Long-term orbit computations with KS uniformly regular canonical elements with oblateness

TLDR: In this paper, a fixed step-size fourth-order Runge-Kutta-Gill method is employed for numerical integration of the canonical equations with Earth's oblateness.

Abstract: This paper concerns with the study of KS uniformly regular canonical elements with Earth's oblateness. These elements, ten in number, are all constant in the unperturbed motion and even in the perturbed motion, the substitution is straightforward and elementary due to the transformation laws being explicit and closed expression. By utilizing the recursion formulas of Legendre's polynomials, we are able to include any number of Earth's zonal harmonics J n in the package and also economize the computations. A fixed step-size fourth-order Runge-Kutta-Gill method is employed for numerical integration of the canonical equations. Utilizing 5 test cases covering a large range of semimajor axis and eccentricity, we have carried out computations to study the effects of Earth's zonal harmonics (up to J 36) and integration step-size variation. Bilinear relations and energy equation are used for checking the accuracies of numerical integration. From the application point of view, the package is utilized to study the behaviour of 900 km height near-circular sun-synchronous satellite orbit over a longer duration of 220 days time (nearly 3078 revolutions) and the necessity of including more number of Earth's zonal harmonic terms is noticed. The package is also used to study the effect of higher zonal harmonics on three 900 km height near-circular orbits with inclinations of 60, 63.2, and 65 degrees, by including Earth's zonal harmonics up to J 24. The mean eccentricity (e m) is found to have long-periods of 459.6, 6925.1 and 1077.6 days, respectively. Sharp changes in the variation of Ωm near the minima to em are noticed. The values of Ω m are found to be very near to +-90 degrees at the extrema of em. The same orbit is employed to study the effect of variation of inclination from 0 to 180 degrees on long-period (T) of eccentricity with J 2 to J 24 terms. T is found to increase rapidly as we proceed towards the critical inclinations.