 

[Janus]

Jupiter's orbital velocity is ~13 km/s. For it to "leave orbit", it would need to gain an additional 5.4 km/sec.
But in an gravity assist maneuver where you are trying to boost the speed of your ship, you are borrowing orbital energy from Jupiter and lowering its orbital speed, not adding to it.
As a rough estimate, a 1 ton spaceship would cause Jupiter to lose 5e-25 km/sec for every km/sec gained by the craft.

Putting that aside, if we use a velocity boost of 4 km/sec (The amount gained by the Horizons probe) as a baseline, then is would take a spacecraft roughly 10 times the mass of the Earth to change Jupiter's orbital velocity by 1 km/sec