A low-cost, liquid-propellant rocket launch vehicle having a central pod that carries an optional final-stage rocket engine cluster, and having additional engine clusters arranged in diametrically opposed pairs of clusters. The pairs of clusters are burned and separated in a staging sequence until the final stage is reached. In the presently preferred embodiment, there are three pairs of engine clusters arranged in a hexagonal configuration about the central pod and each engine cluster contains seven identical engines. The engines are made from light-weight, low-cost materials, without gimbals or other moving parts. Steering of the vehicle is effected by differential control of the engine thrusts of selected engines, using duty-cycle modulation of a plurality of on/off propellant supply valves and, additionally, control of other on/off valves controlling the supply of an inert cryogenic fluid to secondary injection ports on the engine. An onboard gas generator provides inert gas for fluid pressurization and preferably uses as its principal reactant the same material used as the cryogenic fluid. Navigation is effected with inexpensive onboard systems and the entire vehicle provides a dramatic reduction in cost in comparison with conventional launch vehicles.