A numerical solution of the Kepler problem
Abstract
An efficient numerical method is presented for the solution of the Kepler problem of the motion of a body in a closed orbit in a central gravitational field. The method employs the NewtonRaphson interpolation algorithm to obtain successive approximations of the orbital angle starting from the classical initial approximation for cases of orbital eccentricity less than one half the square root of 2, and from a closer, more complex approximation for large eccentricities. A result accurate to six decimal places can thus be obtained in not more than four iterations, even in the case of eccentricities close to unity.
 Publication:

Acta Astronautica
 Pub Date:
 February 1981
 Bibcode:
 1981AcAau...8..225M
 Keywords:

 Celestial Mechanics;
 Equations Of Motion;
 Kepler Laws;
 NewtonRaphson Method;
 Eccentricity;
 Gravitational Fields;
 Interpolation;
 Iterative Solution;
 Astronomy