I remember asking once, we don't we just shoot our surplus trash off into the sun and was told that by the cost of launching it outweighs the benefits. Fair!
But what about all of the old satellites and space stations? Why don't we just send a giant magnet around the earth once or twice and then slingshot all that space junk into the sun and thus giving all science fiction writers (when they return from their strike) a plot point they can no longer use in their film scripts?
Seriously though, without the cost of breaching the atmosphere, this seems really cheap to pull, why don't we do this? Why isn't this a standard thing?
Getting to the sun is EXTREMELY energy intensive. It's a lot easier to get to the outer planets. Also a cloud of space junk is really big and really spread out. It's equivalent to raking a magnet across the surface of the entire earth to look for your house keys
But the speed doesn’t really matter, so it shouldn’t be very energy intensive at all. Just gather up some junk, launch it at the sun with an expendable thruster, and be done with it. If it travels at a couple hundred kph, or even less is completely irrelevant. Let it take a couple hundred years to get there, it is supposed to burn up anyway no? And if it collides or is otherwise destroyed en route during that time won’t matter much either.
It’s not about speed, but energy. Virtually all satellites are gravitationally bound to Earth. Think of Earth’s gravitational potential as a funnel. The satellites sit somewhere on the walls of the funnel. Now, next to the Earth’s funnel, there’s. much deeper funnel: The Sun’s gravitational potential. But between where the satellites are and the point where the Sun’s potential starts attracting them is still a big "hill" or wall separating the two funnels from each other (the top of that hill is the Lagrange Point L1). So to get a satellite out of Earth’s potential to a point from where it could “fall” towards the Sun still requires a large amount of energy.