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    Orbital mechanics

    Orbital Velocity Calculator

    Speed needed to hold a circular orbit at any altitude around the Sun, a planet or the Moon.

    v = √(μ / r)

    Inputs

    Results

    Orbital velocity
    7.6726 km/s
    Orbital radius
    6,771 km
    Orbital period
    92.4143 minutes
    1 h 32 min
    Worked solution
    1. μ (Earth) = 3.986 × 10^14 m³/s²
    2. r = 6,371 km + 400 km = 6,771,000 m
    3. v = √(μ / r) = √(3.986 × 10^14 / 6,771,000) = 7,672.6 m/s

    How the result changes

    Velocity (km/s) plotted against Altitude (km), from one quarter to four times your input, with your input marked.7.27.47.67.85001,0001,500Altitude (km)Velocity (km/s)your input
    Velocity vs altitude

    How it works

    A satellite in a circular orbit is in continuous free fall: gravity supplies exactly the centripetal acceleration v²/r needed to bend its straight-line motion into a circle. Setting GMm/r² = mv²/r gives v = √(GM/r).

    Because r is measured from the centre of the body, higher orbits are slower. The ISS travels at about 7.66 km/s, while a geostationary satellite moves at only about 3.07 km/s.

    Variables

    • v — circular orbital speed
    • μ — standard gravitational parameter GM of the central body
    • r — orbital radius = body radius + altitude

    Assumptions and limits

    • Circular orbit around a spherical, non-rotating body
    • Orbiting mass is negligible compared with the central body
    • No atmospheric drag or third-body perturbations

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.