If a spacecraft was accelerated to just above Earth's escape velocity, it would begin orbiting the sun with an orbit very similar to Earth's. Could the spacecraft then repeatedly perform a gravity assist with the Earth to increase it's apogee over and over until it left the Solar System, while only using a nominal amount of delta-v to perform deep-space maneuvers to fine-tune encounters with the Earth?
Juno did something similar to this, it went on an initial 2 year orbit, with a flyby of Earth 2 years after launch, after which time it went on to Jupiter, to orbit it.
I've been playing a bit with NASA's Trajectory Browser, and found this possibility:
- Launch March 2016- 4.33 km/s beyond Earth Escape
- Deep space maneuver 1 year later
- Slight powered flyby of Earth 10 months later
- Pick the correct course to flyby Jupiter, such that the flight will lead to interstellar space
Total ~ 5 km/s delta v.
If you want to do a purely Earth based escape, it is also possible, the trick is to periodically return to Earth. So the first return time would be in 2 years, the next might be in 4, and so on until you have left the Solar System. It might take a while, but it could be done.