How this calculator works
For an isolated pair of bodies, orbital period depends on relative semi-major axis and the sum of their gravitational parameters. You can enter that parameter directly or supply both masses. Density mode is a separate mathematical limit: a negligible satellite skimming the surface of a spherical body. Substituting the body's mass in terms of mean density makes its radius cancel. That limit ignores terrain and atmosphere.
Formula
T = 2 pi sqrt(a³/mu), mu = G(M+m). Surface orbit: T = sqrt(3 pi/(G rho)); rho = 3 pi/(G T²).
Worked example
For mu = 1 m3/s2 and semi-major axis 1 m, period is 6.283185 s. A period of 50.265482 s at the same mu corresponds to semi-major axis 4 m.
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Frequently asked questions
Is period measured from the rotating surface?
No. This is the orbital period relative to an inertial frame.
Can density predict an orbit at any altitude?
The density expression applies at the ideal spherical surface. Higher orbits also require a radius or mass scale.
Is a surface orbit physically possible?
It is a useful limiting calculation. Real satellites need clearance and must avoid atmospheric drag.