[zxkrrxrf] Russian Roulette to save the Earth

The sun is getting hotter, and if doing nothing, in a billion years or so, the ambient temperature on earth will exceed the boiling point of water.

The standard proposed solution, cosmic pinball, is to shift Earth's orbit away from the Sun (we might need to move Mars out of the way also) by gravitational slingshots with asteroids.  The asteroids themselves may be sent onto slingshot trajectories because of the chaoticity of the n-body problem.  Tiny perturbations on them effected by rockets or solar sails will suffice.

It will take many asteroids, maybe millions (over millions of years).  Each asteroid will be an outrageously difficult chaotic n-body calculation, and a single mistake will send the asteroid into a collision with earth, extinguishing the human race just like the dinosaurs.

Can we really play Russian Roulette with extinction that many times and expect to survive?