Didn't Data say there were hundreds of thousands of collectors?
If there were, then we attempt to destroy the farthest one we can both detect and target. If it emits radiation, okay that won't work on the ones closest to us. If the collector blows up (or simply stops working) then we destroy the ones closest to us and create a path out for the ship.
the captain's using the asteroid's gravity
Even if it was a solid ball of iron, how much could it's gravity have been anyway? maybe if the Enterprise were moving at a slow walking speed.