The human race has colonized the solar system with permanent settlements on all of the inner planets and outposts beyond. Vast space stations pepper the voids between orbits and massive mining/refining facilities stand vigil along the frontier. Interplanetary travel is routine and 25 Billion prosperous humans live within Sol’s gravity well. But not a single human lives beyond our sun’s reach.
FTL is still an elusive dream. We have all the energy we could ever use and have complete mastery over biology and conventional physics, but no miracle solution has been found for getting to other stars. We are still vulnerable and can become extinct from anything that can take out our civilization’s only sun.
This vulnerability troubles many, so after much debate, we decide to solve the problem. With nothing more than slower-than-light travel, humanity will reach for the stars.
We have chosen a large Kuiper belt object as the basis for both our ship and its launcher. The idea is to divide the asteroid into two pieces, one three times as large as the other. The smaller portion will be hollowed out to become the ship’s hull and the larger, the counterweight, will be sacrificed during the launch to help the ship obtain solar escape velocity.
Today’s question is about the launching process. Once the ship is ready and has been firmly reattached to the counterweight, the pair will be pushed out of orbit and dropped on a very deep slope into our sun’s gravity well. Picking up speed during the inbound journey, the pair will miss the sun by a barely survivable margin and then race past on its way out of our solar system. At the optimal moment, the ship and counterweight will detach from each other and the ship will push itself forward using rockets, nuclear explosives and a rail gun-type launcher which is secured to the counterweight. All of that force will push back against the counterweight, stealing its inertia and springing the ship out of our system with enough speed to escape Sol’s gravity well completely.
The counterweight will then fall back sun-ward to either be salvaged before or slagged when it plummets into the sun.
So the question… What percentage of light-speed would a launch technique like this imbue upon the ship portion of the asteroid, after it left our gravity well? Assuming the original asteroid was similar to MakeMake: 5x10^21 kg with a starting point for its sun-dive of 50 AU. Also assume that the rockets, nukes and rail gun successfully transfer 90% of the inertia from the counterweight to the ship.
Also, am I missing anything? Are there other ways to add speed to such a massive ship during its launch?