Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986rpspr.......84y&link_type=abstract
In its USSR Report: Space (JPRS-USP-86-001) p 84-85 (SEE N86-20178 10-88) Transl. into ENGLISH from Astronomicheskiy Zhurnal
Astronomy and Astrophysics
Astronomy
Approximation, Harmonics, Orbital Mechanics, Planetary Gravitation, Satellite Orbits, Satellite Perturbation, Accuracy, Coefficients, Mathematical Models, Problem Solving
Scientific paper
One of the most perfect models of intermediate motion of a satellite is the orbit of the generalized problem of two fixed centers which takes into account the second and third zonal harmonics in the expansion of planetary gravitational potential. However, until now the equations for the elements of such an intermediate orbit have been solved only in the first approximation and there has been no clearly defined scheme for their integration in subsequent approximations. Since for an intermediate orbit, taking the Earth's oblateness into account, the perturbing actor is 1,000 times less than for a Keplerian orbit, the solution is simpler. The coefficients of the equations for such an intermediate orbit and the perturbing function are represented in the form of expansions in powers of the Earth's oblateness and it is an unwieldy problem to write these expansions. Operations which must be performed are clarified. Expansion terms that must be taken into account in order to obtain perturbations of the elements of an intermediate orbit with accuracy are discussed. The problem is solved on the assumption that secular and short-period perturbations must be determined with an accuracy to the third power of the Earth's oblateness and long-period perturbations with an accuracy to the second power of oblateness.
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