Delta-V Maneuver Budget

A spacecraft changes orbit by changing velocity. The size of that velocity change — the delta-v (Δv) — is the single number that sizes a propulsion system: it sets how much propellant you carry, which sets the wet mass, which sets the launch cost. Get the delta-v budget wrong early and the whole mass budget unravels. This tool budgets five canonical maneuvers, each a distinct two-body impulsive problem.

Hohmann transfer — the minimum-energy coplanar path between two circular orbits: a burn to enter an elliptical transfer orbit, a half-orbit coast, then a second burn to circularize at the target altitude. Plane change — a pure inclination rotation at fixed altitude, costing Δv = 2·v·sin(θ/2); it is brutally expensive at orbital speed, which is why launch directly into the right inclination whenever possible. Combined — a Hohmann transfer with the plane change folded into the second burn at apogee, where orbital speed is lowest and rotating the plane is cheapest; the apogee burn becomes the vector sum (law of cosines) of the circularization and rotation. Circularize — a single burn at apogee turning an elliptical orbit circular. Deorbit — a single retrograde burn lowering perigee into the atmosphere (typically 50–80 km) so atmospheric drag does the rest.

Orbital speeds come from the vis-viva equation v = √(μ·(2/r − 1/a)), with Earth's gravitational parameter μ = 398,600.4418 km³/s². Once the total delta-v is known, the Tsiolkovsky rocket equation m_p = m₀·(1 − e^(−Δv/v_e)) converts it to propellant mass, where the exhaust velocity v_e = I_sp·g₀ is set by the propulsion type — cold gas ~70 s, monopropellant ~220 s, bipropellant ~320 s, electric 1,000–3,000 s. Higher specific impulse means more delta-v per kilogram of propellant; the exponential makes high-Δv missions punishingly propellant-hungry on low-I_sp systems.

What this tool does not capture: finite-burn (gravity) losses from non-impulsive thrust, low-thrust spiral transfers (an electric-propulsion mission does not fly a Hohmann), J2 and third-body perturbations, plane-change savings from bi-elliptic transfers, launch-window and phasing constraints, and propulsion-system dry-mass scaling. It is an engineering trade-study tool — fast first-order numbers for sizing and comparison, not a flight-design propagator.