What would happen if there was a Shkadov Thruster in place around a single star in a binary star system? I don't care about the moving stars thing. I just want to know about what would happen in that system.
EDIT: Thank you to Bald Bear for mentioning that there might be a problem with the constant variation in gravity and light. So let's just abra cadabra handwavium that away. (thruster is made of something that would be perfect for its needs to function as a shkadov thruster and not break apart.)
EDIT #2: Since this question is too broad I will clarify. I would like descriptions of what would change in the system. The system is exactly like the solar system, except the sun is now suns and the single star system is now a binary star system. Both stars just so happen to be half the mass of the sun and together have the same mass as them sun.
I would very much like descriptions as to why this would be too broad.