Bahnbewegung

Bahnbewegung is the motion of a body along a trajectory around another body under the influence of a central force. In German scientific usage the term covers orbital motion in both celestial mechanics and, in a broader sense, in atomic and molecular systems. The concept is central to understanding how planets, moons, satellites, and electrons move under gravity or electrostatic attraction.

In classical mechanics, orbital motion arises from Newton's laws with a central potential. The two-body problem yields trajectories that are conic sections: circle, ellipse, parabola or hyperbola. The shape is determined by the total energy and the specific angular momentum. In polar coordinates with the central body at the focus, the orbit can be written as r(θ) = p/(1 + e cos θ), where e is eccentricity and p the semi-latus rectum. Gravitational parameter μ = GM governs the dynamics.

In astronomy, Bahnbewegung explains planetary orbits, satellite trajectories, and trajectories of comets. Kepler's laws describe the properties of these orbits, while Newton's law explains their mechanistic origin and yields relations between period and semi-major axis.

In quantum theory, electrons do not follow fixed classical orbits, but in semi-classical or approximations the notion of motion in a central Coulomb field can describe average paths or angular motion. The term Bahnbewegung may be used in didactic contexts to illustrate central-force motion.

History and usage: The concept originates from the work of Kepler and Newton and is a standard term in German astronomy and physics. It remains a fundamental idea in teaching and research on dynamics of bodies under central forces.