Orbital Period Calculator
Calculate the orbital period of any object orbiting a central body using Kepler's Third Law of Planetary Motion.
Eccentricity does not affect the period — only the semi-major axis matters (Kepler's 3rd Law)
Formula
Kepler's Third Law (Newton's form):
T = 2π √( a³ / GM )
- T — Orbital period (seconds)
- a — Semi-major axis of the orbit (metres)
- G — Gravitational constant = 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²
- M — Mass of the central body (kg)
Note: The orbital period depends only on the semi-major axis and the central mass — not on eccentricity. Two orbits with the same semi-major axis but different eccentricities have identical periods (Kepler's Third Law).
Mean orbital speed (circular approximation): v = 2πa / T
Assumptions & References
- The orbiting body's mass is assumed negligible compared to the central body (m ≪ M). For comparable masses, replace M with (M + m).
- The orbit is a closed ellipse (eccentricity 0 ≤ e < 1). Parabolic (e = 1) and hyperbolic (e > 1) trajectories are unbound and have no period.
- Gravitational constant G = 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018).
- 1 AU = 1.495978707 × 10¹¹ m (IAU 2012 definition).
- 1 Julian year = 365.25 days = 31,557,600 seconds.
- 1 light-year = 9.4607304725808 × 10¹⁵ m.
- Solar mass = 1.989 × 10³⁰ kg; Earth mass = 5.972 × 10²⁴ kg.
- Relativistic effects, oblateness of the central body, and third-body perturbations are ignored.
- Reference: Newton, I. (1687). Principia Mathematica; Kepler, J. (1619). Harmonices Mundi.