What assumptions does this calculator make?

Circular orbit around a spherical central body with constant standard gravitational parameter (μ). No atmospheric drag, oblateness (J2), or perturbations are included.

Which bodies are supported?

Earth, Moon, and Mars, using standard mean radii and gravitational parameters commonly used in education and preliminary mission studies.

Can I compute an altitude for a target period?

Yes. Use the inverse calculator: enter a desired orbital period and it returns the circular-orbit altitude for the selected body.

Yes. All calculations run locally in your browser; nothing is uploaded.

Satellite Orbit Period Calculator (Circular)

Satellite Orbit Period Calculator

Enter altitude to get orbital period (circular orbit). Choose Earth, Moon, or Mars. We also show orbital speed and revolutions per day — privately, in your browser.

Inputs

Central body

Altitude above mean radius (km)

Inverse: target period (minutes) (optional)

Results

Orbital period (T):

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Orbital speed (v):

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Mean motion (n):

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Revolutions per day:

–

Inverse result (if target period set):

Enter a target period to compute required circular altitude.

What this calculator assumes

We assume a circular orbit around a spherical body using the standard gravitational parameter μ and mean planetary radius R. Period is computed by T = 2π √((R + h)³ / μ), and orbital speed by v = √(μ / (R + h)). Real orbits experience oblateness (J2), drag (for low Earth orbits), perturbations, and non-uniform gravity — those effects are intentionally omitted here for simplicity and speed.

Understanding Satellite Orbital Periods

The orbital period of a satellite is the time it takes to make one complete revolution around a celestial body such as the Earth, Moon, or Mars. For circular orbits, the period depends only on the orbital radius — that is, the planet’s mean radius plus the altitude of the satellite. Higher orbits correspond to longer orbital periods. This relationship is fundamental to spaceflight and satellite mission design.

Kepler’s Third Law

The governing principle is Kepler’s Third Law of Planetary Motion, refined by Newtonian mechanics into the formula:

T = 2π √((R + h)³ / μ)

where T is the orbital period, R is the mean radius of the planet, h is the satellite’s altitude, and μ is the planet’s standard gravitational parameter (GM). The orbital speed is given by v = √(μ / (R + h)). Together, these equations let us compute the period and velocity for any circular orbit.

Low Earth Orbit (LEO)

Near Earth, satellites at altitudes of 200–1,000 km belong to low Earth orbit (LEO). At roughly 400 km (the altitude of the International Space Station), the orbital period is about 92 minutes. That means astronauts aboard the ISS see a sunrise and sunset every 45 minutes. Satellites in LEO are ideal for Earth observation, imaging, and communications that require low latency, but they also experience atmospheric drag and eventually reenter if not boosted.

Medium and Geosynchronous Orbits

Higher up, medium Earth orbits (MEO) range from 2,000 to 35,786 km. Global navigation systems like GPS, GLONASS, Galileo, and BeiDou place satellites in this region, typically with periods of 12 hours. At geosynchronous orbit (GEO), about 35,786 km altitude, the orbital period is 23h 56m — matching the Earth’s sidereal day. A satellite here appears fixed in the sky from the ground, making GEO invaluable for telecommunications and weather monitoring.

The Moon and Mars

The same physics applies to other bodies. Around the Moon, a 100 km altitude satellite has a period of about 2 hours. Lunar orbiters such as NASA’s Lunar Reconnaissance Orbiter rely on these calculations for mapping and navigation. Around Mars, a 400 km orbit corresponds to roughly 2 hours as well — close to the periods used by spacecraft like Mars Odyssey or Mars Reconnaissance Orbiter. Just as with Earth, higher altitudes produce longer periods, and a special “areostationary orbit” exists where a satellite would remain fixed over one longitude of Mars.

Orbital Speed and Revs per Day

Orbital velocity decreases as altitude increases. At 400 km above Earth, satellites travel at ~7.7 km/s. At geosynchronous altitude, the speed is only ~3.1 km/s. Our calculator also shows mean motion (radians per second) and revolutions per day. A LEO spacecraft may circle Earth more than 15 times daily, while a GEO satellite completes exactly one revolution per sidereal day.

Limitations and Real-World Effects

The calculator assumes an idealized spherical planet and circular orbit. In reality, factors like Earth’s oblateness (J2 effect), atmospheric drag, solar radiation pressure, and gravitational perturbations from the Sun and Moon alter orbits over time. Mission planners at NASA, ESA, JAXA, ISRO, CNSA, and other agencies use more complex models and numerical integration for precision. Still, Kepler’s law provides the accurate first-order estimate used in education, preliminary mission studies, and quick back-of-the-envelope checks.

Why This Matters

Orbital period calculations are central to satellite deployment, communications planning, and interplanetary mission design. By experimenting with altitudes on this calculator, you can see why low orbits move quickly across the sky, why GPS satellites have half-day periods, and why geostationary satellites sit “fixed” in place. The same math applies whether you are a student exploring physics, an amateur astronomer, or a spaceflight enthusiast simulating mission profiles.

Disclaimer: This tool is for educational purposes only. It does not account for perturbations or mission-critical constraints and should not be used for operational planning.