The Global Solution of the Problem of the Critical Inclination

Details The Global Solution of the Problem of the Critical Inclination The Global Solution of the Problem of the Critical Inclination

Aug 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...8...25g&link_type=abstract

Celestial Mechanics, Volume 8, Issue 1, pp.25-44

Computer Science

17

Scientific paper

The publication of the solution of the Ideal Resonance Problem (Garfinkelet al., 1971) has opened the way for a complete first-orderglobal theory of the motion of an artificial satellite, valid for all inclinations. Previous attempts at such a theory have been only partially successful. With the potential function restricted to V = - 1/r + J_2 P_2 (sin θ )/r^3 + J_4 P_4 (sin θ )/r^5 , the paper constructs aglobal solution of the first order in √J 2 for the Delaunay variablesG, g, h, l and for the coordinatesr, θ, and ϕ. As a check, it is shown that this solution includes asymptotically theclassical limit with the critical divisor 5 cos2 i-1. The solution is subject to thenormality condition eG^2 /(1 + {45}/4e^2 ) ≥slant Oleft[ {left| {1/5(J_2 + J_4 /J_2 )} right|^{1/4} } right], which bounds the eccentricitye away from zero in deep resonance. A historical section orients this work with respect to the contributions of Hori (1960), Izsak (1962), and Jupp (1968).

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