The present paper deals with the study of equilibrium positions of the motion of a system of two artificial satellites connected by a light, flexible, inextensible and non-conducting cable under the influence of solar radiation pressure, earth’s oblateness, shadow of the earth and air resistance. Here, we study the case of circular orbit of the centre of mass of the system. We derive differential equations of motion of the system. General solutions of the differential equations are beyond the reach. On the other hand, the general solutions do not serve our purpose. Jacobian integral of the system has also been obtained. Thereafter equilibrium positions of the motion of the system have been obtained.
References
[1]
Beletsky, V.V. and Novikova, E.T. (1969) About the Relative Motion of Two Connected Bodies in Orbit. Kosmicheskie Issledovania, 7, 377-384.
[2]
Beletsky, V.V. and Novoorebelskii, A.B. (1969) Existence of Stable Relative Equilibria for an Artificial Satellite in a Model Magnetic Field. Institute of Applied Mathematics, Academy of Sciences of the U. S. S. R., Soviet Astronomy, Vol. 17, 213-220.
[3]
Das, S.K., Bhattacharya, P.K. and Singh, R.B. (1976) Effect of Magnetic Force on the Motion of a System of Two Cable-Connected Satellites in Orbit. Proceedings National Academy of Science, India, 46, 287-299.
[4]
Kumar, S. and Bhattacharya, P.K. (1995) Stability of Equilibrium Position of Two Cable-Connected Satellites. In: Bhatnagar, K.B. and Ishwar, B., Eds., Proceedings Workshop on Space Dynamics and Celestial Mechanics, Muzaffarpur, India, 71-74.
[5]
Kumar, S., Srivastava, U.K. and Bhattacharya, P.K. (2005) Equations of Motion of a System of Two Cable-Connected Artificial Satellites under the Influence of Solar Radiation Pressure, Earth’s Oblateness and Shadow of the Earth. Proceedings Mathematical Society, Banaras Hindu University, Varanasi, 21, 51-61.
[6]
Singh, R.B. and Demin, V.G. (1972) About the Motion of a Heavy Flexible String Attached to the Satellites in the Central Field of Attraction. Celestial Mechanics, 6, 268-277.
[7]
Singh, R.B. (1973) Three Dimensional Motion of a System of Two Cable-Connected Satellites in Orbit. Astronautica Acta, 18, 301-308.
[8]
Nechvile, V. (1926) Surune Nouvelic Forme Des Equations Differentielies Du Problem Restriint Elliptique. Academy Paris Compte Rendus, 182, 310-322.
[9]
Prasad, J.D. and Kumar, S. (2011) Equations of Motion of a System of Two Cable-Connected Artificial Satellites Under the Influence of Earth’s Magnetic Field, Earth’s Shadow, Solar Radiation Pressure and Eatrh’s Oblateness. Journal Purvanchal Academy of Sciences, Jaunpur, India, 17 (Physical Science), 27-34.