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I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut wouldn't be able to push in the empty space with his hands or legs to move himself, but with a rocket engine it's possible. How? What might be the explanation for this in General Relativity?

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    $\begingroup$ the rocket doesn't push against empty space, but against its exhaust gas $\endgroup$ – Christoph Nov 3 '14 at 12:06
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    $\begingroup$ If you were an astronaut floating in space with a supply of baseballs, and you started throwing them in a given direction, would that exert force? $\endgroup$ – Hot Licks Nov 3 '14 at 16:41
  • $\begingroup$ And note that the amount of force (and change in momentum) generated by throwing something depends on how hard you throw it. Hence a rocket exhaust is ideally very fast. $\endgroup$ – Hot Licks Nov 3 '14 at 16:44
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Newton's third law is pretty near to the mark.

All of the phenomena you cite stem from the principle of conservation of momentum in an isolated system, itself ultimately a result (through Noether's theorem) of the fact the physical description of that isolated system is unchanged if we shift the spatial origin of our co-ordinate system.

So, if you're in deep space and you throw something with mass $m$ in one direction at a speed $v$, its momentum is $m\,v$ in that direction. The initial total momentum of the system (you + the thrown thing) is nought. So that means that the final total momentum for the system must be nought. Therefore, your own momentum must be $m\,v$ in the direction opposite to the thrown thing. If your mass is $M$, then your speed is $m\,v/M$ in the direction opposite to the thrown thing.

Note that, even though you can't shift your centre of mass without throwing anything (and in any case, the centre of mass of the whole system i.e. you+the thrown thing stays put), you can rotate and shift your orientation without violating conservation of angular momentum by cyclically shifting your shape; this is the same method a cat uses to flip over as it falls. See my answer here to the question "Is there a way for an astronaut to rotate?" and also my article "Of Cats and Their Most Wonderful Righting Reflex"

General relativity doesn't describe rockets (well, almost so, see my caveat below) in the way you might think. General relativity describes the locally freefalling frames and their so called Lie dragging by the system of geodesics defined by the solutions to the Einstein Field Equations. In less jargon: General Relativity tells you what kinds of motions are in keeping with Newton's first law; it tells you the motions within spacetime that something "isolated" (not experiencing a force) will undergo: anything different to this calls for a force to accelerate something relative to these freefalling frames. Chemistry describes the burning of fuel and Newton's third law the production of force from throwing this fuel to allow your rocket to deviate from the freefalling motion given by General Relativity.

To be precise, as the rocket throws its fuel out, the mass-energy distribution and the momentum fluxes (pressure distributions) of the system is changing, and this strictly speaking would need to be taken into account in the Einstein Field equations (this would alter the "source" term, the so-called stress-energy tensor). Thus the rocket's action would, to a fantastically small degree, alter the spacetime around it. But this is a tiny technicality. The main gig is simply that chemical energy allows you to throw fuel and produce a force to let you deviate from a locally freefalling (inertial) frame.

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  • $\begingroup$ Thanks. Your answer to the other question has made it clear. :) $\endgroup$ – Xmindz Nov 3 '14 at 12:08
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    $\begingroup$ One more thing to note. If you now consider the entire rocket as including the fuel, the centre of mass does not change. All that has happened is that the entire assemblage has stretched out. $\endgroup$ – Aron Nov 4 '14 at 11:25
  • $\begingroup$ @Aron indeed. This is an extension of my sentence "(and in any case, the centre of mass of the whole system i.e. you+the thrown thing stays put" $\endgroup$ – WetSavannaAnimal Nov 4 '14 at 11:52
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I'm a little confused why you ask about GR at the very end of your question. If your question is simply how a rocket is able to accelerate in space without having anything to "push" off, then we can tackle your question pretty well with classical mechanics.

Newton's Third Law has its limitations at times, but for this question it will work just fine. Newton's Third Law states that for any force exerted by object $A$ onto object $B$, then object $B$ exerts a force back on object $A$ of equal magnitude, but in the opposite direction. In this example, the rocket accelerates, so some object $A$ must be exerting a force forward on the rocket. In turn, the rocket must exert a reaction force back on this mystery object $A$.

