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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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