Sort of like that, but imagine that the smaller boat is a spaceship and the larger vessel is a bothersome asteroid.
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If the gravitational tractor concept seems too delicate and prissy, you're in luck. A few scientists are proposing another way to make use of a spacecraft that doesn't require slamming it into an asteroid or entering a passive orbit. They studied busy harbors here on Earth and observed how tugboats nudge large ships up to the wharf. Then they developed an asteroid-deflection scenario using a similar technique.
Here's how it works: First, you build a special ship with powerful plasma engines and an array of radiator panels to dissipate heat from the onboard nuclear reactors. After you're alerted of a threat, you launch the vessel and fly it to the offending asteroid. Then you ease the space tug close to the rocky surface and attach the vessel using several segmented arms. Finally, you go easy on the throttle and start a slow, gentle push. If all goes well, 15 to 20 years of pushing in the direction of the asteroid's orbital motion will deflect it just enough to avoid a catastrophe [source: Schweickart].
Still not convinced? Then grab your mitt and keep moving to the next page.
