Physics / Astronomy / Engineering
Rocket motion
Variable mass and the Tsiolkovsky equation, staging and gravity.
What happens
A rocket climbs by throwing mass away: the Tsiolkovsky equation in action. Watch the mass chart fall as fuel burns, jettison empty stages to shed dead weight, throttle through max-Q, and compare Earth, Moon and Mars. The staging trick is the whole point: the same fuel goes much farther in pieces.
Equations used in the module
Equations T = v_e q, q = −dm/dt ≥ 0 m dv/dt = T − mg(h) − C exp(−h/H) v|v| g(h) = g₀/(1+h/R)² g = D = 0: Δv = v_e ln(m₀/m₁) h = 0, v = 0, T ≤ mg: N = mg−T, dh/dt = 0
