Orbital Period Calculator
Enter the semi-major axis and the standard gravitational parameter to compute the orbital period via Kepler's third law T = 2π√(a³/μ).
Input Data
Results
At a glance:Kepler's third law (in Newtonian form) states that the square of the orbital period is proportional to the cube of the semi-major axis: T² = 4π²a³/μ, where a is the semi-major axis of the ellipse and μ = G·M is the standard gravitational parameter of the primary (Earth μ ≈ 3.986×10¹⁴ m³/s², Sun μ ≈ 1.327×10²⁰). Thus T = 2π√(a³/μ). For circular orbits a = r. The law applies to any two-body system; comparing two bodies around the same primary gives (T₁/T₂)² = (a₁/a₂)³. This tool computes T in seconds, minutes, hours and days from a and μ.
Formula
Kepler's third law: T = 2π·√(a³/μ)
μ = G·M
$$T = 2\pi \sqrt{\frac{a^3}{\mu}}$$How to Use
- Enter the semi-major axis a (m).
- Enter the standard gravitational parameter μ (m³/s²).
- The calculator returns T in s, min, h and days.
Case Studies
Earth satellite
a = 7.0e6 m, μ = 3.986e14.
T = 2π√(3.43e20/3.986e14) ≈ 5820 s ≈ 97 min.
Typical low-Earth-orbit period.
FAQ
What is the standard gravitational parameter?
μ = G·M, the product of the gravitational constant and the central mass. It is known more precisely than G or M alone and is tabulated for planets (Earth ≈ 3.986e14 m³/s²).
Does this work for elliptical orbits?
Yes — use the semi-major axis a (not the radius); for a circle a = r. The period depends only on a and μ, not on eccentricity.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.