Book Description

The motion of the satellite and the gravitational field of an oblate planet is considered under the assumptions that the inclination of the orbit may be arbitrary, that the planet has the form of a smooth ellipsoid of revolution, and that the polar compression is small enough so that the expansion of the perturbation function can be restricted to the first degree term. The perturbation function is expanded into a power series in terms of the eccentricity; the coefficients of this series are expressed quite simply in terms of trigonometric functions of the angle of inclination. The integration of the ordinary Lagrange equations yield analytic expressions of the first order perturbations of the orbital elements in terms of the compression of the planet. The precision is up to the fourth power of the eccentricity. (Author).