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 * 6.674e-11 * mass / radius)Escape Velocity (km/s)
escape_vel_kmps = sqrt(2 * 6.674e-11 * mass / radius) / 1000Variables
| Variable | Description | Default |
|---|---|---|
mass | Body Mass(kg) | 5.972e+24 |
radius | Body Radius(m) | 6371000 |
How It Works
Deriving Escape Velocity
Escape velocity is the minimum launch speed at the surface for an object to reach infinity without further propulsion.
Formula
v_esc = √(2 G M / r)
This is exactly √2 times the circular orbital velocity at the same radius. It comes from setting kinetic energy equal to gravitational potential energy: 1/2 m v² = G M m / r.
Worked Example
Find Earth's escape velocity (M = 5.972e24 kg, r = 6 371 km).
mass = 5.972e+24radius = 6371000
- 01v_esc = √(2 G M / r)
- 022 G M = 2 × 6.674e-11 × 5.972e24 = 7.972e14
- 037.972e14 / 6.371e6 = 1.251e8
- 04v_esc = √(1.251e8) ≈ 11 186 m/s ≈ 11.19 km/s
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