Abstract
A new non-singular analytical theory with respect to the Earth’s zonal harmonic terms J2, J3, J4 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 need to be integrated analytically to generate the state vector, due to the symmetry in the equations of motion, and the computation for the other equations is done by changing the initial conditions. King-Hele’s expression for radial distance ‘r’ with J2 is also considered in generating the solution. The results obtained from the analytical expressions in a single step during half a revolution match quite well with numerically integrated values. Numerical results also indicate that the solution is reasonably accurate for a wide range of orbital elements during half a revolution and is an improvement over Sharon et al. [17] theory, which is generated in terms of KS regular elements. It can be used for studying the short-term relative motion of two or more space objects and in collision avoidance studies of space objects. It can be also useful for onboard computation in the navigation and guidance packages. Â
Highlights
In the artificial satellite theory, the motion of a satellite under the effect of Earth’s oblateness, namely the second zonal harmonic J2 in the gravitational potential field is known as the main problem
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
Because of the complexity of the integrals in evaluation for practical problems, the utility of the analytical solution was limited for operational purposes. {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
Summary
In the artificial satellite theory, the motion of a satellite under the effect of Earth’s oblateness, namely the second zonal harmonic J2 in the gravitational potential field is known as the main problem. {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. New non-singular analytical solutions with J3 and J4 in close form in eccentricity and inclination 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 are developed. The solutions can have number of applications It can be used for studying the short-term relative motion of two or more space objects and in collision avoidance studies of space objects and generation of mean orbital elements. It can be useful for onboard computation in the navigation and guidance packages, where the modeling of J2 effect becomes necessary
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