Gravitational Assist Calculator

The hyperbolic excess speed v_inf is the speed a spacecraft would have at infinite distance from the planet — the asymptotic approach speed relative to the planet. For a spacecraft on a hyperbolic orbit with energy E = 0.5*v_inf^2, the speed at any distance r from the planet is v = sqrt(v_inf^2 + 2*GM/r). v_inf is determined by the mission geometry (approach trajectory from the Sun) and cannot be changed during the flyby itself.

Jupiter is by far the best gravity assist planet: it has the largest mass (highest GM = 1.267 x 10^8 km^3/s^2) and moves at 13.1 km/s. Its large radius allows close flybys. Saturn is second best. For inner solar system missions needing deceleration, Venus is commonly used (35 km/s orbital speed). Earth provides useful intermediate assists for outer planet missions (Galileo, Cassini, New Horizons).

During a flyby, if a rocket burn is performed at periapsis (the closest point, where speed is highest), the Oberth effect provides extra energy gain. A burn of delta-v at periapsis speed v_peri changes the orbit energy by v_peri * delta_v (compared to delta_v^2/2 far from the planet). This powered gravity assist is more efficient than either a pure gravity assist or a burn in interplanetary space.

A resonance assist involves a flyby that puts the spacecraft in an orbit whose period is a ratio of the target planet's period, ensuring a second flyby at the same relative geometry. Galileo used multiple Earth-Jupiter resonance flybys to build up energy before reaching Jupiter. This allows multiple assists from the same planet, each adding speed, when a single assist would be insufficient.

Yes. The spacecraft must come close to the planet (small periapsis) to maximize deflection, but cannot go below the planet's surface or dense atmosphere. The flyby duration is typically hours to days, limiting complex maneuvers. Very high v_inf means less deflection (the spacecraft is not deflected as strongly). And gravity assists only work when the target planet is in the right position — it may take years to reach the flyby planet.

Swing-by is another term for gravity assist, used particularly in European (ESA) mission planning. The MESSENGER mission to Mercury used six swing-bys (one Earth, two Venus, three Mercury) to bleed off enough energy to enter Mercury orbit. Each retrograde flyby removed energy, allowing MESSENGER to slow down enough for orbit insertion at Mercury with manageable propellant use.

Yes. A gravity assist can deflect the spacecraft's velocity vector in any direction, including out of the ecliptic plane. The Ulysses solar polar mission used a Jupiter gravity assist to change its trajectory to a polar orbit around the Sun — an inclination change of about 80 degrees that would have been impossibly expensive with rocket propellant alone.

The interplanetary superhighway (IPS) or invariant manifold tubes connect Lagrange points between planets through near-zero-energy pathways in the Sun-planet gravitational field. Spacecraft can travel vast distances using tiny amounts of propellant by following these tubes. This is used for comet and asteroid trajectories and low-energy lunar transfers. It is distinct from gravity assists but complementary.

Very accurate. A targeting error of just 1 km at Jupiter flyby can cause a several-thousand-km error at the eventual destination. Navigation requires very precise measurements of the spacecraft's position and velocity (using Deep Space Network ranging and VLBI astrometry) and trajectory correction maneuvers weeks before the flyby. Voyager's 1980 Saturn flyby was accurate to within a few km.