If space is a vacuum, what does a spacecraft retro-rocket "push" against to manuver it's position?

A rocket doesn't 'push' against anything. It's based on conservation of momentum.

If your rocket is drifting in space and you toss something out the back (say a glove), then there can be no net change in momentum. The momentum of the glove plus the CHANGE in momentum of the rocket add up to zero (one of the momentums has to be negative since the change in momentum will be in the opposite direction of the object you tossed out the back).

The problem with this idea is that if you simply tossed stuff out the back, you couldn't toss it very fast and would quickly run out of stuff to toss.

However, momentum equals mass times velocity. So, instead of tossing a bunch of stuff out the back, you can shoot a little bit of stuff out the back very fast - which is what a rocket is doing. Thanks to explosive chemical reactions, the rocket's fuel is shot out the back at an incredibly high rate of speed, causing a change in momentum in the opposite direction of the fuel being shot out the back.

It doesn't "push" against anything.

It relies on the simple principle first described by Newton: every action has an equal and opposite reaction. This means that the exhaust firing out of the rocket in one direction causes and equal thrust in the opposition direction

It's own exhaust. In a manner of speaking. Push anything out of a rocket in space and it's trajectory is changed.

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It does not push against any thing, It uses thrust, action reaction principle of physics. Like when you throw a ball you have to brace yourself so you don't fall over.

You should pay more attention to your science classes in school, particularly the part where your teacher speaks about Newton's laws of motion: http://www.sciencetoymaker.org/balloon/images/newt...

It pushes against the propellent it carries with it.