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

An Analytical Theory with Respect to the Earth’s Zonal Harmonic Term J₂ in Terms of Eccentric Anomaly for Short-Term Orbit Predictions

“…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 integrals are found to be much simpler than obtained in [20]. The solution can have number of applications.…”

“…Analytical theory in terms of KS elements with J 2 [17], [18] and with J 3 and J 4 [19] was developed by Sharma for short-term orbit predictions. James Raj and Sharma [20] analytically integrated the uniformly regular KS canonical elements with Earth's zonal harmonics J 2 , J 3 and J 4 . The independent variable, fictitious time 's' given by / dt ds r = with t and r being the physical time and radial distance, respectively, and used for analytical integration, resulted in complicated integrals.…”

Analytical theory in terms of J2, J3, J4 with eccentric anomaly for short-term orbit predictions using uniformly regular KS canonical elements

“…Analytical theory in terms of KS elements with J2 [14] and [16], and with J3 and J4 [15] was developed for short-term orbit predictions. [8] analytically integrated the uniformly regular KS canonical elements with Earth's zonal harmonics J2, J3 and J4. The independent variable, fictitious time 's' given by dt/ds = r with t and r being the physical time and radial distance, respectively, and used for analytical integration, resulted in complicated integrals.…”

“…{18] developed a new non-singular analytical solution with J2 in close form in eccentricity 'e' for short-term orbit predictions by analytically integrating the uniformly regular KS canonical equations of motion, using the generalized eccentric anomaly 'E' as the independent variable. The integrals are found to be much simpler than obtained in [8]. In this paper, the analytical solution of [18] is improved by using King-Hele's expression [10] for radial distance r as function of J2.…”