On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three Bodies

Affiliation(s)

Lakshmibai College, University of Delhi, New Delhi, India.

L S College, B.R.A.B University, Muzaffarpur, India.

Lakshmibai College, University of Delhi, New Delhi, India.

L S College, B.R.A.B University, Muzaffarpur, India.

ABSTRACT

The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary body to be in shape of an oblate spheroid. The equilibrium points are sought by the application of the propellant for which it would just balance the gravitational forces. The launching flight of such a satellite is seen to be applicable for having arbitrary space stations for these different missions. Specialty of the result of the investigation lies in the fact that an arbitrary space station can be formed to attain any specified mission.

Cite this paper

K. Ranjana and V. Kumar, "On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three Bodies,"*International Journal of Astronomy and Astrophysics*, Vol. 3 No. 4, 2013, pp. 508-516. doi: 10.4236/ijaa.2013.34059.

K. Ranjana and V. Kumar, "On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three Bodies,"

References

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[2] K. E. Tsiolkovsky, “Extension of Man into Outer Space,” In Proc. Symp. Jet Propulsion, Vol. 2, United Scientific and Technical Presses, 1936. (in Russian)

[3] K. Tsander, “From a Scientific Heritage,” NASA Technical Translation No TTf-541, NASA, Washington DC, 1967.

[4] R. L. Garwin, “Solar Sailing: A Practical Method of Propulsion within the Solar System,” Jet Propulsion, Vol. 28, No. 123, 1958, pp. 188-190.

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[6] M. Leipold, “ODISSEE—A Proposal for Demonstration of a Solar Sail in Earth Orbit,” Paper IAA-L98-1005, International Academy of Astronautics, Stockholm, 1998.

[7] J. M. Logsdon, “Missing Halley’s Comet: The Politics of Big Science,” Isis, Vol. 80, No. 2, 1989, pp. 254-280. http://dx.doi.org/10.1086/355011

[8] M. McDonald and C. R. Mclnnes, “A Near Linear Road Map for Solar Sailing,” Proceedings of the 55th International Astronautical Congress, Vancouver, 4-8 October 2004.

[9] A. Markeev, “Stability of the Triangular Lagrangian Solutions of the Restricted Three-Body Problem in the Three Dimensional Circular Case,” Soviet Astronomy, Vol. 15, No. 4, 1972, pp. 682-686.

[10] C. R. Mclnnes, A. J. C. McDonald, J. F. L. Simmons and E. W. MacDonald, “Solar Sail Parking in Restricted Three Systems,” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, 1994, pp. 399-406.

[11] H. M. Dusek, “Motion in the Vicinity of Libration Points of a Generalized Three Body Model,” AIAA/IODI Astrodynamics Specialist Conference, AIAA, Monterey, 16-17 September 1965, pp. 565-682.

[12] A. A. Perezhogin, “Stability of the Sixth and Seventh Libration Point with Photo-Gravitational Restricted Circular Three Body Problem,” Sovt. Astron. Zh., 1976, pp. 174-175.

[13] A. L. Kunitsyn and A. A. Perezhogin, “On the Stability of Triangular Libration Point of the Photo-Gravitational Restricted Problem of Three Bodies,” Celest. Mech. Dyn. Astron., Vol. 18, 1978, pp. 395-408.

[14] G. Mengali and A. A. Quarta, “Non-Keplerian Orbits for Electric Sails,” Celestial Mechanics and Dynamical Astronomy, Vol. 105, No. 1-3, 2009, pp. 179-195. http://dx.doi.org/10.1007/s10569-009-9200-y

[15] M. Y. Morimoto, H. Yamakawa and K. Uesugi, “Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 5, 2007, pp. 1563-1567. http://dx.doi.org/10.2514/1.26771

[16] R. L. Forward, “Statite: A Spacecraft That Does Not Orbit,” Journal of Spacecraft and Rockets, Vol. 28, No. 5, 1991, pp. 606-611. http://dx.doi.org/10.2514/3.26287

[17] C. Bombardelli and J. Pelaez, “On the Stability of Artificial Equilibrium Points in the Circular Restricted Three-Body Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 109, No. 1, 2011, pp. 13-26. http://dx.doi.org/10.1007/s10569-010-9317-z

[18] P. V. Subba Rao and R. K. Sharma, “Effect of Oblateness on the Non-Linear Stability of L4 in the Restricted ThreeBody Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 65, No. 3, 1997, pp. 291-312.

[19] V. Kumar and R. K. Choudhary, “On the Stability of the Triangular Lagrangian Points Radiating as Well,” Celestial Mechanics and Dynamical Astronomy, Vol. 40, 1987, pp. 155-170.

[20] S. W. McCusky, “An Introduction to Celestial Mechanics,” Addison-Wesley, New York, 1963.

[21] V. Szebehely, “Theory of Orbits: The Restricted Problem of Three Bodies,” Academic Press, New York, 1967.

