Orbital Velocity Calculator
Calculate orbital velocity in km/s for a satellite above Earth, Mars, or the Moon.
Returns orbital period and comparison to the ISS at 408 km altitude.
Orbital Velocity is the speed an object must travel to maintain a stable circular orbit around a celestial body. At this speed, the centripetal acceleration from gravity exactly matches the centrifugal effect of the curved path.
Formula:
v = √(G × M / r)
Where:
- 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 = body radius + altitude (m)
Orbital Period:
T = 2π × r / v
This gives the time for one complete orbit.
Key Celestial Bodies:
| Body | Mass (kg) | Radius (km) | Surface Gravity |
|---|---|---|---|
| Earth | 5.972 × 10²⁴ | 6,371 | 9.81 m/s² |
| Moon | 7.342 × 10²² | 1,737 | 1.62 m/s² |
| Mars | 6.417 × 10²³ | 3,390 | 3.72 m/s² |
| Jupiter | 1.898 × 10²⁷ | 69,911 | 24.79 m/s² |
| Sun | 1.989 × 10³⁰ | 696,340 | 274 m/s² |
Important Orbits Around Earth:
| Orbit | Altitude (km) | Velocity (km/s) | Period |
|---|---|---|---|
| Low Earth Orbit (LEO) | 200–2,000 | 7.8–6.9 | 88–127 min |
| ISS | ~408 | 7.66 | 92 min |
| GPS Satellites | ~20,200 | 3.87 | 12 hours |
| Geostationary (GEO) | ~35,786 | 3.07 | 24 hours |
Escape Velocity:
To leave orbit entirely (not just orbit), an object needs escape velocity:
v_escape = √(2) × v_orbital ≈ 1.414 × v_orbital
For Earth’s surface: orbital velocity ≈ 7.9 km/s, escape velocity ≈ 11.2 km/s.
Practical Example: A satellite at 400 km altitude above Earth: r = 6,371 + 400 = 6,771 km = 6,771,000 m. v = √(6.674×10⁻¹¹ × 5.972×10²⁴ / 6,771,000) = 7,672 m/s ≈ 7.67 km/s ≈ 27,600 km/h ≈ 17,150 mph.
Tips:
- Higher altitude = slower orbital velocity but longer orbital period.
- Geostationary orbit is the altitude where the orbital period matches Earth’s rotation (24 hours).
- This formula assumes circular orbits. Elliptical orbits have varying velocities.