Publications of The Korean Astronomical Society (천문학논총)

The Korean Astronomical Society (한국천문학회)
권호 표지
DOI QR코드

DOI QR Code

LINEAR STABILITY OF TRIANGULAR EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL RESTRICTED THREE BODY PROBLEM WITH TRIAXIAL RIGID BODIES, WITH THE BIGGER ONE AN OBLATE SPHEROID AND SOURCE OF RADIATION

  • KUMAR, AVDHESH (RIMT-Institute of Engineering Technology) ;
  • ISHWAR, B. (University Department of Mathematics B.R.A. Bihar University)
  • Received : 2014.11.30
  • Accepted : 2015.06.30
  • Published : 2015.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

Keywords

References

  1. Douskos, C. N. & Perdios, E. A., 2002, On the Stability of Equilibrium Points in the Relativistic Restricted Three-body Problem, CeMDA, 52, 312
  2. Ishwar, B., 1997, Non-linear Stability in the Generalized Restricted Three Body Problem, CeMDA, 65, 253
  3. Ishwar, B. & Elipe, A., 2001, Secular Solutions at Triangular Equilibrium Point in the Generalise Photogravitational Restricted Three-Body Problem, Ap&SS, 277, 437
  4. Sanjay, J., Ajay, K., & Bhatnagar, K. B., 2009, PeriodicOrbits Around the Collinear Libration Point in the Re-stricted Three-body Problem When the Smaller Primary is a Triaxial Rigid Body and Bigger Primary is a Source of Radiation Pressure, Indian J.phys., 83 (2), 171 https://doi.org/10.1007/s12648-009-0068-1
  5. Khanna, M. & Bhatnagar, K. B., 1998, Existence and Stability of Libration Points in the Restricted Three-body Problem when Thesmaller Primary is a Triaxial Rigid Body, Indian J. Pure. Appl. Math., 29 (10), 1011
  6. Kalantonis,V.S., Perdios, E.A., & Perdiou,A.E., 2008, The Sitnikov Family and the Associated Families of 3D Periodic Orbits in the Photogravitational RTBP with Oblateness, ApSS, 315, 323
  7. Avdhesh, K. & Ishwar. B., 2012, Linear Stability of Triangular Equilibrium Points in the Photogravitational Restricted Three Body Problem with Triaxial Rigid Bodies and Oblate Spheroid, Nova Science Publishers, 6, Number 1, (JNSST 2012)
  8. Lara, M. & Elipe, A., 1997, Periodic Orbits in the Restricted Three Body Problem with Radiation Pressure, CeMDA, 68, 1 https://doi.org/10.1023/A:1008233828923
  9. Mittal, A., Ahmad, I., & Bhatnagar, K. B., 2009, Periodic Orbits Generated by Lagrangian Solutions of the Restricted Three Body Problem When One of the Primaries is an Oblate Body, Ap&SS, 319, 63 https://doi.org/10.1007/s10509-008-9942-0
  10. Papadakis.K. E. & Kanavos.S. S., 2007, Numerical Exploration of the Photogravitational Restricted Five-body Problem, Ap&SS, 310, 119 https://doi.org/10.1007/s10509-007-9486-8