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

    Ready to run the numbers?

    Open Gravity Assist Speed Calculator