The present work studies the stability condition of central control artificial equilibrium points of the planar circular restricted problem of 2 + 2 bodies (PCRP2 + 2B) and also its variant when the shape of larger mass is taken to be an oblate spheroid. We find that the paper will be of great application in choosing an artificial equilibrium point (AEP) in the neighbourhood of numerous planets e.g. Jupiter or the bodies which provide a model of the problem studied. The minimum thrust will save a quantum of energy to be applied to have an arbitrary point as a chosen starter. For solar sailing and magnetic force this minimum thrust will be of great use.
References
[1]
Whipple, A.L. and Szebehely, V. (1983) The Restricted Problem of n+1 Bodies. Celestial Mechanics, 32, 137-144. https://doi.org/10.1007/BF01231121
[2]
Duboshin, G.N. (1982) On Regular Solution in the Problem of Two Rigid Bodies. Celestial Mechanics, 27, 267-284. (In French)
[3]
Duboshin, G.N. (1984) The Problem of Three Bodies. Celestial Mechanics and Dynamical Astronomy, 33, 31-47.
[4]
Milani, A. and Nobili, A.M. (1988) Instability of the 2+2 Body Problem. Celestial Mechanics, 41, 153-160. https://doi.org/10.1007/BF01238759
[5]
Whipple, A.L. (1984) Equilibrium Solutions of the Restricted Problem of 2+2 Bodies. Celestial Mechanics, 33, 271-294. https://doi.org/10.1007/BF01230509
[6]
Tsiolkovsky, K. (1936) In Extension of Man into Outer Space, 2, United Technical Press. (In Russian)
[7]
Tsander, K. (1967) From a Scientific Heritage, NASA Technical Translation TTF-541.
[8]
Mclnnes, C.R. (1999) Solar Sailing Technology, Dynamics and Mission Application. Springer-Praxis, London.
[9]
Subba Rao, P.V. and Sharma, R.K. (1997) Effect of Oblateness on the Non Linear Stability of L4 in the Restricted Three Body Problem. Celestial Mechanics and Dynamical Astronomy, 63, 291-312.
[10]
Bombardelli, C. and Peláez, J. (2011) On the Stability of Artificial Equilibrium Points in the Circular Restricted Problem of Three Bodies. Celestial Mechanics & Dynamical Astronomy, 109, 13-26. https://doi.org/10.1007/s10569-010-9317-z
[11]
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
