Escape Velocity Calculator Formula
Understand the math behind the escape velocity calculator. Each variable explained with a worked example.
Formulas Used
Escape Velocity
escape_vel = sqrt(2 * 6.6743e-11 * mass_body / radius)Escape Velocity (km/h)
escape_vel_kmh = sqrt(2 * 6.6743e-11 * mass_body / radius) * 3.6Variables
| Variable | Description | Default |
|---|---|---|
mass_body | Mass of Celestial Body(kg) | 5.972e+24 |
radius | Radius from Center(m) | 6371000 |
How It Works
Escape Velocity
Escape velocity is the minimum speed an object must have to permanently leave a gravitational field without further propulsion.
Derivation from Energy Conservation
Setting kinetic energy equal to gravitational potential energy:
(1/2)mv² = GMm/r
Solving for v: v = sqrt(2GM/r)
Note that escape velocity is independent of the escaping object's mass.
Worked Example
Escape velocity from Earth's surface.
- 01v = sqrt(2 * G * M / r)
- 02v = sqrt(2 * 6.6743e-11 * 5.972e24 / 6.371e6)
- 03v = sqrt(1.251e8)
- 04v ≈ 11,186 m/s ≈ 40,270 km/h
Frequently Asked Questions
Does escape velocity depend on the object's mass?
No. Escape velocity depends only on the mass and radius of the body being escaped from, not on the mass of the escaping object.
What is Earth's escape velocity?
Approximately 11,186 m/s or about 40,270 km/h from Earth's surface.
Does direction matter for escape velocity?
The magnitude is the same regardless of direction (as long as the path doesn't intersect the body). However, launching parallel to the surface requires slightly more energy due to the need to also gain altitude.
Ready to run the numbers?
Open Escape Velocity Calculator