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Kepler's Third Law Two-Body Orbital Period — result sheet
Calculate a Newtonian two-body orbital period in seconds and days from semimajor axis and primary and secondary masses.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: T = 2 pi sqrt(a^3 / (G (M1 + M2))), using G = 6.67430e-11 m^3/(kg s^2), semimajor axis a in metres, and both body masses in kilograms.
This calculator evaluates the Newtonian two-body Kepler period for a positive semimajor axis and positive primary and secondary masses. It returns the period in seconds and days; eccentricity, perturbations, relativistic effects, body sizes, and mission planning are outside the ideal orbit model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Semimajor axis — m; Finite positive center-to-center relative-orbit semimajor axis in metres.; minimum 1.0E-6; maximum 10000000000000000
- Primary mass — kg; Finite positive mass of the primary body in kilograms.; minimum 1.0E-6; maximum 1.0E+31
- Secondary mass — kg; Finite positive mass of the secondary body in kilograms.; minimum 1.0E-6; maximum 1.0E+31
Worked example
| Input | Value |
|---|---|
| Semimajor axis | 149597870700 |
| Primary mass | 1.98847E+30 |
| Secondary mass | 5.9722E+24 |
An Earth-Sun-scale two-body input gives an ideal period of about 365.26 days, with the exact seconds value returned by the formula.
Assumptions and limits
- Semimajor axis is a finite positive relative-orbit length in metres, and both primary and secondary masses are finite positive kilograms.
- The orbit is treated as a bound Keplerian two-body problem with total mass M1 + M2 and fixed Newtonian gravitational constant G = 6.67430e-11 m^3/(kg s^2).
- The supplied semimajor axis describes the relative orbit; eccentricity does not enter the period for a fixed semimajor axis in this ideal model.
- Third-body perturbations, tides, oblateness, mass change, relativistic corrections, body radii, launch trajectories, and mission advice are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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