Gravity Assist Speed Calculator Formula

Understand the math behind the gravity assist speed calculator. Each variable explained with a worked example.

Use the Gravity Assist Speed Calculator

Formulas Used

Max Speed Change

dv_max = 2 * planet_velocity * sin(bending_angle * pi / 360)

Speed Change (km/s)

dv_max_kms = 2 * planet_velocity * sin(bending_angle * pi / 360) / 1000

Variables

VariableDescriptionDefault
planet_velocityPlanet Orbital Velocity(m/s)13070
bending_angleBending Angle(deg)90

How It Works

Gravity Assist (Slingshot) Effect

A spacecraft flying past a planet can gain or lose speed by exchanging momentum with the planet.

Maximum Speed Change

dv = 2 * v_planet * sin(theta/2)

  • *v_planet* = planet's orbital velocity around the Sun
  • *theta* = total bending angle of the flyby trajectory

    • The theoretical maximum (theta = 180 degrees) gives dv = 2 * v_planet.

    Worked Example

    Jupiter flyby: v_planet = 13 070 m/s, bending angle = 90 degrees.

    planet_velocity = 13070bending_angle = 90
    1. 01dv = 2 * v_planet * sin(theta/2)
    2. 02dv = 2 * 13070 * sin(45 deg)
    3. 03dv = 26140 * 0.7071
    4. 04dv = 18 483 m/s = 18.48 km/s

    Frequently Asked Questions

    Does the planet lose energy in a gravity assist?

    Yes, but by an immeasurably tiny amount. The planet's enormous mass makes its velocity change negligible.

    Can gravity assists slow a spacecraft down?

    Yes. By flying in front of the planet (against its orbital motion), the spacecraft transfers energy to the planet and slows down. This was used by Messenger at Venus.

    Why is Jupiter the best planet for gravity assists?

    Jupiter has the highest orbital velocity times the largest gravity well, offering the most speed change per flyby.

    Ready to run the numbers?

    Open Gravity Assist Speed Calculator