Bahnperioden

Bahnperioden, often referred to in English as orbital periods, denote the time required for a celestial body to complete one full orbit around another body under the influence of gravity. In classical mechanics, the period depends on the size of the orbit and the masses involved, and is independent of the position along the orbit for a given two-body configuration.

The standard relation linking period to orbital size is P^2 = 4π^2 a^3 / μ, where P is the orbital period, a is the orbit’s semi-major axis, and μ = G(M+m) is the system’s standard gravitational parameter (G is the gravitational constant, M and m are the masses of the two bodies). In systems where one mass dominates (for example, a planet around the Sun or a satellite around a planet), μ is well approximated by GM, with M the central mass.

In the solar system, Kepler’s third law provides a convenient form: for objects orbiting the Sun, P^2 ≈ a^3 when P is measured in years and a in astronomical units. This yields familiar values, such as Earth with P ≈ 1 year at a ≈ 1 AU. The Moon around Earth has a sidereal period of about 27.3 days, while artificial satellites in low Earth orbit have periods around 90 minutes, and geostationary satellites have a 24-hour period.

Bahnperioden are fundamental in determining system masses and distances. Variations over time may arise from gravitational perturbations by other bodies or relativistic effects, which can slightly modify the period or introduce additional orbital phenomena such as precession of the orbit.