Orbital Velocity Calculator — Speed for Circular Orbit
Calculate orbital velocity and period for satellites and planets. Covers v = √(GM/r), Kepler's third law, ISS orbit, geostationary orbit, and Moon calculations.
Satellites don't fall because they're going sideways fast enough that Earth curves away beneath them at the same rate they fall. Orbital velocity is exactly that critical horizontal speed — fast enough to keep missing the ground as you fall. It's not magic; it's geometry and gravity working together at just the right speed.
The CalcHub orbital velocity calculator computes circular orbital velocity and period for any orbit around any body.
The Formulas
Orbital velocity (circular orbit): v = √(GM/r) Orbital period: T = 2πr / v = 2π√(r³/GM)- v = orbital velocity (m/s)
- G = 6.674 × 10⁻¹¹ N·m²/kg²
- M = mass of central body (kg)
- r = orbital radius (distance from center, not surface)
- T = orbital period (seconds)
Kepler's Third Law
T² ∝ r³ — orbital period squared is proportional to semi-major axis cubed. Outer planets orbit slower AND take longer. Saturn takes 29 Earth years to orbit the Sun; Mercury takes only 88 days.
Key Earth Orbits
| Orbit | Altitude | Velocity | Period |
|---|---|---|---|
| Low Earth (LEO) | 400 km | 7.67 km/s | 92 min |
| ISS | 408 km | 7.66 km/s | 92.68 min |
| GPS satellites | 20,200 km | 3.87 km/s | 12 hours |
| Geostationary (GEO) | 35,786 km | 3.07 km/s | 24 hours |
| Moon | 384,400 km | 1.02 km/s | 27.3 days |
Worked Example
Find orbital velocity for a satellite at 400 km altitude above Earth.
Orbital radius = 6,371 km + 400 km = 6,771 km = 6.771 × 10⁶ m
Earth's mass M = 5.972 × 10²⁴ kg
v = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 6.771 × 10⁶)
= √(5.888 × 10⁷)
≈ 7673 m/s ≈ 7.67 km/s
The ISS orbits at almost exactly this speed, completing about 15.5 orbits per day.
Why do lower orbits have higher velocity?
Gravity is stronger closer to Earth (1/r²). Faster speed is needed to balance the stronger gravitational pull. Lower orbit = stronger gravity = more centripetal force needed = higher velocity. This is the inverse of most speed intuitions.
What is a geostationary orbit?
At exactly 35,786 km altitude, the orbital period equals 24 hours. The satellite appears stationary relative to Earth's surface — useful for communications and weather satellites. All geostationary satellites share the same altitude, in the equatorial plane.
Can I calculate orbital mechanics for the Moon?
Yes. Use Earth's mass (5.972 × 10²⁴ kg) and the Moon's orbital radius (~384,400 km). The calculator will give you about 1.022 km/s orbital velocity and a period of 27.32 days — matching observations closely.