Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

Jagadish Singh; Sunusi Haruna

doi:doi:10.11648/j.ajaa.20140202.12

| Peer-Reviewed

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

Jagadish Singh, Sunusi Haruna

Published in American Journal of Astronomy and Astrophysics (Volume 2, Issue 2)

Received: 29 December 2013 Published: 20 March 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.

Published in	American Journal of Astronomy and Astrophysics (Volume 2, Issue 2)
DOI	10.11648/j.ajaa.20140202.12
Page(s)	22-26
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

RTBP, Orbits, Oblateness, Radiation

References

[1]	AbdulRaheem, A., Singh, J.: AJ, 131, 1880 (2006)
[2]	AbdulRaheem, A., Singh, J.: Astrophys. Space Sci. 317, 9 (2008)
[3]	Elipe, A., & Ferrer, S. Celest. Mech., 37, 59 (1985)
[4]	Kishor, R., Kushvah, B.S.: Astrophys. Space Sci. 334, 333(2013)
[5]	Perdios, E. A.: Astrophys. Space Sci., 286, 501(2003)
[6]	Perdios, E. A., Kalantonis, V.S.: Astrophys. Space Sci., 305, 331(2006),
[7]	Perdiou, A.E., Nikaki, A.A., Perdios, E.A.: Astrophys. Space Sci., 345, 57(2013)
[8]	Radzievskii, V.V.: Astron. J. 27, 250(1950)
[9]	Rambaux, N.: Astron. & Astrophys., 556, 151 (2013).
[10]	Ragos, O., Zagouras, C. G., Perdios, E.: Astrophys. Space Sci. 182, 313 (1991)
[11]	Sharma, R.K.: Astrophys. Space Sci. 185, 271 (1987)
[12]	Sharma, R.K., Taqvi, Z.A., Bhatnagar, K. B.: Celest. Mech. Dyn. Astron. 79, 119 (2001).
[13]	Simmons, J.F.L., McDonald, J.C., Brown, J.C.: Celest. Mech. 35, 145 (1985)
[14]	Singh, J.: Astrophys. Space Sci., 342, 303(2012)
[15]	Singh, J.: AJ. 137, 3286 (2009)
[16]	Singh, J.: Astrophys. Space Sci., 346, 41(2013)
[17]	Singh, J., Leke, O.: Astrophys. Space Sci., 326, 305(2010)
[18]	Singh, J., Begha, J. M.: Astrophys. Space Sci., 331, 511(2011)
[19]	Singh, J., Leke, O.: Astrophys. Space Sci., 340, 27(2012)
[20]	Singh, J., Leke, O.: Astrophys. Space Sci., 344, 51(2013)
[21]	Singh, J., Leke, O.: Astrophys. Space Sci. 10.1007/s10509-013-1702-0 (2014)
[22]	Singh, J., Haruna, S.: Astrophys. Space Sci., 349, 107 (2014)
[23]	SubbaRao, P.V., Sharma, R. k.: Astron. & Astrophys.43, 381(1975)
[24]	Szebehely, V.G.: Theory of Orbits, Academic press, New York (1967)

Cite This Article

Plain Text BibTeX RIS

APA Style

Jagadish Singh, Sunusi Haruna. (2014). Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. American Journal of Astronomy and Astrophysics, 2(2), 22-26. https://doi.org/10.11648/j.ajaa.20140202.12

Copy | Download

ACS Style

Jagadish Singh; Sunusi Haruna. Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. Am. J. Astron. Astrophys. 2014, 2(2), 22-26. doi: 10.11648/j.ajaa.20140202.12

Copy | Download

AMA Style

Jagadish Singh, Sunusi Haruna. Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. Am J Astron Astrophys. 2014;2(2):22-26. doi: 10.11648/j.ajaa.20140202.12

Copy | Download

@article{10.11648/j.ajaa.20140202.12,
  author = {Jagadish Singh and Sunusi Haruna},
  title = {Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {2},
  pages = {22-26},
  doi = {10.11648/j.ajaa.20140202.12},
  url = {https://doi.org/10.11648/j.ajaa.20140202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140202.12},
  abstract = {This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies
AU  - Jagadish Singh
AU  - Sunusi Haruna
Y1  - 2014/03/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajaa.20140202.12
DO  - 10.11648/j.ajaa.20140202.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 22
EP  - 26
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20140202.12
AB  - This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.
VL  - 2
IS  - 2
ER  -

Copy | Download

Author Information

Jagadish Singh

Department of Mathematics, Faculty of Science, Ahmadu Bello University Zaria, Nigeria
Sunusi Haruna

Kano state Polytechnic, School of general studies, basic studies department, kano-Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Jagadish Singh, Sunusi Haruna. (2014). Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. American Journal of Astronomy and Astrophysics, 2(2), 22-26. https://doi.org/10.11648/j.ajaa.20140202.12

Copy | Download

ACS Style

Jagadish Singh; Sunusi Haruna. Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. Am. J. Astron. Astrophys. 2014, 2(2), 22-26. doi: 10.11648/j.ajaa.20140202.12

Copy | Download

AMA Style

Jagadish Singh, Sunusi Haruna. Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. Am J Astron Astrophys. 2014;2(2):22-26. doi: 10.11648/j.ajaa.20140202.12

Copy | Download

@article{10.11648/j.ajaa.20140202.12,
  author = {Jagadish Singh and Sunusi Haruna},
  title = {Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {2},
  pages = {22-26},
  doi = {10.11648/j.ajaa.20140202.12},
  url = {https://doi.org/10.11648/j.ajaa.20140202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140202.12},
  abstract = {This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies
AU  - Jagadish Singh
AU  - Sunusi Haruna
Y1  - 2014/03/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajaa.20140202.12
DO  - 10.11648/j.ajaa.20140202.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 22
EP  - 26
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20140202.12
AB  - This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.
VL  - 2
IS  - 2
ER  -

Copy | Download