Calculadora de Período Orbital

T = 2π√(r³/GM) — 3ª Lei de Kepler, período de órbita circular.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

Período T
31.554.897 s
T em dias
365,22 dias

Formula

T = 2π√(r³/GM)

About this calculator

The Orbital Period Calculator determines the time a celestial body takes to complete one circular orbit around another body. The formula used is T = 2π√(r³/GM), where T is the period, r is the orbital radius, G is the gravitational constant, and M is the mass of the central body. This tool is based on Kepler's Third Law, adapted for circular orbits.

To use the calculator, enter the orbital radius (distance between the centers of the bodies) and the mass of the central body. The result is the orbital period in seconds, which can be converted to other units like hours or days. Ensure units are consistent: r in meters, M in kilograms, and G = 6.67430×10⁻¹¹ m³/kg·s².

This calculator is useful for astronomy students, space engineers, and enthusiasts who want to estimate periods of satellites, planets, or binary stars. For example, you can calculate the orbital period of the Moon around Earth or a geostationary satellite. Note that the formula assumes a circular orbit and that the central body's mass is much larger than the orbiting body's mass.

Caution: the formula does not apply to elliptical orbits, where the period depends on the semi-major axis. Also, ignore relativistic effects or perturbations from other bodies. Always ensure the orbital radius is measured from the center of the central body, not from its surface.

Frequently asked questions

What is orbital period?

It is the time a body takes to complete one orbit around another body, such as Earth around the Sun.

Does this calculator work for elliptical orbits?

No, it is accurate only for circular orbits. For elliptical ones, use the semi-major axis instead of r.

What units should I use for radius and mass?

Use meters for radius and kilograms for mass. The result will be in seconds.

Can I calculate the period of an artificial satellite?

Yes, as long as the orbit is roughly circular and the planet's mass is much larger than the satellite's.

What is the value of the gravitational constant G?

G = 6.67430×10⁻¹¹ m³/kg·s². The calculator already uses this value.

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