Violation of the Newton's first law of motion in the movement of spacecrafts in the vacuum of space [closed]

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

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

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• 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? – mbeckish Jan 13 '16 at 18:07
• "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. – CuriousOne Jan 13 '16 at 18:07
• 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. – mithridates2000 Jan 13 '16 at 18:18
• 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? – mithridates2000 Jan 13 '16 at 18:25
• Gas doesn't expand to infinity immediately. – CuriousOne Jan 13 '16 at 19:37