dreikörperische

The term "dreikörperische" refers to phenomena or problems involving three bodies in a gravitational system, commonly known in English as the three-body problem. It describes the motion of three masses interacting through mutual gravitation according to Newton's laws, or their relativistic extensions in general relativity. The three-body problem is noted for its lack of a general analytic solution, making it one of the classic examples of a chaotic dynamical system.

Historically the problem was first tackled by Isaac Newton, who provided the foundational equations for two-body motion but could not resolve the general three-body case. In the 19th century Henri Poincaré proved the system's sensitivity to initial conditions, establishing modern chaos theory. Since then, numerous special cases have been solved analytically, such as Lagrange's triangular solutions and the Euler collinear solutions, which occur when the three masses remain at the vertices of a triangle or line while rotating uniformly.

Numerical methods, including symplectic integrators and variational techniques, dominate contemporary study. The three-body problem has practical applications in celestial mechanics, such as predicting satellite trajectories around Earth-Moon or Earth-Sun systems, guiding space missions that exploit Lagrange points for station-keeping, and modeling dynamics in triple star systems. It also informs n-body simulations in galactic dynamics and cosmology, particularly in understanding hierarchical clustering and interaction histories.

The field continues to evolve with advances in computational power and analytic approximation methods. Current research focuses on stability criteria, resonant interactions, and extensions to include relativistic corrections and non-gravitational forces.