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Rocket propulsion
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Exhaust gas gives thrust and velocity change.
Δv = v_e ln(m₀/m)A rocket expels gas backward at speed vₑ relative to itself, gaining forward momentum. Thrust is F = vₑ dm/dt, and the final speed from the rocket equation is Δv = vₑ ln(m₀/m).
With vₑ = 3 km/s and mass ratio 10: Δv ≈ 6.9 km/s.
Rockets work in vacuum; they don't push against air.
In more detail
A rocket generates thrust by expelling exhaust gas backwards at high speed. The thrust equals the exhaust speed times the rate at which mass is expelled.
Real-world uses
- Launch vehicles use thrust calculations to plan lift-off.
- Ion thrusters on satellites produce small but continuous thrust.
- Spacecraft use rockets to change their speed in orbit, and the amount of fuel needed follows from the rocket equation.
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Frequently asked questions
Does a rocket need air to push against?
No. It pushes against its own exhaust, so it works in a vacuum.
How can I increase thrust?
Increase the exhaust speed or the rate of mass flow.
Why must a rocket carry so much fuel?
Most of its mass is fuel, and the change in velocity depends on the logarithm of the mass ratio, so large speed changes need a lot of propellant.
Related topics in Newton's Laws & Forces
Linear momentum · Second law as rate of momentum change · Variable mass systems · Conservation of momentum · Circular motion dynamics · Banking of roads