Could a really tall tube suck garbage in to space? When I was around 10 years old, I had this idea that was supposed to solve our waste problems; I imagined having tubes miles high that would stretch in to space.  Every tube would have a door at the bottom that would be initially closed, and all of the atmosphere inside the tube would then be pumped out.  A gigantic pile of garbage would be placed underneath the tube, the door would open, and the vacuum would suck the garbage and eject it in to space.
To what extent could this idea work?  Putting aside the problems of keeping a large tube of that size stable(or even manufacturing it), I'm wondering if the force created by the vacuum would be enough to send matter into orbit or if it would immediately come back down the tube once the pressure equalizes.  I can't imagine there would be enough inertia to break the earth's gravitational pull, but maybe most of the garbage would stay in orbit for a long time or just burn up on re-entry?
 A: I'm not sure why people are posting what they've put into comments and answers.  It's quite simple:  a "sucking" system can't pull anything higher than one atmospheric pressure equivalent.  That's why barometers work:  the height of the material in the tube is limited by the existing atmospheric pressure.
If you want to dump garbage to space, you'll have to pump from below, not evacuate from above. 
A: There are a few design issues that would need to be worked out.
First, is structural integrity. We currently don't have any material strong enough to withstand the strain of reaching out into space. 
In order to have the tube in a stationary position, the tube is built from geostationary orbit and extended in both directions (to maintain balance and position).
As pointed out in the comments, the vacuum would not be sufficient to eject the payload (garbage) into space. Although an elevator could be used. 
Allowing the garbage to fall into the atmosphere to burn up is not a good idea. Since most of the garbage is carbon based, it would create a lot of carbon dioxide in the upper atmosphere. The amount of carbon dioxide would easily turn the planet into a desert.
Allowing the garbage to accumulate in space would probably create a small moon. Which may create more problems in the future.
