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Suppose a rocket at rest in space where there is a complete vacuum and no force to influence the rocket:

Rocket

In the left we have the rocket with a metal ball in it. After the ball is thrown out of the rocket, according to Newton's first law of motion, because no force is influencing the system ($ \sum F = 0)$ and the system is initially at rest, the center of mass of the system will continue to be at rest, although the ball and the rocket will move in opposite directions. In this case we may reduce the Newton's first law of motion to this equation:

$$m_1 v_1 = m_2 v_2$$
(as it might be interpreted as the conservation of momentum)

Thus, dependent on the mass of the rocket $(m_1)$ and the mass of the metal ball $(m_2)$ and the velocity of the ball when moving out of the rocket $(v_2)$, we can calculate the velocity of the rocket $(v_1)$.

Now, in the right we have the same rocket but this time with a tank of liquefied gas (a real gas) instead of the metal ball. After opening the tank the gas will flow out of the rocket in the vacuum and we expect the rocket to move in the opposite direction the same way jet spacecrafts allegedly move in the vacuum of space. Suppose the mass of the liquefied gas initially is again $m_2$ and suppose after the gas flows out of the tank completely the rocket gets the velocity of $v_1$ and the mass of the rocket(including the empty tank) is again $m_1$. Applying the Newton's first law of motion again in this case we are (or should be) able to calculate the mean velocity $(v_2)$ of the total mass of the gas that have been flowed and scattered in the vacuum, HOWEVER obviously it is impossible to logically think of such a velocity! The molecules of the gas are moving in any direction in the vacuum of space; they won't move in the space the same way that a metal ball will move. In other words we can't THROW a mass of gas in the space and get some movement in the opposite direction out of it.

Conclusion: Movement of a jet spacecraft in the vacuum of space is impossible!

Question: What's wrong with the above reasoning?

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closed as unclear what you're asking by CuriousOne, Daniel Griscom, Ali, yuggib, Kyle Kanos Jan 14 '16 at 11:05

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  • $\begingroup$ You went wrong with: "The molecules of the gas are moving in any direction in the vacuum of space; they won't move in the space the same way that a metal ball will move." I'm not sure why you assume that the gas from a rocket sprays out in all directions. Maybe you are picturing the turbulence exhibited by rocket exhaust when the rocket is first leaving the launch pad? $\endgroup$ – mbeckish Jan 13 '16 at 18:07
  • $\begingroup$ "HOWEVER" (not even capitalized) and "obviously" are not logical statements. Using them together isn't one, either. In space the center of gravity of a rocket always stays the same. The rocket body moves one way, the propellant another and the center of gravity stays where it was (or moves at a constant velocity in your choice of inertial system). Can you calculate the center of gravity of a rocket body and a gas cloud? Yes. $\endgroup$ – CuriousOne Jan 13 '16 at 18:07
  • $\begingroup$ Thanks for your comment > Curious That gas cloud that you say is just a mental imagination. You are thinking of that gas cloud just the same as you think of a cloud in the earth's atmosphere. We are talking about vacuum in which you may never have such a cloud of gas. The expansion of that gas cloud to the space infinity will be immediate. after a few moments you may never have such cloud as you may have in an atmosphere. $\endgroup$ – mithridates2000 Jan 13 '16 at 18:18
  • $\begingroup$ mbeckish: Here we are talking about the moment when the gas is completely flowed in the vacuum and the moments after that. Wouldn't you have the total mass of gas scattered all in the space? Can you think of a gas cloud that is moving with the velocity of v2 as Curious mentioned it? $\endgroup$ – mithridates2000 Jan 13 '16 at 18:25
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    $\begingroup$ Gas doesn't expand to infinity immediately. $\endgroup$ – CuriousOne Jan 13 '16 at 19:37
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If you added up the momentum of all the molecules of gas (vectorially), the combined momentum will be equal in magnitude to that of the rocket, and in the opposite direction. In other words, the velocities of the molecules will be biased away from the rocket.

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Consider what happens if, in your first model, a small meteor collides with the ball after it has been thrown from the craft. It changes the center of gravity of the system but does it affect the motion of the craft? It doesn't because once the ball is ejected from the craft, it no longer has any effect on the craft. It's the force applied to the ball prior to it being ejected that causes the movement of the craft. It's the same with the gas. If they happen to say, bump into each other after ejection (because of inconsistent speeds, perhaps) it doesn't affect the movement of the craft.

I'm not disagreeing with Chester's answer, all of that is true in the Newtonian model. What I am saying is that whether the gas molecules hang together in a cloud, shoot into the void like little metal balls, dance a jig, or decay into radiation makes no difference to the trajectory of the spacecraft after they have been ejected.

The center of mass is a useful construct for mathematical models but is little more than that.

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  • $\begingroup$ Actually you can't say the movement of the gas cloud is not important after it is flowed out in the space. Motion of masses is based on laws and those laws as presented by mathematics CAN'T be violated. The gas cloud SHOULD move in the predicted manner and it WILL, otherwise we should doubt if we are awake or asleep. That gas dancing in the space would be possible only in a dream! I finally came to accept CuriousOne comment that the gas cloud while expanding fast in any direction will move in the space in such a way that its center of mass will move with the velocity of V2. $\endgroup$ – mithridates2000 Jan 15 '16 at 0:08
  • $\begingroup$ And, If that meteor collides with the ball as you said, the system won't be an isolated system anymore and again it will behave exactly according to the laws of motion, however this time not the Newtons' first law but the second. Thanks. $\endgroup$ – mithridates2000 Jan 15 '16 at 0:08
  • $\begingroup$ You are confusing mathematics with physics. Mathematical models are always that: models. There are necessarily simplified in order to be useful. The fact is that reality doesn't follow mathematical laws, it follows physical laws. Newton's laws were long ago shown to not be complete and are based on the incorrect assumption that time is absolute. They are still very very useful but mathematics doesn't control physics, it's used to attempt to explain it. Once the gas is expelled, it doesn't have any more effect on the ship at least not in the Newtonian model. $\endgroup$ – JimmyJames Jan 15 '16 at 14:57
  • $\begingroup$ If you can't understand mathematical principles behind physical phenomena you actually do not understand physics. $\endgroup$ – mithridates2000 Jan 16 '16 at 15:51

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