Orbital Velocity Calculator

Orbital velocity is the speed at which an object must travel to maintain a stable circular orbit around a central body. Too slow, and gravity pulls the object inward; too fast, and it escapes into a higher orbit or escapes entirely. The concept lies at the heart of satellite technology, space station design, planetary science, and celestial mechanics. Every satellite orbiting Earth—from the International Space Station to GPS constellations—operates at a speed governed by this single elegant formula.

The Orbital Velocity Formula

For a circular orbit, the gravitational force provides exactly the centripetal acceleration needed to keep the object on its curved path. Setting these two forces equal yields v = √(GM / r), where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²·kg⁻²), M is the mass of the central body, and r is the distance from the center of that body to the orbiting object.

Orbital velocity depends only on the mass of the central body and the orbital radius—not on the mass of the orbiting object. A single atom and a space station at the same altitude orbit at the same speed. As altitude increases, r increases and v decreases: objects in higher orbits move more slowly than those in lower orbits.

Orbital Velocity vs. Escape Velocity

Escape velocity at any given radius is exactly √2 times the circular orbital velocity at that same radius. Escape velocity is v_esc = √(2GM / r) while orbital velocity is v_orb = √(GM / r). The ratio v_esc / v_orb = √2 ≈ 1.414 holds for any central body.

A spacecraft already in circular orbit needs to increase its speed by roughly 41.4% of its current orbital speed to reach escape trajectory. For Earth’s low orbit at about 7.66 km/s (400 km altitude), this means adding roughly 3.17 km/s to escape Earth’s gravity entirely, ignoring atmospheric drag.

Orbital Period and Kepler’s Third Law

The orbital period T—the time for one complete revolution—follows directly from the velocity and the circumference of the orbit: T = 2πr / v = 2π√(r³ / GM). This is a form of Kepler’s Third Law, which states that T² is proportional to r³ for all orbits around the same central body.

For Earth, a satellite in low Earth orbit (roughly 400 km altitude) completes one orbit in about 92 minutes. The Moon, orbiting at an average distance of 384,400 km, takes about 27.3 days. GPS satellites operate at about 20,200 km altitude with a period of approximately 12 hours.

Altitude and Orbital Radius

Since v = √(GM / r) and r = R_body + h (where h is altitude above the surface), increasing altitude decreases orbital velocity. The relationship is not linear: doubling the orbital radius reduces velocity by a factor of √2, not by half.

At geostationary orbit—35,786 km above Earth’s equator—the orbital period equals Earth’s rotation period of 24 hours, so the satellite appears stationary above a fixed point. The orbital velocity at GEO is about 3.07 km/s, compared with about 7.66 km/s at 400 km altitude.

Orbital Velocity Across the Solar System

The formula applies to any central body, scaling with mass. Surface orbital velocity—the speed needed to orbit just above the surface, ignoring atmosphere—varies widely. Earth’s surface orbital velocity is about 7.91 km/s; the Moon’s is only about 1.68 km/s. Mars, with roughly 11% of Earth’s mass but about 53% of Earth’s radius, has a surface orbital velocity of roughly 3.55 km/s.

Jupiter’s enormous mass gives it a surface orbital velocity of about 42.1 km/s. The Sun’s surface orbital velocity exceeds 437 km/s. Mercury’s orbital velocity around the Sun averages about 47.4 km/s—the fastest of any planet, consistent with its small orbital radius.

Real-World Considerations

Real satellite orbits are rarely perfectly circular. Elliptical orbits follow the vis-viva equation: v² = GM(2/r − 1/a), where a is the semi-major axis. For a circular orbit, r = a and the equation reduces to v = √(GM / r).

Station-keeping against atmospheric drag, lunar gravity, solar radiation pressure, and Earth’s non-uniform gravity field requires periodic small burns. The ISS loses altitude due to atmospheric drag and must reboost several times per year. All calculations in this tool assume a circular, two-body orbit in a vacuum and are intended as reference estimates.