Orbital Period

\[T=2\pi\sqrt{\frac{r^{3}}{\mu}}\]

Variables

Torbital period (s)

rorbital radius from the central body's center (m)

mu[μ]standard gravitational parameter (m³/s²)

Description

What is this formula?

The Orbital Period equation calculates the time required for a satellite or spacecraft to complete one full circular orbit around a central body.

It is derived from Newtonian gravitation and circular orbital motion and is one of the fundamental equations of astrodynamics.

When to use it

Use this equation when determining the orbital period of satellites around planets, moons around planets, or spacecraft in circular or nearly circular orbits.

It is commonly used in mission planning, satellite operations, and aerospace engineering.

Example

A satellite orbits Earth at:

Orbital radius = 7.0×10^6 m

Earth gravitational parameter = 3.986×10^14 m³/s²

Formula:

T = 2π√(r³/μ)

Substitution:

T = 2π√((7.0×10^6)³/(3.986×10^14))

T = 5828 s

Result:

Orbital period = 5828 s

Orbital period = 97.1 min

Applications

Satellite mission design

Spacecraft trajectory analysis

Orbital mechanics education

Ground station scheduling

Earth observation satellites

Space mission planning