Analytical short-term orbit prediction with J2 , J3, J4 in terms of K-S uniformly regular canonical elements Original Research Article

A new non-singular, analytical theory with respect to the Earthʹs zonal harmonic terms J2, J3 , J4 has been developed for short-periodic motion, by analytically integrating the uniformly regular K-S canonical equations. Only one of the eight equations need to be integrated analytically to obtain the state vector, due to symmetry in the equations of motion and computation for the other equations is by changing the initial conditions. The solution is valid for very small to very high eccentricity and inclination orbits. Numerical experimentation with a wide range of orbital parameters reveals that the orbital elements obtained from the analytical expressions in a single step during one revolution match quite well with numerically integrated values. Numerical comparison with respect to J2 with other analytical solutions shows the superiority of the present solution. The analytical solution with J3 and J4 is found to be very accurate and compared well with the analytical solution of Sharma.