This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0<A1<1)？and ？A2(0<A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.
References
[1]
[1] Szebehely, V. (1967) Theory of Orbits. The Restricted Problem of Three-Bodies. Academic Press, New York.
[2]
Subbarao, P.V. and Sharma, R.K. (1975) A Note on the Stability of the Triangular Points of Equilibrium in the Restricted Three-Body Problem. Astronomy & Astrophysics, 43, 381-383.
[3]
Bhatnagar, K.B. and Chawla, J.M. (1977) The Effect of Oblateness of the Bigger Primary on Collinear Equilibrium Points in the Restricted Problem of Three Bodies. Celestial Mechanics and Dynamical Astronomy, 16, 129-136. https://doi.org/10.1007/BF01228595
[4]
Tsirogiannis, G.A., Douskos, C.N. and Perdios, E.A. (2006) Computation of the Lyapunov Orbits in the Photogravitational Restricted Three-Body Problem with Oblateness. Research in Astronomy and Astrophysics, 305, 389-398.
[5]
Mittal, A., Ahmad, I. and Bhatnagar, K.B. (2009) Periodic Orbits in the Photogravitational Restricted Problem with the Smaller Primary an Oblate Body. Astrophysics and Space Science, 323, 65-73. https://doi.org/10.1007/s10509-009-0038-2
[6]
Singh, J. (2011) Combined Effects of Perturbations, Radiation, and Oblateness on the Nonlinear Stability of Triangular Points in the Restricted Three-Body Problem. Astrophysics and Space Science, 332, 331-339. https://doi.org/10.1007/s10509-010-0546-0
[7]
Beevi, A.S. and Sharma, R.K. (2012) Oblateness Effect of Saturn on Periodic Orbits in the Saturn-Titan Restricted Three-Body Problem. Astrophysics and Space Science, 340, 245-261.
[8]
Abouelmagd, E.I. (2013) The Effect of Photogravitational Force and Oblateness in the Perturbed Restricted Three-Body Problem. Astrophysics and Space Science, 346, 51-69. https://doi.org/10.1007/s10509-013-1439-9
[9]
Jain, M. and Aggarwal, R. (2015) A Study of Non-Collinear Equilibrium Points in Restricted Three-Body Problem with Stokes Drag Effect When Smaller Primary Is an Oblate Spheroid. Astrophysics and Space Science, 358.
[10]
Zotos, E.E. (2016) Fractal Basins of Attraction in the Planar Circular Restricted Three-Body Problem with Oblateness and Radiation Pressure. Astrophysics and Space Science, 361. https://doi.org/10.1007/s10509-016-2769-1
[11]
Srivastava, V.K., Kumar, J. and Kushvah, B.S. (2017) Regularization of Circular Restricted Three-Body Problem Accounting Radiation Pressure and Oblateness. Astrophysics and Space Science, 362. https://doi.org/10.1007/s10509-017-3021-3
[12]
Farquhar, R.W. (1967) Lunar Communications with Libration-Point Satellites. Spacecraft and Rockets, 4, 1383-1384. https://doi.org/10.2514/3.29095
[13]
Dusek, H.M. (1966) Motion in the Vicinity of Equilibrium Points of a Generalized Restricted Three-Body Model. Prog. Astronaut. Rocket, 17, 37-54. https://doi.org/10.1016/B978-1-4832-2729-0.50009-0
[14]
McInnes, C.R., McDonald, A.J.C., Simmons, J.F.L. and MacDonald, E.W. (2004) Solar-Sail Parking in Restricted Three-Body Systems. Journal of Guidance, Control, and Dynamics, 17, 399-406. https://doi.org/10.2514/3.21211
[15]
Broschart, S.B. and Scheeres, D.J. (2005) Control of Hovering Spacecraft near Small Bodies: Application to Asteroid 25143 Itokwa. Journal of Guidance, Control, and Dynamics, 28, 343-354. https://doi.org/10.2514/1.3890
[16]
Morimoto, M.Y., Yamakawa, H. and Uesugi, K. (2007) Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem. Journal of Guidance, Control, and Dynamics, 30, 1563-1567. https://doi.org/10.2514/1.26771
[17]
Baig, S. and McInnes, C.R. (2008) Artificial Three-Body Equilibria for Hybrid Low-Thrust Propulsion. Journal of Guidance, Control and Dynamics, 31, 1644-1655. https://doi.org/10.2514/1.36125
[18]
Bombardelli, C. and Pelaez, J. (2011) On the Stability of Artificial Equilibrium Points in the Circular Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy, 109, 13-26. https://doi.org/10.1007/s10569-010-9317-z
[19]
Aliasi, G., Mengali, G. and Quarta, A. (2011) Artificial Equilibrium Points for a Generalized Sail in the Circular Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy, 110, 343-368. https://doi.org/10.1007/s10569-011-9366-y
[20]
Aliasi, G., Mengali, G. and Quarta, A. (2012) Artificial Equilibrium Points for a Generalized Sail in the Elliptic Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy, 114, 181-200. https://doi.org/10.1007/s10569-012-9425-z
[21]
Ranjana, K. and Kumar, V. (2013) On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three-Bodies. International Journal of Astronomy and Astrophysics, 3, 508-516. https://doi.org/10.4236/ijaa.2013.34059
[22]
Yang, H.W., Zeng, X.Y. and Baoyin, H. (2015) Feasible Region and Stability Analysis for Hovering around Elongated Asteroids with Low-Thrust. Research in Astronomy and Astrophysics, 15, 1571-1585. https://doi.org/10.1088/1674-4527/15/9/013
[23]
Lei, H.L. and Xu, B. (2017) Invariant Manifolds around Artificial Equilibrium Points for Low-Thrust Propulsion Spacecraft. Astrophysics and Space Science, 362, 75. https://doi.org/10.1007/s10509-017-3053-8
[24]
Bu, S., Li, S. and Yang, H. (2017) Artificial Equilibrium Points in Binary Asteroid Systems with Continuous Low-Thrust. Astrophysics and Space Science, 362, 8.
[25]
McCusky, S.W. (1963) Introduction to Celestial Mechanics. Addision-Wesley Publishing Company, New York.
