What formula does this use?

For circular orbits, orbital period T = 2π√(r³/GM), orbital velocity v = √(GM/r), where r is the orbital radius from the center of the body, G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, and M is the mass of the central body. Altitude above surface = r − R, where R is the body's equatorial radius.

What is geostationary orbit altitude?

For Earth, geostationary orbit (GEO) requires a period equal to Earth's sidereal rotation period (23h 56m 4s ≈ 86,164 s). Using T = 2π√(r³/GM) gives r ≈ 42,164 km, so altitude ≈ 35,786 km above the equator.

Does this work for elliptical orbits?

No. This tool is for circular orbits only. For elliptical orbits, use the semi-major axis in Kepler's third law — the orbital period calculator (orbital-period-kepler) handles that case.

What is the minimum orbital altitude?

For Earth, drag limits practical orbits to altitudes above roughly 160–200 km. This tool calculates any altitude mathematically, but note that very low values are physically impractical due to atmospheric drag.

What is escape velocity and how does it relate?

Escape velocity from a given radius r is v_esc = √(2GM/r) = √2 × v_orbital. Orbital velocity is always 1/√2 (about 70.7%) of escape velocity at the same radius.

Orbital Mechanics Calculator

Name: Orbital Mechanics Calculator
Availability: InStock
Author: Nham Vu

Compute orbital period, velocity, and altitude for circular orbits using Kepler's third law and standard gravitational parameters.

Central Body

Orbit Parameter

Solve from

Altitude Orbit Radius Period Velocity

Altitude above surface

Select a body, enter one orbit parameter, and click Calculate.

Results include period, velocity, and altitude.

Summary

Compute orbital period, velocity, and altitude for circular orbits using Kepler's third law and standard gravitational parameters.

How it works

Select the central body from the presets or enter a custom mass and equatorial radius.
Enter one of the three orbit parameters: altitude above surface, orbital radius, period, or orbital velocity.
Click Calculate to derive all remaining parameters instantly.
Results show period (in seconds, minutes, hours, and days), orbital velocity (km/s and m/s), and altitude above the surface.
Use the reverse solver to work backward from a desired period or velocity to find the required altitude.

Use cases

Verify satellite orbit parameters for physics coursework or aerospace projects.
Find the orbital altitude needed for a specific revisit period.
Calculate ISS or GPS satellite orbital speed from published altitudes.
Explore how orbital velocity changes with altitude for low, medium, and high Earth orbits.
Compute geostationary orbit altitude (GEO) for any planet.
Cross-check textbook problems involving circular orbit dynamics.
Design hypothetical orbits for science fiction world-building.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu