Satellite Orbital Period Calculator — Period, Speed and Altitude
Calculator inputs
Reference radius and gravitational parameter are shown in the worked solution.
Distance above the selected body's reference surface.
Lowest altitude above the reference surface.
Highest altitude; it must be at least the periapsis altitude.
Preset altitudes are representative and approximate.
Results
Calculation steps
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Period versus altitude
The selected ISS-like Earth orbit is marked at 420 km and 92.94 minutes.
| Marker | Altitude | Period |
|---|
Static orbital period examples
| Orbit | Altitude | Orbital radius | Period | Speed | Revs/day |
|---|---|---|---|---|---|
| Earth LEO (ISS-like) | 420 km | 6,791 km | 92.824 min | 7.661 km/s | 15.513 |
| Earth MEO (GPS-like) | 20,200 km | 26,571 km | 11.97 hr | 3.873 km/s | 2.004 |
| Earth GEO altitude | 35,786 km | 42,157 km | 23.93 hr | 3.075 km/s | 1.003 |
| Low lunar orbit | 100 km | 1,837 km | 117.791 min | 1.634 km/s | 12.225 |
| Low Mars orbit | 400 km | 3,790 km | 118.042 min | 3.362 km/s | 12.199 |
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
- JPL Astrodynamic Parameters for gravitational parameters and Earth sidereal day.
- JPL Planetary Physical Parameters for planetary mean radii.
- JPL Satellite Physical Parameters for the Moon.
- NASA Sun Fact Sheet for solar mean radius.
- NASA ISS Orbit Tutorial for the real 90–93 minute comparison.
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.