Progress in Observational Two-Body Problem : Discovery of the Exact Solution for an Unsolved Classical Problem

Abstract

Two-body problem for the gravity is very classical, which dates back to the beginning of the seventeenth century, when Kepler discovered the laws of motion of celestial objects. This problem has been solved in the Newtonian mechanics. Nevertheless, there still remains an unsolved inverse problem related with observations: When an orbital plane of two bodies is inclined with respect to the line of sight, observables are their positions projected onto a celestial sphere. How do we determine the orbital elements from observations? Recently, the "exact solution" has been found. It is reviewed with some related topics.