Slingshot acceleration from alpha centauri?

[farmerben]

 

I'm not sure which equations to use to set up this problem.  I want to calculate the velocity boost on a spaceship which could manage to slingshot Alpha Centauri A and B.  Either with a .1 c flyby.  Or launching from Centauri B.  

 

Or for simplicity.  Solve this problem.  You fly at .1c by a sun sized star whose orthoganol velocity component is .01 c (as viewed from outside)at PE = 0.00001 ly

[UmbralRaptor]

I've occasionally poked at analytic approximations with hyperbolae and adding vectors, but have no idea how they compare with proper numeric simulations. That said...

23 hours ago, farmerben said:

 

I'm not sure which equations to use to set up this problem.  I want to calculate the velocity boost on a spaceship which could manage to slingshot Alpha Centauri A and B.  Either with a .1 c flyby.  Or launching from Centauri B.  

 

Or for simplicity.  Solve this problem.  You fly at .1c by a sun sized star whose orthoganol velocity component is .01 c (as viewed from outside)at PE = 0.00001 ly

Approximately 0. To get speeds useful for interstellar travel, you need to do a close flyby of a close in binary system with neutron stars and/or blackholes. A 0.63 au flyby of a sunlike star will not meaningfully bend your trajectory. (And even if you skim A's photosphere, you're looking at <6 arcminutes of deviation from a straight line!)