Out-of-plane Equilibrium Points in the Photogravitational Restricted Four-body Problem with Oblateness

2016 ◽  
Vol 15 (5) ◽  
pp. 1-15 ◽  
Author(s):  
Jagadish Singh ◽  
Aguda Vincent
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Out Of Plane ◽  
Four Body Problem ◽  
Plane Equilibrium

scholarly journals The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4

2021 ◽  
Vol 17 ◽  
pp. 1-11
Author(s):  
Jagadish Singh ◽  
Tyokyaa K. Richard
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Out Of Plane ◽  
Three Body ◽  
Plane Equilibrium

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

scholarly journals Comment on “Out-of-plane equilibrium points in the restricted three-body problem with oblateness (Research Note)”

2018 ◽  
Vol 614 ◽  
pp. A67 ◽  
Author(s):  
Nan Wu ◽  
Xuefeng Wang ◽  
Li-Yong Zhou
Keyword(s):  
Potential Function ◽  
Body Problem ◽  
Equilibrium Points ◽  
Point Of View ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Physical Point ◽  
Out Of Plane ◽  
Three Body ◽  
Plane Equilibrium

Douskos & Markellos (2006, A&A, 446, 357) first reported the existence of the out-of-plane equilibrium points in restricted three-body problem with oblateness. This result deviates significantly from the intuitive physical point of view that there is no other force that can balance the combined gravitation in Z direction. In fact, the out-of-plane equilibrium in that model is illusory and we prove here that such equilibrium points arise from the improper application of the potential function.

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