How this calculator works
In Newton's two-body form of Kepler's third law, both masses contribute to the relative motion. The semi-major axis is the separation orbit's semi-major axis, not one body's smaller path around the barycentre. A secondary mass of zero gives the test-particle approximation. The default gravitational constant is the CODATA value; a custom value is provided for checking symbolic or scaled examples.
Formula
T² = 4 pi² a³/[G(M+m)]; a = cbrt[G(M+m)T²/(4 pi²)]. M+m = 4 pi² a³/(GT²).
Worked example
In a scaled system with G = 1, masses 0.75 and 0.25 and semi-major axis 1, the period is 2 pi. Increasing the axis to 4 increases period by a factor of eight to 16 pi.
Frequently asked questions
Can the orbit be elliptical?
Yes. The period law uses semi-major axis and does not depend on eccentricity for a bound two-body ellipse.
Why include the planet mass?
It matters for comparable-mass binaries and is usually negligible for a small planet around a star.
Why can an inferred mass be impossible?
If the measured total dynamical mass is smaller than the other supplied mass, the missing mass would be negative and is rejected.