Starlight Tools

Satellite Orbital Period Calculator — Period, Speed and Altitude

Calculate an orbital period from altitude, orbital radius, semi-major axis, or apogee and perigee—or find circular-orbit altitude from a target period. Circular inputs use an ideal circular orbit; apogee/perigee uses an ideal elliptical two-body orbit.

Calculator inputs

Calculation mode

Reference radius and gravitational parameter are shown in the worked solution.

Distance above the selected body's reference surface.

Preset altitudes are representative and approximate.

Results

Orbital period
1 hour 32 minutes 49 seconds
5,569.45 s · 92.824 min · 1.5471 hr
Orbit classification
Low Earth orbit (LEO)
Semi-major axis used
6,791.0 km
Circular speed
7.661 km/s
Orbit circumference
42,669 km
Centripetal acceleration
8.643 m/s²
Revolutions per Earth day
15.513

Calculation steps

    Period versus altitude

    The selected ISS-like Earth orbit is marked at 420 km and 92.94 minutes.

    Text data fallback for the chart. Reference points are approximate.
    MarkerAltitudePeriod

    Static orbital period examples

    Worked ISS example: using Earth radius 6,371.0084 km, altitude 420 km, and μ = 398,600.435507 km³/s² gives orbital radius 6,791.0084 km, period 5,569.45 seconds (92.824 minutes), circular speed 7.661 km/s, and 15.513 revolutions per day. The ISS altitude changes, so this is an approximate ideal result.
    Representative ideal circular-orbit values, rounded for comparison.
    OrbitAltitudeOrbital radiusPeriodSpeedRevs/day
    Earth LEO (ISS-like)420 km6,791 km92.824 min7.661 km/s15.513
    Earth MEO (GPS-like)20,200 km26,571 km11.97 hr3.873 km/s2.004
    Earth GEO altitude35,786 km42,157 km23.93 hr3.075 km/s1.003
    Low lunar orbit100 km1,837 km117.791 min1.634 km/s12.225
    Low Mars orbit400 km3,790 km118.042 min3.362 km/s12.199

    How to calculate orbital period

    For a satellite whose mass is negligible compared with the central body, Kepler’s third-law form is T = 2π√(a³/μ). Here T is period in seconds, a is semi-major axis in kilometres, and μ = GM is the body’s gravitational parameter in km³/s². For circular orbits, a is the constant orbital radius and speed is v = √(μ/a).

    Altitude versus orbital radius

    Altitude starts at a reference surface; orbital radius starts at the body’s center. For a circular orbit, a = r = R + h. Mixing them up can change the answer dramatically—especially near a small body.

    Circular versus elliptical orbits

    A circle has the same radius everywhere. For an ellipse, this calculator takes periapsis and apoapsis altitudes, converts them to radii, and uses a = (rp + ra)/2. Period depends on a, but speed varies around the ellipse; the result therefore shows periapsis and apoapsis speeds rather than one circular speed.

    Worked example

    For an ISS-like 420 km circular Earth orbit, a = 6,371.0084 + 420 = 6,791.0084 km. Substitution gives T = 2π√(6,791.0084³ / 398,600.435507) = 5,569.45 s = 92.824 min.

    Common orbit periods

    Low Earth satellites commonly complete an orbit in roughly 90–130 minutes; GPS-like medium Earth orbits are close to 12 hours. A geosynchronous orbit matches Earth’s sidereal day, about 23 h 56 min 4 s. A geostationary orbit is specifically circular, equatorial, and prograde; an inclined or elliptical geosynchronous orbit returns on the same daily rhythm but does not remain fixed above one point.

    Model limitations

    This is an ideal two-body, spherical-body model. It excludes atmosphere and drag, oblateness and uneven gravity, third-body perturbations, radiation pressure, relativity, maneuvers, and surface clearance beyond the reference radius. It is suitable for learning and first-order estimates, not mission design or operational navigation.

    Frequently asked questions

    How is orbital period calculated?

    For an ideal two-body orbit, orbital period is T = 2π√(a³/μ), where a is the semi-major axis and μ is the central body's standard gravitational parameter.

    Why do higher orbits take longer?

    Period increases with semi-major axis to the three-halves power. A satellite farther from the body travels more slowly and follows a larger path, so one revolution takes longer.

    Does satellite mass affect orbital period?

    Not in this calculator's small-satellite approximation. Satellite mass cancels from the two-body equation when it is negligible compared with the central body's mass.

    What is the difference between altitude and orbital radius?

    Altitude is measured above the body's reference surface. Orbital radius is measured from the body's center, so for a circular orbit radius equals reference radius plus altitude.

    How are circular and elliptical orbits calculated?

    A circular orbit uses one constant radius, which is also its semi-major axis. For an elliptical orbit, the calculator converts perigee and apogee altitudes to radii and uses their average as the semi-major axis.

    What is the ISS orbital period?

    At an approximate altitude of 420 km, this ideal model gives about 92.9 minutes. The real ISS generally takes about 90 to 93 minutes because its altitude and orbit change.

    What is the geostationary orbital period?

    A geostationary orbit has Earth's sidereal-day period: about 23 hours 56 minutes 4 seconds. It is a circular, equatorial, prograde geosynchronous orbit; other geosynchronous orbits do not remain fixed over one point.

    How do I convert orbital period to altitude?

    Select Orbital period to altitude, enter the period and unit, and choose the central body. The calculator solves a = ∛(μ(T/2π)²) and subtracts the body's reference radius.

    Why do real satellite periods vary?

    Real periods vary because of atmospheric drag, body oblateness, uneven gravity, third-body gravity, radiation pressure, maneuvers, and the difference between osculating and mean orbital elements.

    Methodology and sources

    Reference values

    Calculations use mean radii of 6,371.0084 km (Earth), 1,737.4 km (Moon), 3,389.50 km (Mars), 69,911 km (Jupiter), and 695,700 km (Sun). Gravitational parameters use JPL values: Earth 398,600.435507; Moon 4,902.800118; Mars system 42,828.375816; Jupiter system 126,712,764.1; and Sun 132,712,440,041.279 km³/s².

    Sources and rounding

    Full-precision constants are retained internally. Displayed values are normally rounded to 3–6 significant decimal places based on magnitude; presets and static examples are explicitly approximate.

    Author: Starlight RoboticsTechnical review: Starlight RoboticsPublished: 22 November 2025Reviewed and updated: 16 July 2026

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