Planet Escape Velocity Calculator Formula

Understand the math behind the planet escape velocity calculator. Each variable explained with a worked example.

Use the Planet Escape Velocity Calculator

Formulas Used

Escape Velocity

escape_vel = sqrt(2 * 6.674e-11 * mass / radius)

Escape Velocity (km/s)

escape_vel_kms = sqrt(2 * 6.674e-11 * mass / radius) / 1000

Variables

VariableDescriptionDefault
massPlanet Mass(kg)5.972e+24
radiusPlanet Radius(m)6371000

How It Works

Planetary Escape Velocity

The escape velocity is the minimum speed an object needs to leave a planet's gravitational well without further propulsion.

Formula

v_esc = sqrt(2 G M / R)

  • *G* = 6.674 x 10^-11 N m2 / kg2
  • *M* = planet mass
  • *R* = planet radius

    • For Earth this is about 11.2 km/s.

    Worked Example

    Earth: M = 5.972e24 kg, R = 6.371e6 m.

    mass = 5.972e+24radius = 6371000
    1. 01v_esc = sqrt(2 G M / R)
    2. 022 G M = 2 * 6.674e-11 * 5.972e24 = 7.972e14
    3. 03v_esc = sqrt(7.972e14 / 6.371e6)
    4. 04v_esc = sqrt(1.251e8)
    5. 05v_esc = 11 186 m/s = 11.19 km/s

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