Exoplanet calculator

Exoplanet catalogs quote an orbital period in days or a semi-major axis in astronomical units, but rarely both at once, and both still need the host star's mass before Kepler's third law closes. This calculator takes a positive stellar mass in solar masses plus exactly one orbital parameter — period in days or semi-major axis in AU — and returns the missing quantity under the standard two-body approximation that the planet is much lighter than the star. The identity is P squared equals a cubed over M when period is expressed in years, axis in AU, and mass in solar masses; days are converted with a Julian year of 365.25 days. Zero or negative stellar mass is rejected as invalid input rather than producing a nonsense orbit.

Kepler's third law for a planet around a star

Kepler's third law relates the time an object takes to complete one closed orbit to the size of that orbit and the mass that sits at the focus. For a planet whose mass is negligible compared with its host star, the convenient astronomical form is P_yr squared equals a_AU cubed divided by M_star, where P_yr is the period in Julian years of 365.25 days, a_AU is the semi-major axis in astronomical units, and M_star is the stellar mass in solar masses.

Rearranged, the period in days is 365.25 times the square root of a cubed over M, and the axis is the cube root of M times P_yr squared. That is exactly the identity this exoplanet calculator applies: you supply the star's mass and whichever orbital number you already know, and the missing number is filled in. A one-solar-mass star with a one-AU orbit recovers a 365.25-day year, which is the textbook sanity check every implementation should pass.

A three-and-a-half-day hot Jupiter around a sun-like star sits near 0.045 AU, which is the scale of the first transiting giants. The approximation drops the planet's own mass; for a Jupiter around a sun that correction is about one part in a thousand, far smaller than typical stellar-mass uncertainty from spectroscopy. Binary stars, circumbinary planets, and comparable-mass pairs belong to a two-mass Kepler solve, not this landing.

Where an exoplanet period–axis calculator earns its keep

Transit surveys such as Kepler, K2, TESS, and PLATO report orbital period in days almost immediately, while the physical separation in AU is what observers need for insolation, equilibrium temperature, and habitable-zone membership. Combining that period with a spectroscopic or isochrone stellar mass is the first Kepler step before a more expensive light-curve model. Radial-velocity teams often start from a period and a stellar mass to quote a minimum a before the eccentricity is fully constrained.

Classroom astrophysics courses assign the same identity with catalog rows — recover Earth's year from one AU and one solar mass, then invert a hot-Jupiter period — and they need an oracle that refuses a zero-mass star instead of returning NaN. Mission-planning notebooks that stack hypothetical planets around nearby bright stars use the same closed form to sketch inner working angles and angular separations. Failed validation does not consume balance.

Keep requests small, pin the rounded solutions in tests, and you get reproducible exoplanet orbits for homework, LMS plugins, and survey reduction without standing up an N-body integrator for a two-body massless-planet problem.