The exhaust gases move in one direction the rocket moves in the opposite direction. What am I missing?
So where exactly is the rocket pushed from to make it take flight?
I know this is useless, but
From the fuel accelerated out the back. Vacuums don't have any force associated with them. If you took a bucket full of air and somehow teleported it to, say, 100,000 feet the air would move from the bucket to the lower pressure around it. But how? There's nothing in the low pressure 'pulling' the air out of the bucket. It is pushed.
If you divide the bucket's volume into smaller segments, than each segment would be putting 101 kPa of pressure out of its borders. This is fine, since most of these volumes are bordered by other volumes, pushing back with 101 kPa, equalizing the force. The exception is those volumes at the very edge, which push out and aren't met with equal force. This presents a force imbalance, which accelerates the air out of the bucket.
If we cut this down into two air molecules in a one-molecule-wide tube with one side opened and the other closed. The outer molecule, let's say, is currently traveling away from the open end. Since there are only two molecules, it's already
in a vaccum, so everything's fine. But as there are two molecules in the tube, technically the air pressure is larger inside the tube than outside, so the air should, eventually leave it.
The outer molecule flies toward the inner one, and they collide, sending the outer one toward the open end and the inner one back to the closed end. The outer molecule collides with nothing else, and so leaves. It wasn't dragged out by the vacuum, it was pushed out by the inner molecule.
The inner molecule then hits the end of the tube and bounces back out. It, too, encounters nothing else, and so it leaves. But that bounce against the back of the tube put a very small amount of force on the tube itself, as the tube accelerated that air molecule about 1 km/s (from 500 mps one directly to 500 mps the other).
So, back to our bucket, the volumes just shy of the edge push the ones on the edge out, and are in turn pushed out by the volumes farther inside. For each molecule that is pushed out, another hits the back wall, so each molecule pushed out puts a small force on the bucket. By the time the bucket is emptied, it has been accelerated a small but measurable amount.
Thus, the rocket it pushed forward by the fuel itself. In fact, the presence of air around our bucket would hinder it, as the each tiny acceleration caused by a molecule bouncing off the back wall would be transferred from the bucket to the air in front of the bucket.
Get it? Feel free to tl;dr this post, ignore it, and say "Wrong." without providing a counter to this argument.