Steal some momentum from Jupiter, a little at a time. Add a little to Earth. Over the millions of years the Earth would slowly drift into a larger orbit, and Jupiter would do the opposite but much more slowly because of its huge mass.
And we are really good at kinematics. We can launch a probe towards Saturn with multiple planetary flybys to gain velocity and reduce fuel use. We can put the craft into orbit around Saturn and land a sub probe on one of the moons and keep the main probe orbiting, taking pics and measurements for years, changing its orbit to get close to some of the 60+ bodies orbiting Saturn when we want to.
And that is just the Cassini mission. Don't get me started about what we did in the 70's with the Voyagers, especially Voyager 2 which went by all four gas giants.
Yup! We got this shit down. We could do what you suggest.
We could also change the orbit of an asteroid headed on a collision course with Earth. We'd need some warning time, but we could (as Bill Nye says) get 'er done. That would be the same tech used for your scenerio.
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