A new means of space propulsion... closed loop pulse propulsion... here's the idea

[caraher]

22. Physics PhD here - can't work.

There are several ways to pick this apart. We're dealing with a system that I'll conceptualize as having three main parts: the slug, the gun barrel, and the armored astronaut. (I won't worry about, say, the gases that result from firing the gun, as the analysis would be no different for a railgun or even a spring-loaded slug launcher.)

Let's begin our analysis from the moment the slug first reaches its top speed but before it hits the curved barrel. We'll also use the center of mass reference frame and assume everything was at rest in this frame before we fired the gun. We'll also do a 1-D analysis of the problem (we could replace the curved barrel with a "slug reflector" while maintaining the basic physics of the proposal; modeling the curve of the barrel isn't important). At this moment, if the initial momentum of astronaut (plus gun; this won't work if the astronaut isn't holding the gun!) is +p, the momentum of the bullet is -p.

Why does the slug change directions 180 degrees? Because of the force the barrel exerts on the slug. Newton's 3rd Law of Motion says that this is equal in magnitude to the force the bullet exerts on the barrel, and opposite in direction.

The physics concept that relates force and change in momentum is called "impulse" and it's basically the force multiplied by the time during which the force acts. Let's assume our barrel does its job perfectly and doesn't slow the slug at all as it slings it back toward our astronaut. In doing so, the barrel imparts an impulse of +2p to the bullet, so its final momentum is the initial momentum +p plus the impulse of -2p for a final momentum of -p for the bullet as it leaves the barrel, but before it hits our astronaut.

Thanks to Newton's 3rd Law, the impulse imparted during this process to the gun barrel (and therefore astronaut) by the slug is equal in magnitude and opposite in direction to the impulse the slug imparted to the barrel. So the astronaut begins with momentum +p, experiences an impulse of -2p, and therefore winds up with a final momentum of -p.

So the effect of the ideal curved barrel is that both slug and astronaut simply reverse speed and direction!

From here, the best-case scenario is the slug bouncing off the astronaut in a perfectly elastic collision. In that case, the bullet simply changes direction without slowing, giving the slug a momentum of -p. The astronaut's suit imparted an impulse of -2p to the slug, therefore the slug imparts an impulse of +2p to the astronaut. But before this collision the astronaut had a momentum of -p, so the astronaut's new momentum is -p +2p = +p. Which is exactly what it would have been had the barrel never been curved.

The worst case, BTW, at this last step, is for the slug to simply stick to the spacesuit. The bullet then experiences an impulse of -p, the astronaut experiences an impulse of +p, and both wind up at rest again.

Basically the whole scheme is a version of trying to pull yourself up by your bootstraps. Only a net external force can cause a change in the momentum of a system. Because the reversal of direction of the slug (which indeed requires no external energy source) is effected by the gun barrel, the analysis needs to consider the fact that the gun also imparts momentum to the astronaut (by the mechanism of holding it). Only by neglecting this interaction can you obtain the magic result of the slug imparting still more momentum to the astronaut by hitting her.

Finally... you do know that ChatGPT knows zero physics, right? So-called AI actually can help spot things like typos in computer code mainly because there are huge sets of examples to draw from in their training sets. But it does so by a kind of pattern matching. It's not out of the question for a more intelligent form of AI to come along that can actually recognize a certain context calls for specific models of physics and apply those in a consistent way, but the tools we can play with today fall very far short of that. Doing this kind of physics by ChatGPT is strictly for entertainment value, not valid physical insight.