It turns out that object $A$ is the gases escaping the rocket. As the gases escape the nozzle of the rocket, they interact with the rocket itself. The gases exert a force forward on the rocket, and the rocket pushes back on the gases because of Newton's Third Law. Although it may seem strange, this is all you need to accelerate your rocket. Your rocket does not need ground, or an atmosphere, or another space vehicle to "push off"; the interaction between the gases and the rocket occurring within the rocket is sufficient to accelerate the rocket.

If you don't believe me, sit on a chair or a scooter on a low friction surface, at rest. Hold a heavy object like a bowling ball or medicine ball on your lap. As hard as you can, throw the ball away from you. If the coefficient of friction between your chair and the floor is low enough, you will experience an acceleration in a direction opposite of the ball. Because of Newton's Third Law, the ball exerted a force back on you, and if the friction is low enough, there is a net force in that direction that produces an acceleration.

As a bonus, please note in both of these examples that momentum will be conserved. so no cause for panic there.

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  • $\begingroup$ The GR came to my mind because, for me the explanations by GR for many physical problems & forces like gravity to be more clear and convincing than the Newtonian laws. $\endgroup$ – Xmindz Nov 4 '14 at 10:15
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A model I encountered as a kid, back when the Space Race was in full swing, is still the simplest explanation I've found:

Think about an inflated balloon with its neck closed. It doesn't go anywhere, because the pressure in all directions is equal. (Which is what keeps it inflated, too.)

Now open the neck. What makes the balloon fly around isn't actually the air escaping through the neck -- it's the fact that there's no longer pressure backward against the balloon at that point, so the pressure on the opposite side is unbalanced and there's a net force pushing the balloon forward.

A rocket engine is, essentially, a rigid balloon with an open neck which continuously re-inflates itself. High pressure inside, a nozzle designed to exhaust as fast as possible minimizing pressure in the backward direction, unbalanced pressure forward... "Zoom!"

(Yes, I know this is an oversimplification. But it's an explanation which is so straightforward that a third-grader, which I was at the time, could look at it and say "Of course, that's obvious!" Unfortunately my teacher at the time didn't take well to having her wrong explanation corrected by a third-grader, but that's a separate story.)

Late addition: This is also why Project Orion -- the ultimate low-tech nuclear rocket engine -- would have worked. Build a huge shield, mount your craft to it with shock absorbers, and set off an atom bomb on the far side. The part of the bomb's shock wave which hits the plate will drive the craft forward. The fact that the rest of the shock wave is completely uncontained is wasteful but doesn't keep this from working. You could do the same thing with smaller explosives, but then the inefficiency becomes a serious problem -- which is why an rocket engine has a reaction chamber and nozzle, to capture much more of that energy and use it as thrust.

(Calculating just how inefficient Orion would have been, how much thrust it would have produced anyway, and how to build a shield and shock absorbers which could handle this, is left as an exercise for the reader. Or you can look up the report of the team that first examined it. No joke.)

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  • $\begingroup$ This is an explanation which makes sense to a third-grader, but it's wrong; if you think it over more carefully you should realize that it doesn't explain the rigid rocket, nor the phenomenon in a vacuum. $\endgroup$ – zwol Nov 3 '14 at 19:36
  • $\begingroup$ Sorry, but it does explain both. Elasticity is not required; pressure is -- whether pumped up as in a balloon, or provided by combustion as in a rocket. And because the entire explanation is self-contained within the rocket engine, presence or absence of surrounding air is completely irrelevant. In this case, the intuitive model really does work just fine. You can, of course, go into the whole action/reaction thing, but that's effectively details of how the pressure is released -- necessary if you want mathematical accuracy, NOT necessary to explain functionality. $\endgroup$ – keshlam Nov 3 '14 at 21:34
  • $\begingroup$ (Note that this is a simplified version of the description @CountIblis provides -- but emphasizes that thrust does not involve gasses pressing against gasses, but gasses pressing against the engine. Or, if you want the action/reaction model, the engine pressing inward against the expanding gasses.) $\endgroup$ – keshlam Nov 3 '14 at 21:37
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    $\begingroup$ @Zack This explanation is right. It's not one that you can adapt easily to a quantitative computation, but the physics is correct. $\endgroup$ – dmckee Nov 4 '14 at 2:57
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    $\begingroup$ It really is just the conservation of momentum (or Newton's 3rd law; they are interchangeable in the context of plain mechanics). The gas goes one way, the rocket goes the other, the mechanism of momentum exchange is a detail but in most cases it is impacts between atoms of the fuel and the walls of the pressure chamber and nozzle. Taken together those impacts are understood as pressure just as in the kinetic theory of gases. $\endgroup$ – dmckee Nov 4 '14 at 5:34
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If I'm not wrong, it's basically the same principle in which an astronaut would throw something in empty space and, with so, move in the opposite direction.

