Calculateur de Période Orbitale — Formule

How the Orbital Period Is Calculated

The orbital period is the time a body takes to complete one full orbit around a central mass.

Kepler's Third Law (Generalized)

T = 2π √(a³ / (G M))

  • *a* is the semi-major axis of the orbit (metres)
  • *G* is the gravitational constant, 6.674 × 10⁻¹¹ N m² kg⁻²
  • *M* is the mass of the central body (kg)

    • This assumes the orbiting body's mass is negligible compared to the central body.

    Exemple Résolu

    Find the orbital period of Earth around the Sun (a = 1.496e11 m, M = 1.989e30 kg).

    1. T = 2π √(a³ / (G M))
    2. a³ = (1.496e11)³ = 3.348e33 m³
    3. G M = 6.674e-11 × 1.989e30 = 1.327e20
    4. a³ / (G M) = 2.524e13
    5. T = 2π × √(2.524e13) ≈ 3.156e7 s ≈ 365.25 days