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.
Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of triangular equilibrium points in non-resonance case, in the photogravitational restricted three body problem under the influence of radiation pressures and P-R drags of the radiating primaries. The Hamiltonian of the system is normalized up to fourth order through Lie transform method and then to apply the Arnold-Moser theorem, Birkhoff normal form of the Hamiltonian is computed followed by nonlinear stability of the equilibrium points is examined. Similar to the case of classical problem, we have found that in the presence of assumed perturbations, there always exists one value of mass parameter within the stability range at which the discriminant D 4 vanish, consequently, Arnold-Moser theorem fails, which infer that triangular equilibrium points are unstable in nonlinear sense within the stability range. Present analysis is limited up to linear effect of the perturbations, which will be helpful to study the more generalized problem.
In the history of space, for the first time an operational US communications satellite Iridium 33, in low-Earth orbit was struck and destroyed by the collision of a long defunct Russian communications satellite COSMOS 2251 on 10 th February 2010. It is necessary to understand the circumstances of this collision for avoiding similar incidents in the future. In this direction a detailed conjunction analysis of all space objects is essential. Since a large number of objects are orbiting in space, it is very difficult to find out the close approach for all objects with simulations. Hence, a study related to the prefiltering of close approaches between space objects using analytical techniques is carried out in this paper. It is found that the presented methodology with prefiltering techniques is effective in reducing the number of objects for simulations.
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