Long-term orbit computations with KS uniformly regular canonical elements with 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, in the package and also economize the computations. A fixed step-size fourth-order Rung+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& 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 Jz4. The mean eccentricity (e,) is found to have long-periods of 459.6, 6925.1 and 1077.6 days, respectively. Sharp changes in the variation of o, near the minima to e, are noticed. The values of w, are found to be very near to + 90 degrees at the extrema of e,,,. 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 Jz to Jz4 terms. T is found to increase rapidly as we proceed towards the critical inclinations.

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

“…where 3 x and 2 3 x are given as [16] : 3 0 1 2 2 2 3 0 1 2 3 4 cos sin cos cos sin sin cos x into the equations (6), we get …”

“…Sharma and James Raj [16] numerically integrated these equations to obtain accurate orbit prediction under the effect of Earth's oblateness with zonal harmonic terms up to J 36 . 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.…”

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

“…The KS uniform regular canonical equations of motion [19] are a particular canonical form where all the ten elements are constant for unperturbed two-body problem and are applicable to elliptic, parabolic and hyperbolic orbital motion. In [13] these equations were numerically integrated to obtain accurate orbits under the effect of Earth's oblateness with zonal harmonic terms up to J36. 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.…”

J2-Gravity Perturbed Motion of Artifical Satellite in Terms of Euler Parameters

“…The applications of the special perturbation methods to the equations of motion in terms of the redundant variables, provide the most powerful and accurate techniques that have been devised recently for satellite ephemeris with respect to any type of perturbing forces [1][2][3].…”