Rocket equation

The rocket equation relates a rocket’s change in velocity to its exhaust velocity and the ratio of its initial mass to its final mass. It quantifies how propellant consumption changes the vehicle’s speed.

Tsiolkovsky rocket equation: The ideal rocket equation, Δv = vₑ ln(m₀/m_f), for motion under constant effective exhaust velocity. This is the standard mathematical form of the rocket equation.
Conservation of momentum: The principle that a system’s total momentum remains constant when no net external force acts. It yields the ideal relationship between expelled propellant and rocket velocity.
Delta-v budget: An accounting of the velocity changes required and available across a spacecraft mission. Rocket-equation calculations translate each maneuver’s velocity demand into propellant needs.
Ideal rocket equation: A model relating velocity change to exhaust velocity and mass ratio while neglecting external forces and losses. It isolates the rocket equation’s ideal assumptions from actual flight conditions.
Specific impulse: A measure of rocket-engine propellant efficiency, defined as thrust per unit propellant weight flow. It provides a common way to compare the engines’ effective exhaust velocities.
Momentum: A physical quantity equal to an object’s mass multiplied by its velocity. Rocket thrust arises as expelled mass carries momentum in the opposite direction.
Orbital maneuver: A controlled change to a spacecraft’s trajectory or orbit, usually using propulsion. Each propulsive maneuver consumes a portion of the vehicle’s available delta-v.
Gravity loss: The portion of a rocket’s potential velocity gain spent opposing gravity during powered flight. Gravity reduces the realized velocity change below the ideal equation’s prediction.
Mass ratio: The ratio of a system’s initial mass to its final mass after a specified change. The equation’s logarithm makes this ratio a direct driver of achievable velocity change.
Exhaust velocity: The speed of propellant relative to a rocket as it leaves the engine. This sets the proportional scale of velocity change in the equation.

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