[22] V. Coverstone and J. E. Prussing, “Technique for Escape from Geosynchronous Transfer Orbit Using a Solar Sail,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4, 2003, pp. 628-634. http://dx.doi.org/10.2514/2.5091

[1] C. R. Mclnnes, “Solar Sailing Technology, Dynamic and Mission Application,” Springer Application, Springer-Praxis, London, 1999.

[2] K. E. Tsiolkovsky, “Extension of Man into Outer Space,” In Proc. Symp. Jet Propulsion, Vol. 2, United Scientific and Technical Presses, 1936. (in Russian)

[3] K. Tsander, “From a Scientific Heritage,” NASA Technical Translation No TTf-541, NASA, Washington DC, 1967.

[4] R. L. Garwin, “Solar Sailing: A Practical Method of Propulsion within the Solar System,” Jet Propulsion, Vol. 28, No. 123, 1958, pp. 188-190.

[5] J. L. Wright and J. M. Warmke, “Solar-Sail Mission Applications,” Proceedings of AIAA/AAS Astrodynamics Conference, San Diego, 1976, paper no.AIAA-76-808.

[6] M. Leipold, “ODISSEE—A Proposal for Demonstration of a Solar Sail in Earth Orbit,” Paper IAA-L98-1005, International Academy of Astronautics, Stockholm, 1998.

[7] J. M. Logsdon, “Missing Halley’s Comet: The Politics of Big Science,” Isis, Vol. 80, No. 2, 1989, pp. 254-280. http://dx.doi.org/10.1086/355011

[8] M. McDonald and C. R. Mclnnes, “A Near Linear Road Map for Solar Sailing,” Proceedings of the 55th International Astronautical Congress, Vancouver, 4-8 October 2004.

[9] A. Markeev, “Stability of the Triangular Lagrangian Solutions of the Restricted Three-Body Problem in the Three Dimensional Circular Case,” Soviet Astronomy, Vol. 15, No. 4, 1972, pp. 682-686.

[10] C. R. Mclnnes, A. J. C. McDonald, J. F. L. Simmons and E. W. MacDonald, “Solar Sail Parking in Restricted Three Systems,” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, 1994, pp. 399-406.

[11] H. M. Dusek, “Motion in the Vicinity of Libration Points of a Generalized Three Body Model,” AIAA/IODI Astrodynamics Specialist Conference, AIAA, Monterey, 16-17 September 1965, pp. 565-682.

[12] A. A. Perezhogin, “Stability of the Sixth and Seventh Libration Point with Photo-Gravitational Restricted Circular Three Body Problem,” Sovt. Astron. Zh., 1976, pp. 174-175.

[13] A. L. Kunitsyn and A. A. Perezhogin, “On the Stability of Triangular Libration Point of the Photo-Gravitational Restricted Problem of Three Bodies,” Celest. Mech. Dyn. Astron., Vol. 18, 1978, pp. 395-408.

[14] G. Mengali and A. A. Quarta, “Non-Keplerian Orbits for Electric Sails,” Celestial Mechanics and Dynamical Astronomy, Vol. 105, No. 1-3, 2009, pp. 179-195. http://dx.doi.org/10.1007/s10569-009-9200-y

[15] M. Y. Morimoto, H. Yamakawa and K. Uesugi, “Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 5, 2007, pp. 1563-1567. http://dx.doi.org/10.2514/1.26771

[16] R. L. Forward, “Statite: A Spacecraft That Does Not Orbit,” Journal of Spacecraft and Rockets, Vol. 28, No. 5, 1991, pp. 606-611. http://dx.doi.org/10.2514/3.26287

[17] C. Bombardelli and J. Pelaez, “On the Stability of Artificial Equilibrium Points in the Circular Restricted Three-Body Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 109, No. 1, 2011, pp. 13-26. http://dx.doi.org/10.1007/s10569-010-9317-z

[18] P. V. Subba Rao and R. K. Sharma, “Effect of Oblateness on the Non-Linear Stability of L4 in the Restricted ThreeBody Problem,” Celestial Mechanics and Dynamical Astronomy, Vol. 65, No. 3, 1997, pp. 291-312.

[19] V. Kumar and R. K. Choudhary, “On the Stability of the Triangular Lagrangian Points Radiating as Well,” Celestial Mechanics and Dynamical Astronomy, Vol. 40, 1987, pp. 155-170.

[20] S. W. McCusky, “An Introduction to Celestial Mechanics,” Addison-Wesley, New York, 1963.

[21] V. Szebehely, “Theory of Orbits: The Restricted Problem of Three Bodies,” Academic Press, New York, 1967.

[22] V. Coverstone and J. E. Prussing, “Technique for Escape from Geosynchronous Transfer Orbit Using a Solar Sail,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4, 2003, pp. 628-634. http://dx.doi.org/10.2514/2.5091