ABSTRACT
This chapter deals with the problem of the motion of a celestial body in an elliptic orbit. The orientation in space of the planet is determined by coordinates called rectangular heliocentric ecliptic coordinates or Descartes heliocentric ecliptical coordinates of the celestial body. In the case of a parabola the angle between the radius-vector of the celestial body and the parabola axis is also called the true anomaly. From the mathematical point of view, the treatment of the problem of determination of the position of a celestial body in a hyperbolic orbit is analogical with that of the elliptic orbit. Kepler’s equation had an essential role not only in celestial mechanics but in mathematics in general. Such fundamental concepts and powerful methods of mathematical calculus such as the Bessel functions, the Fourier series, the topological number of vector fields, and the “argument principle” in the theory of complex calculus appeared during the study of Kepler’s equation.
