Even though I agree much of the rocket launch footage appears to be staged, I will have to agree with Heiwa that rockets can theoretically work in a vacuum.
By quoting the analogy of the energy produced by firing an M16 bullet, you are in fact validating the idea that a rocket can "push against its own fuel."
Newton's Law states that "for every action there is an equal and opposite reaction." This statement is expressed by the following formula:
M(1) x V(1) = M(2) x V(2)
Where M stands for mass and V stands for velocity.
We are using meters and Kg.
Let's calculate the recoil distance
involved in firing an M16 rifle:
Weight of M16 = 4Kg; Weight of M16 bullet = 0.004Kg; velocity of M16 bullet = 950m/s
If we plug in the numbers:
4Kg x V(M16 rifle) = 0.004Kg x 950m/s
So using this formula the recoil, or the velocity of the M16 rifle going in the opposite direction to the bullet = (0.004Kgx950m/s)/4 = 0.95m/s
Thus the bullet is fired 950m/s in one direction, and the M16 rifle "travels" 1m/s
in the opposite direction, which seems intuitively about right when considering rifle recoil.
Let's use the same formula to calculate the speed of Ariane 5 one second after lift-off (T=1):
Weight of Ariane 5= 760,000Kg; Fuel mass ejected = 3,925Kg/s
; Average exhaust velocity (all 3 engines) =2,415.42m/s
If I plug the numbers in the formula:
(760,000Kg-4,000) x V(Ariane 5 at T=1) = 4,000Kg/s x 2,400m/s
V(Ariane 5 at T=1) = 12.7m/s
The Ariane 5 is accelerating
at 12.7m per second per second. This acceleration is larger than the effect of gravity (9.8m per second per second), so the rocket is indeed rising.
Just like if I attempt to run faster and faster, or paddle harder and harder, or if my free-moving
M16 rifle fired a continuous and steady stream of bullets, my speed will continually increase
, as my acceleration is cumulative
Not only that, but my rocket acceleration will also
increase over time as a result of the decrease in my total rocket mass due to fuel consumption:
Let's consider the weight of Ariane 5 at T=120 seconds, right before the two boosters are jettisoned.
M(Ariane 5 at T=120) = 760,000Kg - (120s x 4,000Kg/s) = 280,000Kg
At 120 seconds after launch, Ariane 5 will have total mass 280,000Kg.
Let's plug this mass in our initial formula M(rocket) x V(rocket) = M(Fuel) x V(fuel):
280,000Kg x V(Ariane 5 at T=120) = 4,000Kg/s x 2,400m/s
This gives us:
V(Ariane 5 at T=120) = 34.3 m/s
At time T = 120 seconds, Ariane 5 will be accelerating
34m every second
, minus the effects due to gravity and air drag.
Now is the fuel exhaust velocity of the Ariane 5 correct? How does such a large rocket slowly rise and not tumble? I don't know, but on paper rockets can work in a vacuum.
* Data from https://campus.tum.de/tumonline/LV_TX.w ... DocNr=7357