Does the orbiting body's mass affect the period?

For most situations the orbiting body is far less massive than the central body, so its contribution is negligible. For a binary of comparable masses, replace M with (M1 + M2).

What shape of orbit does this assume?

The formula applies to any Keplerian elliptical orbit. The semi-major axis alone determines the period regardless of eccentricity.

How accurate is this for real solar-system bodies?

Accurate to better than 0.01% for planets, with tiny deviations from perturbations and relativistic effects.

Free Orbital Period Calculator

Calculate the orbital period of a body circling a central mass using Kepler's relation T = 2pi * sqrt(a^3 / (G * M)).

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Semi-Major Axis

Central Body Mass

Orbital Period

31,554,223.24 s

Period in Days365.2109 days

Period in Years0.999893 yr

Orbital Period vs Semi-Major Axis

View formula & how it works →

How the Orbital Period Is Calculated

The orbital period is the time a body takes to complete one full orbit around a central mass.

Kepler's Third Law (Generalized)

T = 2π √(a³ / (G M))

*a* is the semi-major axis of the orbit (metres)

*G* is the gravitational constant, 6.674 × 10⁻¹¹ N m² kg⁻²

*M* is the mass of the central body (kg)

This assumes the orbiting body's mass is negligible compared to the central body.

Example Calculation

Find the orbital period of Earth around the Sun (a = 1.496e11 m, M = 1.989e30 kg).

01T = 2π √(a³ / (G M))
02a³ = (1.496e11)³ = 3.348e33 m³
03G M = 6.674e-11 × 1.989e30 = 1.327e20
04a³ / (G M) = 2.524e13
05T = 2π × √(2.524e13) ≈ 3.156e7 s ≈ 365.25 days

Free Orbital Period Calculator

How the Orbital Period Is Calculated

Kepler's Third Law (Generalized)

Example Calculation

Frequently Asked Questions

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