# Delta-v budget

## Description

In astrodynamics and aerospace, a delta-v budget is an estimate of the total delta-v required for a space mission. It is calculated as the sum of the delta-v required for the propulsive maneuvers during the mission, and as input to the Tsiolkovsky rocket equation, determines how much propellant is required for a vehicle of given mass and propulsion system.

Delta-v is a scalar quantity dependent only on the desired trajectory and not on the mass of the space vehicle. For example, although more fuel is needed to transfer a heavier communication satellite from low Earth orbit to geosynchronous orbit than for a lighter one, the delta-v required is the same. Also delta-v is additive, as contrasted to rocket burn time, the latter having greater effect later in the mission when more fuel has been used up.

Tables of the delta-v required to move between different space venues are useful in the conceptual planning of space missions. In the absence of an atmosphere, the delta-v is typically the same for changes in orbit in either direction; in particular, gaining and losing speed cost an equal effort. An atmosphere can be used to slow a spacecraft by aerobraking.

A typical delta-v budget might enumerate various classes of maneuvers, delta-v per maneuver, and number of each maneuver required over the life of the mission, and simply sum the total delta-v, much like a typical financial budget. Because the delta-v needed to achieve the mission usually varies with the relative position of the gravitating bodies, launch windows are often calculated from porkchop plots that show delta-v plotted against the launch time.

We may apply the formula (where μ = GM is the standard gravitational parameter of the sun, see Hohmann transfer orbit) to calculate the Δv in km/s needed to arrive at various destinations from Earth (assuming circular orbits for the planets, and using perihelion distance for Pluto).

Related formulas## Variables

Δ_{v} | Delta-v budget (m/s) |

μ | Gravitational parameter (m^{3}/s^{2}) |

r_{1} | Initial radius (m) |

r_{2} | Final radius (m) |