Rocket Propulsion

Rocket propulsion is a clean application of conservation of momentum: rocket ejects exhaust mass backward, gaining forward momentum.

Thrust F = u_e × (dm/dt), where u_e = exhaust velocity relative to rocket, dm/dt = mass-burning rate.

Tsiolkovsky rocket equation: Δv = u_e · ln(m_0/m_f), where m_0 = initial mass, m_f = final mass.

Δv determines mission feasibility. Reaching low Earth orbit: Δv ≈ 9-10 km/s.

Specific impulse I_sp = u_e/g₀ — measure of fuel efficiency. Chemical rockets: I_sp ≈ 300-450 s. Ion thrusters: ~3000+ s.

Mass ratio m_0/m_f determines how much velocity you can build up. Beyond ~10-20, structural and engineering limits dominate.

Multistaging (jettisoning empty fuel tanks) allows higher final Δv with reasonable mass ratios.

Newton's 3rd law in disguise: exhaust gas pushed backward ⇒ rocket pushed forward.