Orbital Period Calculator
Calculate circular orbital period from central mass and orbital radius.
Orbital Period Formula
T = 2π√(r³/GM).
What Is Orbital Period?
Orbital period is the time an object takes to complete one full orbit around a central body. For an ideal circular orbit, the period depends on orbital radius and the central mass through Newtonian gravity.
Example Calculation
A low-Earth satellite at a radius of about 6.771 × 10⁶ m around Earth has an orbital period of roughly 5,545 seconds, or about 92.4 minutes.
Factors and Interpretation
Increasing orbital radius makes the period longer because the path is larger and orbital speed is lower. A more massive central body shortens the period at the same radius. Use distance from the center of the body, not altitude above its surface.
Frequently Asked Questions
Does satellite mass affect the period?
In the common approximation where the satellite is much less massive than the central body, its mass does not affect the result.
Is this valid for elliptical orbits?
Kepler’s third law also applies to ellipses when semi-major axis replaces circular radius.
Why are higher orbits slower?
Gravity is weaker farther away, so a lower circular speed is sufficient.
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Formula and Practical Limits
The common circular-orbit period formula assumes a two-body gravitational model and a circular orbit. Eccentric orbits and significant secondary mass require appropriate orbital parameters rather than a simple circular approximation.