Delta-v budget

In astrodynamics and aerospace, a delta-v budget is an estimate of the total change in velocity (delta-v) required for a space mission. It is calculated as the sum of the delta-v required to perform each propulsive maneuver needed during the mission. As input to the Tsiolkovsky rocket equation, it determines how much propellant is required for a vehicle of given empty 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. Delta-v is also 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 regime 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, then 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.

The Tsiolkovsky rocket equation shows that the delta-v of a rocket (stage) is proportional to the logarithm of the fuelled-to-empty mass ratio of the vehicle, and to the specific impulse of the rocket engine. A key goal in designing space-mission trajectories is to minimize the required delta-v to reduce the size and expense of the rocket that would be needed to successfully deliver any particular payload to its destination.

The simplest delta-v budget can be calculated with Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bi-elliptic transfer can give a lower delta-v.

A more complex transfer occurs when the orbits are not coplanar. In that case there is an additional delta-v necessary to change the plane of the orbit. The velocity of the vehicle needs substantial burns at the intersection of the two orbital planes and the delta-v is usually extremely high. However, these plane changes can be almost free in some cases if the gravity and mass of a planetary body are used to perform the deflection^{[citation needed]}. In other cases, boosting up to a relatively high altitude apoapsis gives low speed before performing the plane change, thus requiring lower total delta-v.

The slingshot effect can be used to give a boost of speed/energy; if a vehicle goes past a planetary or lunar body, it is possible to pick up (or lose) some of that body's orbital velocity relative to the Sun or another planet.