Effects of Radiation and Triaxiality of Primaries on Existence and Stability of Collinear Equilibrium Points in Elliptical Restricted Three Body Problem
DOI:
https://doi.org/10.26713/jims.v12i1.1094Keywords:
ER3BP, Lagrangian points, Triaxiality, Dynamical system, Collinear pointsAbstract
This paper deals with the motion of infinitesimal mass around primaries whose are radiating and triaxial. They are moving around each other in elliptic orbits about the common barycenter in the neighborhood of collinear equilibrium points. It is observed that location and stability of collinear points are effected by radiation and triaxiality of primaries. The results shows that collinear points \(L_1\) and \(L_2\) are having unstable behavior, while \(L_3\) is showing stable behavior for some values of radiation and triaxiality.Downloads
References
M. K. Ammar, The effect of solar radiation pressure on the Lagrangian points in the elliptical restricted three body problem, Astrophysics and Space Science 313 (2008), 393 – 408, DOI: 10.1007/s10509-007-9709-z.
A. Bennet, Analytical determination of characteristic exponents, in Astrodynamics Specialist Conference, Monetary, California, 101 (1965), DOI: 10.2514/6.1965-685.
C. D. Murray and S. F. Dermott, Solar System Dynamics, Cambridge University Press (1999), https://books.google.co.in/books?hl=en&lr=&id=aU6vcy5L8GAC&oi=fnd&pg=PR11&ots=CBgL_E0CNn&sig=aPcBisG7mc87oV_9JDDXVc31r2c#v=onepage&q&f=false.
A. Chakraborty, A. Narayan and A. Shrivastava, Existence and stability of collinear points in elliptical restricted three body problem with radiating and oblate primaries, International Journal of Advanced Astronomy 4(2) (2016), 95 – 104, DOI: 10.14419/ijaa.v4i2.6523.
J. M. A. Danby, Stability of the triangular points in the elliptical restricted problem of three bodies, Astronomical Journal 69 (1964), 165 – 172, DOI: 10.1086/109254.
E. A. Grebnikov, On the stability of the Lagrangian triangle solutions of the restricted elliptic three body problem, Soviet Astronomy 8(3) (1964), 567 – 578.
J. Gyorgyey, On the non-linear motions around the elliptical restricted problem of three bodies, Celestial Mechanics and Dynamical Astronomy 36(3) (1985), 281 – 285, DOI: 10.1007/BF01230741.
G. Gómez and M. Mondelo, The dynamics around the collinear equilibrium points of the RTBP, Physica D: Nonlinear Phenomena 157(4) (2001), 283 – 321, DOI: 10.1016/S0167-2789(01)00312-8.
B. Ishwar and S. K. Sahoo, Stability of collinear equilibrium points in the generalized photogravitational elliptic restricted three body problem, Celestial Mechanics, Recent Trends 99 (2006).
S. Kumar and B. Ishwar, Location of collinear equilibrium points in the generalized photogravitational elliptic restricted three body problem, International Journal of Engineering, Science and Technology 3(2) (2011), 157 – 162, DOI: 10.4314/ijest.v3i2.68143
V. V. Markellos, E. Perdios and P. Labrapoulou, Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted three body problem, Astrophysics and Space Science 194 (1992), 207 – 214, DOI: 10.1007/BF00643991.
F. R. Moulton, On the stability of direct and retrograde orbits, Monthly Notices of the Royal Astronomical Society 75 (1914), 40 – 57, DOI: 10.1093/mnras/75.2.40.
A. Narayan and C. R. Kumar, Effects of photogravitational and oblateness on the triangular Lagrangian points in the Elliptical Restricted three body problem, Indian Journal of Pure and Applied Mathematics 68(2) (2011), 201 – 224, http://ijpam.eu/contents/2011-68-2/6/6.pdf.
A. Narayan, K. K. Pandey and S. K. Shrivastava, Effects of radiation and triaxiality of triangular equilibrium points in elliptical restricted three body problem, International Journal of Advanced Astronomy 3(2) (2015), 97 – 106, DOI: 10.14419/ijaa.v3i2.5302.
A. Narayan, K. K. Pandey and S. K. Shrivastava, Characteristics exponents of the triangular solutions in elliptical restricted three- body problem under radiating and triaxial primaries, International Journal of Advanced Astronomy 5(1) (2017), 12 – 18, DOI: 10.14419/ijaa.v5i1.7114.
A. Narayan and N. Singh, Motion and stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries, Astrophys. Space Sci. 352(1) (2014), 57 – 70, DOI: 10.1007/s10509-014-1903-1.
A. Narayan and N. Singh, Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary system, Astrophys. Space Sci. 353(1) (2014), 457 – 464, DOI: 10.1007/s10509-014-2014-8.
A. Narayan and N. Singh, Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the radiating primaries, Astrophysics Space Sci. 354(2) (2014), 355 – 368, DOI: 10.1007/s10509-014-2094-5.
A. Narayan and T. Usha, Stability of triangular equilibrium points in the elliptic restricted problem of three bodies with radiation and triaxial primaries, Astrophysics and Space Science 351(1) (2014), 135 – 142, DOI: 10.1007/s10509-014-1818-x.
J. Singh and U. Aishetu, Motion in the photogravitational elliptic restricted three body problem under an oblate primary, Astronomical Journal 143(5) (2012), 109 (22 p), DOI: 10.1088/0004-6256/143/5/109.
J. Singh and U. Aishetu, On the stability of triangular points in the elliptic restricted three bodies under the radiating and oblate primaries, Astrophysics and Space Science 341 (2012), 349 – 358, DOI: 10.1007/s10509-012-1109-3.
J. Singh and A. Umar, Collinear equilibrium points in the elliptic r3bp with oblateness and radiation, Advances in Space Research 52(8) (2013), 1489 – 1496, DOI: 10.1016/j.asr.2013.07.027.
V. Szebebely, Stability of the points of equilibrium in the restricted problem, Astronomical Journal 72 (1967), 7 – 9, DOI: 10.1086/110195.
T. Usha, A. Narayan and B. Ishwar, Effects of radiation and triaxiality of primaries on triangular equilibrium points in elliptic restricted three body problem, Astrophysics and Space Science 349(1) (2014), 151 – 164, DOI: 10.1007/s10509-013-1655-3.
T. Usha and A. Narayan, Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the radiating primary and triaxial secondary, Modelling, Measurement and Control A 91(1) (2018), 1 – 8, DOI: 10.18280/mmc_a.910101.
V. P. Vinti, Orbital and celestial mechanics, IAA 177 (1998), DOI: 10.2514/4.866487.
A. S. Zimvoschikov and V. N. Thkai, Instability of libration points and resonance phenomena in the photogravitational elliptical restricted three body problem, Solar System Research 38(2) (2004), 155 – 163, DOI: 10.1023/B:SOLS.0000022826.31475.a7.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
