Resonance in the perturbations of a synchronous satellite due to angular rate of the earth-moon system around the sun and the earth’s rotation rate

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    This paper investigates resonances in the perturbations of a synchronous satellite including its latitude, angular rate of the earth-moon system around the sun and the earth’s rotation rate about its axis. This is found that resonances occur due to the commensurability between (i) angular velocity of the satellite and angular rate of earth’s rotation about its axis and (ii) angular rate of the earth-moon system around the sun and angular rate of the rotation of the earth. Amplitude and time-period of the oscillation at the resonance points are determined using the procedure of Brown and Shook [3]. Effect of  (orbital angle of the mass-centre of the earth-moon system around the sun) on amplitude and time period is also analyzed. It is found that for increasing the values of  from to  amplitude decreases and time period also decreases. Effect of time on the latitude of the satellite including earth oblateness is also studied. It is seen that for increasing the value of , there is a small change in ,  the latitude of the synchronous satellite.


  • Keywords


    Earth Oblateness; Perturbations; Resonance; Synchronous Satellite.

  • References


      [1] Allan RR (1963) Perturbations of a geostationary satellite by the longitude-dependent terms in the Earth’s gravitational field. Planet Space Science, 11, 1325–1334.

      [2] Breiter S (1999) Lunisolar apsidal resonances at low satellite orbits. Celestial Mechanics and Dynamical Astronomy, 74, 253–274. http://dx.doi.org/10.1023/A:1008379908163.

      [3] Brown EW & Shook CA (1933) planetary theory, Cambridge University Press, London and New York. Reprinted by Dover, New York.

      [4] Cook GE (1962) Luni-solar Perturbations of the orbit of an earth satellite. The Geophysical Journal of the Royal Astronomical Society, 6 (3), 271–291. http://dx.doi.org/10.1111/j.1365-246X.1962.tb00351.x.

      [5] Frick R H & Garber T B (1962) Perturbations of a synchronous satellite. The RAND Corporation, R–399, NASA.

      [6] Gallardo T (2008) Evaluating the signatures of the mean motion resonances in the solar system. Journal of Aerospace Engineering, Sciences and Applications, vol.1, No.1.

      [7] Garfinkel B (1982) On Resonance in celestial mechanics (A Survey). Celestial Mechanics, 28(1-2), 275–290. http://dx.doi.org/10.1007/BF01243738.

      [8] Giacaglia G E O (1970) Double resonance in the motion of a satellite. Symposis Mathematics, 5, 45–63.

      [9] Hadjidemetrio J D (1987) Resonances in the solar system and in planetary system. Proceedings 10th ERAM of IAU, 3, 27–32.

      [10] Hagihara Y (1972) Perturbation theory. Vol.II, Part-I, 462–469.

      [11] Henrard J (1988) Resonances in the planar elliptic restricted body problem, in long term dynamical behavior of natural and artificial N body systems. (A. E. Roy ed.), NATO ASI series C-246, Kluwer Academic Publication, 405–425. http://dx.doi.org/10.1007/978-94-009-3053-7_38.

      [12] Michtchenko T A, Ferraz Mello S & Beaugé, C (2006) Stationary orbits in resonant extra-solar planetary systems. Celestial Mechanics and Dynamical Astronomy, 94(4), 411–432. http://dx.doi.org/10.1007/s10569-006-9009-x.

      [13] Narayan a & Singh N (2014) Resonance stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries. Astrophysics and Space Science, 353, 441–445. http://dx.doi.org/10.1007/s10509-014-2085-6.

      [14] Wisdom J (1985) A perturbative treatment of the motion near the 3/1 commensurability. Icarus, 63, 279–282.


 

View

Download

Article ID: 6227
 
DOI: 10.14419/ijaa.v4i2.6227




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.