What Is an Orbital Velocity Calculator?

An orbital velocity calculator computes the speed required for an object to maintain a stable circular orbit around a celestial body at a given altitude. Pre-filled with Earth at 400 km altitude (the ISS orbit), the orbital velocity is approximately 7.67 km/s (27,600 km/h or Mach 22). This calculator supports 7 celestial bodies from the Moon to the Sun.

The Orbital Velocity Formula

v = √(GM/r) where G = 6.674 × 10⁻¹¹ N⋅m²/kg² (gravitational constant), M = mass of central body (kg), r = orbital radius = body radius + altitude (m). For Earth at 400 km: v = √(6.674e-11 × 5.972e24 / 6.771e6) = 7,672 m/s. The formula derives from equating gravitational force (GMm/r²) with centripetal force (mv²/r).

Orbital Mechanics Fundamentals

Kepler and Newton established that orbital velocity decreases with altitude: v ∝ 1/√r. Low orbits are fast but experience atmospheric drag. High orbits are slower but more stable. The sweet spot for many applications is medium Earth orbit (MEO, 2,000-35,786 km) — used by GPS satellites (20,200 km altitude, ~3.87 km/s).

Types of Earth Orbits

Low Earth Orbit (LEO, 200-2,000 km): ISS, Hubble, Starlink. Period 88-127 min. Medium Earth Orbit (MEO, 2,000-35,786 km): GPS, Galileo. Geostationary (GEO, 35,786 km): Communications, weather. Period exactly 24h. High Earth Orbit (HEO): Highly elliptical orbits for specialized missions. Each orbit type has distinct velocity, period, and application characteristics.

Escape Velocity vs Orbital Velocity

Escape velocity is exactly √2 times orbital velocity at the same altitude: v_escape = √2 × v_orbital. At Earth's surface: orbital velocity ≈ 7.9 km/s, escape velocity ≈ 11.2 km/s. To leave Earth entirely requires 41% more velocity than to orbit. This relationship holds for any celestial body.

Practical Applications

Satellite deployment: rockets must accelerate payloads to orbital velocity. Space debris tracking: knowing orbital velocities helps predict collision risks. Spacecraft rendezvous: matching orbits requires precise velocity adjustments (delta-v). Planetary missions: calculating transfer orbits between planets requires knowing orbital velocities at departure and arrival.