The Critical Inclination Problem in Satellite Orbit Theory
National Aeronautics and Space Administration, 1962 - Artificial satellites - 29 pages
"Solutions of the satellite orbit problem are obtained that do not exhibit singularities at the critical inclination angle. Series representations are obtained. Their region of convergence are exhibited, and quantitative measures of their speeds of convergence are provided for use in numerical computations."--p. 1.
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approximation apsidal motion argument ASSe become bound boundary branches coefficients complete constant contain critical inclination angle CRITICAL INCLINATION PROBLEM curve dco/dv defined dependence determined dimensionless Earth eccentricity elliptic functions elliptic region equation equation 31 essentially exhibit expressed figure given gives grazing Hence inclination angle independent initial initial conditions integral intermediate orbit introduce libration region limiting long-period means Mersman modulus motion NASA TR National Aeronautics NeSe node obtained occurs origin oscillations parabolic orbits pericenter distance period phase-plane integral planet present procedure quantities radius of convergence reference regarded regions of convergence relations remaining represents respectively satellite orbit problem Saturn secular semilatus rectum separatrix Series representations shown shows solution Space Administration speeds of convergence tative measures TECHNICAL REPORT R-148 throughout tion transition region trigonometric region true anomaly values variable yield