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?
So can't you have a tiny rocket and a computer to do the calculations and angle adjustments? Isn't that how they landed on Mercury?
You generally do something like multiple gravity-assists perhaps coupled with going to a higher orbit first before coming back in. You have to remember that each individual space mission is centered around moving an object roughly the size of a minivan. It's just completely not worth it to try and send our garbage or even just our space garbage anywhere far from where it is right now.
For a while they did nothing with space junk. These days low-earth orbit is actually getting kind of crowded and people realized we have to be a little more responsible. Each mission has plans for how every piece of debris will be handled. For some, that means sending back down to earth, for others, that means crashing it into whatever planetary body is nearby, and for others that means putting the object into a graveyard orbit. A graveyard orbit is just an orbit where we've decided to leave the junk in an "out of the way" place where it's unlikely to change orbit or collide with anything.
These might help get you an intuitive understanding of how orbital mechanics works.
https://youtube.com/playlist?list=PLSL-UN9SB11jK2pNTDffUS7vU-hJn7-Zf&feature=share9
Thank you very much