Delta-V Calculator

From the rocket equation, delta_v = Isp * g0 * ln(m0/mf). To double the delta-v, you must square the mass ratio. This means each additional km/s of delta-v requires exponentially more propellant, making very high delta-v missions extremely propellant-intensive. This is why interplanetary missions take years and use gravity assists to save delta-v.

A gravity assist (slingshot) uses a planet's gravity to change a spacecraft's speed and direction without expending propellant. As a spacecraft approaches a planet, it falls into the planet's gravity well and gains speed (relative to the Sun). Used correctly, this can add several km/s of delta-v for free — critical for missions to the outer solar system.

Changing an orbit's inclination requires a vector velocity change, not just a magnitude change. For a 90-degree plane change in LEO (orbital velocity ~7.9 km/s), the required delta-v is 7.9*sqrt(2) = 11.2 km/s — more than reaching orbit from the ground. For this reason, missions are launched as close to their target inclination as possible from the ground.

The vis-viva equation gives the speed of an object in any point of an elliptical orbit: v^2 = GM * (2/r - 1/a), where GM is the gravitational parameter, r is current distance from center, and a is the semi-major axis. It is used to compute velocities at orbital insertion and departure points for designing maneuvers.

High-thrust burns (chemical rockets) are nearly impulsive — they complete in minutes. This allows maneuvers to be treated as instantaneous velocity changes in the analysis. Low-thrust burns (electric propulsion) are long and continuous; the spacecraft spirals slowly through orbits, requiring different trajectory optimization techniques.

LEO from ground: 9.4 km/s. LEO to GEO: 4.2 km/s. LEO to TLI (Moon): 3.1 km/s. LEO to Mars transfer: 3.6 km/s. Mars orbit insertion: ~1.0 km/s. Venus flyby: ~0.5 km/s. Saturn transfer: ~7 km/s from Earth departure. These values assume optimal Hohmann transfers at the right launch windows.

Propellant slosh is the movement of liquid propellant inside tanks during maneuvers. It affects the spacecraft's center of mass and can cause attitude control problems. Engineers use baffles inside tanks to dampen slosh. Slosh is particularly important for long burns and attitude-critical maneuvers near sensitive instruments.

Yes. For multiple burns with the same engine, add the propellant masses required for each burn, accounting for the changing spacecraft mass between burns. For the second burn, the dry mass equals the spacecraft mass after the first burn (wet mass minus first burn propellant).

The Oberth effect states that a rocket burn is most efficient when performed at the point of highest velocity in an orbit (usually closest approach to the attracting body). The same delta-v produces more kinetic energy change at higher velocity. This is why rocket burns for departure from a planetary orbit are performed at periapsis rather than apoapsis.