EFFECTS OF PERTURBATIONS IN THE CORIOLIS AND CENTRIFUGAL FORCES ON THE STABILITY OF GENERALIZED PHOTO-GRAVITATIONAL RESTRICTED THREE-BODY PROBLEM
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Date
2017-02
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UNIVERSITY OF ILORIN
Abstract
The study of classical Restricted Three-body Problem (RTBP) and its generalizations have been of major interest to researchers over the years. This is due to the rise in the need for accuracy in determining astrometric positions which would help to reveal some peculiarities of components of motion and draw conclusions on the stability of space vehicles to be launched. This has led to the necessity of considering all possible physical properties (oblateness/triaxiality, radiation pressure, Poynting-Robertson (PR) drag, perturbing forces etc.) that affect the motion of particles in space. The effect of perturbations in the coriolis and centrifugal forces on the stability of the generalized photo-gravitational RTBP has been a major focus of investigations. However, the effect under the influence of the PR-drag from both oblate bodies has received little or no attention. Therefore, the aim of this research work was to investigate how perturbations in the coriolis and centrifugal forces affect the stability of the triangular libration points of the RTBP when the primaries were considered to be oblate, radiating with PR-drag effects. The objectives of this study were to: determine the effect of PR-drag on the stability of the libration of the generalized RTBP; investigate the effects of and on the stability of the generalized RTBP in the linear sense; establish the periodic orbit: period of oscillation, orientation and semi-axes of the proposed system; and verify the results obtained using astrophysical data for the Kruger 60 and RXJ0450, 1-5658 binary systems.
The Hamiltonian and Lagrangian methods were employed to establish the relevant equations of motion, obtain the triangular libration points and investigate their stability using Murray’s and Routh Hurwitz’s criteria and verifying the results for the two binary systems using, MATLAB and Microsoft Excel Mathematical softwares.
The findings from this study showed that the:
• generalized system was unstable around the triangular libration points due to the presence of the PR-drag effect from both bodies;
• presence of the parameter of the stabilizing factor, , in the roots of the characteristics equation does not change the instability of the system around the libration points;
• period for the growth of the particle oscillation is dependent on the PR-drag parameter only, in the linear sense;
• orientation and length of semi- axes are dependent on all the perturbing parameters; and
• change in the values of and affects the values of the libration points and roots of the characteristics equations computed for the two binary but does not satisfy the criteria for stability.
The study concluded that the system remained unstable even with the significant influence of perturbations due to the strong destabilizing effect of the PR-drag force. This work as a generalization of the classical case and the work of others, is therefore recommended to serve as a form of reference to achieving more interesting and vital results in Space Dynamics and also an added value to designers of space crafts and aerospace agencies.
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PERTURBATIONS, CENTRIFUGAL FORCE, CORIOLIS FORCE, STABILITY, GENERALIZED, RESTRICTED THREE-BODY PROBLEM, PHOTO-GRAVITATIONAL, Poynting-Robertson (PR) drag