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An Analytical Theory with Respect to the Earth’s Zonal Harmonic Term J2 in Terms of Eccentric Anomaly for Short-Term Orbit Predictions
Authors: Smibi M.J., Harishkumar Sellamuthu, Ram Krishan Sharma
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A new non-singular, analytical theory with respect to the Earth’s zonal harmonic term J2 has been developed for short-periodic motion, by analytically integrating the uniformly regular KS canonical equations of motion using generalized eccentric anomaly ‘E’ as the independent variable. Only one of the eight equations needs to be integrated analytically to generate the state vector, as a result of symmetry in the equations of motion, and the computation for the other equations is by changing the initial conditions. The integrals are much simpler than earlier obtained in [20] in terms of the independent variable ‘s’. Numerical results indicate that the solution is reasonably accurate for a wide range of orbital parameters during a revolution. The error in computing the most important orbital parameter ‘semi-major axis’ which is the measure of energy is less than five percentage during a revolution. The analytical solution can have number of applications. It can be used for studying the short-term relative motion of two or more space objects. It can also be useful in collision avoidance studies of space objects. It can be used for onboard computation in the navigation and guidance packages, where the modeling of J2 effect becomes necessary.