Fly the asteroid probe Hayabusa — build up delta-v with coin-weight ion thrust, drop a ball in Itokawa's hundred-thousandth gravity, touch down at centimeters per second, rewire two broken ion engines into one, and bring the capsule home on June 13, 2010.
In May 2003, the small probe Hayabusa set out atop an M-V rocket. Its hope rested on four μ10 ion engines — engines that accelerate xenon electrically and breathe it out. Even at full throttle, the thrust is about the weight of two one-yen coins. The craft hardly seems to accelerate at all. But try speeding up time. A few metres per second of velocity change per day, stacked for months on end. A weak force wins, as long as it never stops. That is the discovery of the ion engine.
The craft is a historically-informed model of the probe Hayabus, launched in 2003.
Raise the throttle, then speed up time, and watch the delta-v — the stacked change in velocity — grow.
How could an ion engine with only a coin-weight of thrust make a six-billion-kilometre round trip possible?