A new means of space propulsion... closed loop pulse propulsion... here's the idea

[indigoth]

39. Starting at rest

Ke of the system is zero
Shoot the bullet
The net Ke of the system is still zero with both the space ship and the bullet having some of their own kinetic energy, but their directions are opposite so the net combined energy is zero.

Now

You gotta turn the bullet around. Work is REQUIRED to change any direction of travel of ANYTHING. In the close system which YOU described, the only mechanism that can change the direction of the bullet is attached to the space ship. And so. All energies required to change the bullet’s direction come from the space ships kinetic energy.

Assuming zero energy losses (which is actually impossible) the bullet is turned 180 degrees and travels in the direction the space ship was originally going.

Since the both kinetic energies were the same, they remain the same … but … they are now both traveling in opposite directions. No energy lost or gained in the system. The net energy for the system is still zero.

Assuming the bullet hits the space ship with perfect energy transfer(again, not possible in the real world) the kinetic energies cancel each other out and both objects wind up with zero velocity.