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Resonance in a geo-centric satellite due to earth’s equatorial ellipticity

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Abstract

The resonances in a geocentric satellite due to earth’s equatorial ellipticity have been investigated. The resonance at five points resulting from the commensurability between the mean motion of the satellite and the earth’s equatorial ellipticity is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. A comparison of their effects on the orbital elements has also been studied. It is observed that the amplitude and the time period of the oscillation decrease as Γ (angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) increases in the first quadrant for all the resonance cases.

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Acknowledgement

We are thankful to the Centre for Fundamental Research in Space Dynamics and Celestial Mechanics (CFRSC) for providing all facilities for this research work.

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  1. Maharaja Agrasen College, Department of Mathematics, University of Delhi, Delhi, India

    Sushil Yadav

  2. Sri Aurobindo College, Department of Mathematics, University of Delhi, New Delhi, India

    Rajiv Aggarwal

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  1. Sushil Yadav
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  2. Rajiv Aggarwal
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Correspondence to Sushil Yadav.

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Yadav, S., Aggarwal, R. Resonance in a geo-centric satellite due to earth’s equatorial ellipticity. Astrophys Space Sci 347, 249–259 (2013). https://doi.org/10.1007/s10509-013-1515-1

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  • DOI: https://doi.org/10.1007/s10509-013-1515-1

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