Escape Velocity Formula
Calculate the minimum speed needed to escape a planet or star's gravitational pull.
Essential for space travel calculations.
The Formula
v = √(2GM / r)
Escape velocity is the minimum speed an object needs to break free from a body's gravitational pull without further propulsion. It depends only on the mass and radius of the body — not on the mass of the escaping object.
Variables
| Symbol | Meaning |
|---|---|
| v | Escape velocity (m/s) |
| G | Gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²) |
| M | Mass of the body being escaped from (kg) |
| r | Distance from the center of the body (meters) |
Example 1
Find Earth's escape velocity
M = 5.972 × 10²⁴ kg, r = 6.371 × 10⁶ m
v = √(2 × 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 6.371 × 10⁶)
v = √(1.251 × 10⁸)
v ≈ 11,186 m/s ≈ 11.2 km/s (about 40,270 km/h)
Example 2
Find the Moon's escape velocity
M = 7.342 × 10²² kg, r = 1.737 × 10⁶ m
v = √(2 × 6.674 × 10⁻¹¹ × 7.342 × 10²² / 1.737 × 10⁶)
v ≈ 2,376 m/s ≈ 2.38 km/s
When to Use It
Use the escape velocity formula when:
- Planning spacecraft launches and trajectories
- Comparing the gravitational strength of different planets or moons
- Understanding why some bodies retain atmospheres and others do not
- Calculating whether an object will remain in orbit or fly away