Orbital Velocity Formula
Calculate the speed needed to maintain a stable circular orbit around a planet, star, or other massive body.
The Formula
v = √(GM / r)
Orbital velocity is the speed needed for an object to stay in a stable circular orbit. Going slower causes the object to fall inward. Going faster moves it to a higher orbit.
Variables
| Symbol | Meaning |
|---|---|
| v | Orbital velocity (m/s) |
| G | Gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²) |
| M | Mass of the central body (kg) |
| r | Orbital radius — distance from center of the central body (meters) |
Example 1
Find the orbital velocity of the ISS (altitude 408 km above Earth)
M = 5.972 × 10²⁴ kg
r = 6,371 km + 408 km = 6,779 km = 6.779 × 10⁶ m
v = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 6.779 × 10⁶)
v ≈ 7,661 m/s ≈ 27,580 km/h
Example 2
Find the orbital velocity for a geostationary orbit (35,786 km altitude)
r = 6,371 + 35,786 = 42,157 km = 4.216 × 10⁷ m
v = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 4.216 × 10⁷)
v ≈ 3,075 m/s ≈ 11,070 km/h
When to Use It
Use the orbital velocity formula when:
- Designing satellite orbits at specific altitudes
- Understanding why higher orbits have slower speeds
- Calculating launch requirements for space missions
- Comparing orbital speeds around different planets