How does a rocket work in a vacuum

[pomodoro]

You have just answered yourself the question as to why there is no back pressure from the air. As far as the work is concerned it went into heating the exhaust gases. The molecules of the gas got hotter and the gas expanded. The expansion in one dimention (the opening of the exhaust) pushed the rocket the other way . If you did press against air, then all of the momentum available will push the rocket and would not be shared with the exhaust.

The Gas molecules from the rocket may have a great distance from each other but the molecules in the atmosphere that they collide with do not. In the absence of an atmosphere in the infinite vacuum of space gas molecules will never collide with anything. They will just continue to move outwards. As they do not have anything to collide with there is no increase in pressure inside the combustion chamber or outside in the atmosphere. As the gas molecules heat up and expand they will simply exit the combustion chamber without a force to push against.  This is the free expansion of gas. During free expansion no actual work is done as there is no opposing force so there is no pressure that would result in the creation of work.

[LibreEnergia]

F = MA

Relative to the rocket gas (a  mass) is accelerated out the exhaust,  producing a force.

Nothing is required to push against. I can't believe why you'd think any differently.

[Nink]

F = MA

Relative to the rocket gas (a  mass) is accelerated out the exhaust,  producing a force.

Nothing is required to push against. I can't believe why you'd think any differently.

If we go with the F=MA please help me with the math as I am obviously not able to work out the formula.  What is the mass of the Gas ejecting. What is the acceleration rate of the gas ejecting.  Is this greater than the force of the Mass of the rocket and the deceleration caused by gravity.  Please give me some numbers to work with.  You choose the variables and lets plug them in and see if we can get enough force to be greater than the combined mass of the rocket and the fuel it has to move and also counteract the force of gravity.   

1 what is the Mass of the fuel ejected
2 what is the acceleration rate of that fuel ejected
3 what is the total mass of the fuel on board at 100km
what is the Mass * that acceleration so we can calculate Newtons.

We know gravity at 100km high is 9.5m/s^2
We know the mass of the Apollo 11 rocket is  28,801 kg

So if you can provide me the rest of the values lets plug them in and see how far our rocket will move in the absence of an atmosphere to push against

[LibreEnergia]

If we go with the F=MA please help me with the math as I am obviously not able to work out the formula.  What is the mass of the Gas ejecting. What is the acceleration rate of the gas ejecting.  Is this greater than the force of the Mass of the rocket * the acceleration of the rocket.  Please give me some numbers to work with.  You choose the variables and lets plug them in and see if we can get enough force to be greater than the combined mass of the rocket and the fuel it has to move and also counteract the force of gravity.   

1 what is the Mass of the fuel ejected
2 what is the acceleration rate of that fuel ejected
3 what is the total mass of the fuel on board at 100km
what is the Mass * that acceleration so we can calculate Newtons.

We know gravity at 100km high is 9.5m/s^2
We know the mass of the Apollo 11 rocket is  28,801 kg

We don't actually know any of those numbers since we would need to know how the velocity and mass of the rocket varied as it flew. All we know for sure is that the rocket accelerated and continued to do so till it reached orbital velocity.

The mass ejected was the entire mass of the fuel and oxidiser which was about 2.4 million kg. We don't know the dynamics of how that was accelerated, other than the thrust on take off was about 75 mega Newtons. Without knowing the flight profile we cant calculate anything else.

[Nink]

We don't actually know any of those numbers since we would need to know how the velocity and mass of the rocket varied as it flew. All we know for sure is that the rocket accelerated and continued to do so till it reached orbital velocity.

The mass ejected was the entire mass of the fuel and oxidiser which was about 2.4 million kg. We don't know the dynamics of how that was accelerated, other than the thrust on take off was about 75 mega Newtons. Without knowing the flight profile we cant calculate anything else.

2,400,000 kg of fuel or the equivalent of 800 elephants worth of fuel wow.  Quick search this thing was heavy. You would think there would be tonnes of data available so we can extract the mass of the rocket and remaining stages and fuel when it crossed the karman line.  If we can't get stats for Apollo how about we pick any rocket that flew into space.    Don't rockets go there all the time?  Someone must have that data.

Saturn V
Height    363.0 ft (110.6 m)
Diameter    33.0 ft (10.1 m)
Mass    6,540,000 lb (2,970,000 kg)[3]
Stages    3
Payload to LEO    310,000 lb (140,000 kg)[4][5]
Payload to TLI    107,100 lb (48,600 kg)[3]