The gas coming out of the bottom of the rocket produces a force on the subsurface, which in turn produces an equal, opposite force on the gas and finally initiates the launch (Newton’s 3rd Law). But if no matter is present in (empty) space, what then provides the reaction force that can cause an acceleration?
Answer
In a car, the engine turns the wheels and the wheels push off against the ground. The propeller of a boat pushes against the water, but a rocket engine works on a different principle where there is no need for anything to push against. It must indeed be able to work in a vacuum as you say. The principle is the conservation of momentum.
What is impulse ?
The momentum of a moving mass is the product of the mass x the speed
p = mv
Conservation of momentum can now be applied as follows. Suppose that a mass of 10 kg and a mass of 2 kg first sit against each other (and do not move so that the momentum is zero) and then move apart with a mutual speed of, for example, 6 m/s by some internal mechanism. Then the heavy mass (which makes up 5/6 of the total initial mass) will get 1/6 of the speed, and the light mass (which makes up 1/6 of the total initial mass) will get 5/6 of the speed. In other words, the heavy mass moves at 2 m/s and the light one at -10 m/s. Why the minus sign? Since velocity also has a direction, and the two velocities are opposite, you have to take one of the two negative and the other positive.
What is the total impulse after the split?
10 kg. 2 m/s + 2 kg . (-10) m>/s = still zero !
The total impulse is thus conserved.
Even if they first move together with for example 25 m/s, (the total momentum is then 12 . 25 = 300) there will still be conservation of momentum after the split: 10 ( 25 + 2 ) + 2 ( 25 – 10 ) = 300
And now our rocket :
This now happens with a rocket: In the rocket engine, an amount of mass (namely the gases that arise from the fuel) is added to the rear with huge speed emitted. By preserving momentum, the rest of the rocket (ie the rocket itself + the remaining fuel) is accelerated forward inversely proportionally. So if a 100-ton rocket emits 1 tonne at 3000 km/h, it will accelerate itself forward by about 30 km/h by preserving momentum.
So a rocket does not react against any external medium, but dutifully obeys the law of conservation of momentum. Vacuum or not, it doesn’t matter. On the contrary, it works even better in vacuum because there is no air resistance there.
The nice thing about a rocket engine is that it is becoming more and more efficient, even if it continues to work on a constant emission. After all, the more fuel that is consumed, the less remaining mass that still needs to be accelerated, so the better that acceleration becomes.
Answered by
prof.dr. Paul Hellings
Department of Mathematics, Fac. IIW, KU Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/
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