It's not thrusting against something but throwing energy and power by burning fuel according to the law of inertia... I could be wrong so I'd like someone more knowledgeable to double-check, please :)

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  • $\begingroup$ Suggestion to the answer (v1): Replace throw something in a direction of anti-gravitational space with throw something in empty space. $\endgroup$ – Qmechanic Nov 3 '14 at 22:25
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    $\begingroup$ throw something in a direction of anti-gravitational space sounds more badass $\endgroup$ – Gabriel Canongia Nov 4 '14 at 2:13
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    $\begingroup$ It sounds muddled and imprecise and invites endless misunderstanding as well as being easily mistaken for some kind of left-field theory. $\endgroup$ – dmckee Nov 4 '14 at 2:59
  • $\begingroup$ Fine u.u... (but it sounded nice ¬¬) $\endgroup$ – Gabriel Canongia Nov 4 '14 at 15:36
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No need to call the general relativity. You can understand it using only classical mecanics laws.

If you are on a skateboard, and throw a mass in front of you, you will move backwards. As long as the mass does not hit the floor, the center of mass of {you+the mass} is the same, however you did move.

The rocket engine ejects gaz from combustion. The movement is based on the very same property. You really should not imagine that it is the resistance of the outside atmosphere "resisting" to the ejected gaz that creates the moving force.

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    $\begingroup$ I was wondering if there is a reason to spell "gas" as "gaz" in your answer? $\endgroup$ – Zack Nov 3 '14 at 16:23
  • $\begingroup$ Just my native language contaminating my English ! $\endgroup$ – TZDZ Nov 3 '14 at 20:55
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    $\begingroup$ Which language? $\endgroup$ – Zack Nov 3 '14 at 22:33
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The simplest way to get this intuitively is to consider a rocket where the exhaust gasses escape in two opposite directions. So, there is a nozzle at one side and also the opposite side. In this case, the rocket will go nowhere. The chemical reactions produce gasses at high temperature and pressure and they then accelerate and escape in both directions. If we now close one nozzle, the rocket will move in the opposite direction. The gasses that would have escaped if that nozzle were open, will now bump into the boundary and exert a force on the rocket there. The third law implies that the rocket must be exerting an opposite force on the gas there. There is therefore a net force on the exhaust gasses in the direction of the open nozzle, while the rocket is pushed in the opposite direction.

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I am wondering how the rockets could thrust in the empty space and move in the opposite direction.

In very simplistic terms the rocket motor thrusts against the closed end of the nozzle. Once the gas leaves the nozzle it no longer has any interaction with the rocket - there is no need for it to 'hit' anything else.

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The best common example is often shown in HS physics classes. A student in a low friction chair holds a CO2 fire extinguisher and points it in a safe direction. When they pull the trigger and release CO2 gas moving very fast from the nozzle of the fire extinguisher that rapidly moving gas leaving the system (chair student and gas bottle) causes the system to move in the other direction directly opposite the gas flow.

Some rocket engines actually use charged ions and electric forces to accelerate those charged ions away from the ship in the opposite direction that the ship's system needs to accelerate towards. The weight of the ions is very low, but the speed with which they are emitted can approach the speed of light, so these engines are very efficient and can run for long periods of time compared to traditional "rocket" engines.

Jet engines operate exactly like rocket engines. The atmosphere provides oxygen for the reaction which generates the rapid expansion of the fuel/air mixture. But the engine doesn't need air to "push" against. Rocket engines supply their own oxidizer, rather than using air's oxygen content.

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protected by Qmechanic Nov 3 '14 at 22:17

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