Orbital period calculator.

Kepler's third law in practice

Kepler's third law says the square of an orbital period is proportional to the cube of the semi-major axis. In solar units it reduces to P² = a³ / M, with P in years, a in AU and M in solar masses. The tool uses the exact form P = 2π √(a³ / GM) with the Sun's GM of 1.327124 x 10²⁰ m³/s² from NASA JPL, scaled by the star mass you enter.

Worked example. Jupiter's mean distance from the Sun is 778.5 million km (5.204 AU). The tool gives 4,336 days, or 11.87 years. NASA's Jupiter fact sheet lists a sidereal orbit period of 4,332.6 days, so the gap is about 3.5 days. About 2.1 of those come from ignoring Jupiter's own mass (0.0954 percent of the Sun's mass changes the period by about 0.048 percent); the rest is rounding in the distance and pull from other planets. For Earth, 1 AU returns 365.26 days.

The law assumes the orbiting body is much lighter than the star, so it suits planets, asteroids and comets. For two stars of similar mass, add both masses.