[exDM69]

I'm sure the idea has been considered - and then ignored as completely ridiculous when you do the math.

The biggest rocket ever built (the Saturn V) could take 140,000kg to low earth orbit. That's nowhere near big enough to have any kind of significant gravitational attraction to "mop" objects away from their orbits. Some kind of magnet would be more feasible, but still not practical because operating a huge magnet in the Earth's magnetic field would affect the spacecraft itself.

Finally, once you would have "mopped" these objects into neat bunches, it would take 4 km/s additional velocity to escape the earth and a whopping 30 km/s to send things towards the sun (without any gravitational slingshot). Now you can calculate the amount of propellant (using the Rocket Equation) that it would take to send any meaningful payload that distance.