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