There's a lot of talk on futurist blogs about mining asteroids for propellant and other resources for space travel, but I have something else in mind. Could a spaceship, starting out in geocentric orbit, somehow grab onto an asteroid with a highly elliptical orbit and use that asteroid's momentum to toe the craft out into heliocentric orbit?
The biggest problem with this idea is the enormous difference in relative speed between the spaceship and the asteroid - it's hard to imagine any way the spacecraft could physically interact with the asteroid that wouldn't result in the immediate annihilation of the craft. Perhaps some sort of magnetic device used on a metallic asteroid?
If safety is a concern, would this be possible for an unmanned cargo craft?