A Theory of Satellite Motion about an Oblate Planet. I. A Second-Order Solution of Vinti's Dynamical Problem

Details A Theory of Satellite Motion about an Oblate Planet. I. A Second-Order Solution of Vinti's Dynamical Problem A Theory of Satellite Motion about an Oblate Planet. I. A Second-Order Solution of Vinti's Dynamical Problem

Nov 1960

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1960saosr..52.....i&link_type=abstract

SAO Special Report #52 (1960)

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The accurate description of the motion of artificial satellites has presented a new problem in celestial mechanics. It is true that satellites of some other planets- for instance, the five inner satellites of Jupiter and the five inner satellites of Saturn-have quite significant perturbations caused by the oblateness of the parent planet, but the obtainable planetocentric accuracy of the observations did not demand a highly sophisticated theory. In the case of artificial satellites of the earth, however, the accuracy of the topocentric observations made by the Baker-Nunn cameras amounts to a few seconds of arc, while the time record is accurate to a few thousandths of a second. It would be very difficult to construct an analytical theory that would represent the motion with such an accuracy, either for the computation of exact ephemerides or, what is even more important, for the best possible use of the observations. The oblateness perturbations are only a part of the factors that influence the satellite motion. For instance, low-orbiting satellites suffer large perturbations of an "irregular" character caused by atmosphere drag, and high-orbiting satellites are affected by lunisolar perturbations. Solar-radiation pressure is another factor complicating the situation, expecially in the case of satellites with small mass ratio. The present paper deals with the motion in the gravitational field of the earth only, and takes in to account the second, third, fourth, and fifth zonal harmonics in the earth's potential. An approach is used that is based on approximation to the actual gravitational field of the earth, originated by Vinti.

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