Planet Escape Velocity Calculator Formula
Understand the math behind the planet escape velocity calculator. Each variable explained with a worked example.
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) / 1000Variables
| Variable | Description | Default |
|---|---|---|
mass | Planet Mass(kg) | 5.972e+24 |
radius | Planet 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)
For Earth this is about 11.2 km/s.
Worked Example
Earth: M = 5.972e24 kg, R = 6.371e6 m.
- 01v_esc = sqrt(2 G M / R)
- 022 G M = 2 * 6.674e-11 * 5.972e24 = 7.972e14
- 03v_esc = sqrt(7.972e14 / 6.371e6)
- 04v_esc = sqrt(1.251e8)
- 05v_esc = 11 186 m/s = 11.19 km/s
Frequently Asked Questions
Does escape velocity depend on the direction of launch?
No. Escape velocity is a scalar quantity and applies regardless of direction, as long as the path avoids the planet's surface.
Do rockets need to reach escape velocity?
Not necessarily. A rocket with continuous thrust can leave Earth at any speed. Escape velocity applies to unpowered (ballistic) trajectories.
What is the escape velocity of the Moon?
About 2.38 km/s, much lower than Earth's, which is why the Apollo lunar modules needed relatively small engines.
Ready to run the numbers?
Open Planet Escape Velocity Calculator