Orbit altitude from period calculator

Given a planet's mass and radius and the orbital period you want, this calculator solves for the circular altitude above the surface that produces that period under Newtonian two-body gravity. From Kepler's third law the orbital radius is the cube root of G times M times T squared over four pi squared, and altitude is that radius minus the planet radius. Send mass in kilograms, desired period in seconds, and planet radius in metres; receive orbital radius and altitude in metres and kilometres, gravitational parameter mu, mean motion, circular orbital speed, and intermediate a cubed for audit. A zero period is rejected with invalid input so a singular formula never returns Infinity or NaN. Non-positive mass and radius are also rejected as non-physical under Newtonian gravity.

How orbital altitude follows from a desired period

Start from Newtonian two-body gravity with a central mass M that dominates the satellite mass. For a circular orbit the mean motion n equals the square root of G M over a cubed, and the orbital period is T equals two pi over n. Solving for the orbital radius a yields a cubed equals G M T squared over four pi squared, or equivalently a equals the cube root of G M T squared over four pi squared.

Altitude above the surface is then h equals a minus R, where R is the equatorial or mean planetary radius you choose for the problem. Period T must be a finite non-zero positive number of seconds; zero fails with invalid input because the formula becomes singular and would not define a finite orbit. Mass M and radius R must likewise be finite and strictly positive.

Classic classroom checks include Earth mass, a ninety-minute period of five thousand four hundred seconds, and Earth equatorial radius, recovering a low Earth orbit altitude on the order of a few hundred kilometres. This page intentionally uses the circular two-body approximation only; eccentric orbits, drag, J2 drift, and n-body ephemerides are separate search intents and separate landings. Geostationary altitude when T is locked to the sidereal day is also a different product page for people who specifically search for GEO.

What you send and what you get back

Send three required finite numbers under the fields mass, period, and radius. Mass is the planet mass M in kilograms and must be strictly greater than zero; for Earth use about five point nine seven two two times ten to the twenty-four kilograms. Period is the desired circular orbital period T in seconds and must be non-zero and positive; for a ninety-minute low Earth orbit use five thousand four hundred seconds, for a two-hour orbit use seven thousand two hundred seconds, and convert hours or minutes to seconds before calling.

Radius is the planet radius R in metres and must be strictly greater than zero; for Earth equatorial radius use about six point three seven eight one three seven times ten to the six metres. Keep units consistent: convert kilometres, Earth masses, and hours to metres, kilograms, and seconds before calling so the numeric product matches the SI interpretation your report claims.

Where orbit altitude from period calculators show up in real work

Secondary-school and introductory university physics and astronomy courses assign low Earth orbit altitude drills, period-to-height rearrangements of Kepler's third law, and multi-planet comparisons that reuse the same closed form; a single trusted oracle speeds grading and demo setup. CubeSat and amateur radio teams convert a target period or pass pattern into a first-cut altitude before full numerical propagators and link budgets. Constellation concept studies map revisit or coverage periods onto circular parking altitudes for Earth, Mars, and other bodies from tabulated masses and radii without re-deriving constants each time.

Mission concept trade studies compare circular altitudes for custom periods against geostationary and medium Earth options without overloading a GEO-only page. If you later need orbital period from semi-major axis and mass alone, geostationary altitude locked to sidereal rotation, Hohmann transfer times, or n-body ephemerides, treat those as separate search intents and landings rather than overloading this orbit altitude from period calculator page.