Kostenloser Orbital Period Rechner
Berechnen Sie den orbital period of a planet, moon, or satellite aus its semi-major axis und central body mass.
Umlaufzeit
31,554,223.24 s
Orbital Period vs Semi-Major Axis
Formel
## 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.
Lösungsbeispiel
Find the orbital period of Earth around the Sun (a = 1.496e11 m, M = 1.989e30 kg).
- 01T = 2π √(a³ / (G M))
- 02a³ = (1.496e11)³ = 3.348e33 m³
- 03G M = 6.674e-11 × 1.989e30 = 1.327e20
- 04a³ / (G M) = 2.524e13
- 05T = 2π × √(2.524e13) ≈ 3.156e7 s ≈ 365.25 days
Häufig Gestellte Fragen
Does the orbiting body's mass affect the period?
For most situations the orbiting body is far less massive than the central body, so its contribution is negligible. For a binary of comparable masses, replace M with (M1 + M2).
What shape of orbit does this assume?
The formula applies to any Keplerian elliptical orbit. The semi-major axis alone determines the period regardless of eccentricity.
How accurate is this for real solar-system bodies?
Accurate to better than 0.01% for planets, with tiny deviations from perturbations and relativistic effects.