Out-of-plane Equilibrium Points in the Photogravitational Restricted Four-body Problem with Oblateness
Jagadish Singh, Aguda Ekele Vincent
Journal of Advances in Mathematics and Computer Science · pp. 1–15 · Published 9 Nov 2016
10.9734/BJMCS/2016/29698Abstract
The restricted four-body problem consists of an infinitesimal particle which is moving under the Newtonian gravitational attraction of three massive bodies, called primaries. The three bodies are moving in circles around their common centre of mass fixed at the origin of the coordinate system, according to the solution of Lagrange, where they are always at the vertices of an equilateral triangle. The fourth body does not affect the motion of the primaries. We consider that the primary body P1 is dominant and is a source of radiation while the other two small primaries P2 and P3 modeled as oblate spheroids have equal masses and oblateness coefficients. The out of equilibrium points of the problem are sought and we found that such critical points exist. These points lie in the xz - plane in symmetrical positions with respect to xy - plane. We investigate numerically the effects of radiation and oblateness on the positions of out-of-plane equilibrium points, their stability, as well as the regions allowed to motion of the infinitesimal body as determined by the zero velocity surface. It is found that radiation and oblateness have strong effects on the positions of the critical points. We examined the stability of these points and found that the out of plane equilibrium points are unstable.
Cited by 7
Jagadish Singh, Tyokyaa K. Richard · New Astronomy · 2022
Abdullah A. Ansari, Ziyad A. Alhussain · Journal of Dynamical Systems and Geometric Theories · 2019
R. R. Dewangan, A. Chakraborty, M. D. Pandey · AIP Conference Proceedings · 2023
Abdullah A. Ansari · Applied Mathematics and Nonlinear Sciences · 2017
R.R. Dewangan, A. Chakraborty, A. Narayan · New Astronomy · 2020
Aguda Ekele Vincent, Benson Ade Eniola Afere, Elbaz I. Abouelmagd · Archive of Applied Mechanics · 2025
Ziyad A. Alhussain · Journal of Taibah University for Science · 2019
Related research
- Assessment of Patients’ Knowledge of Radiation Exposure during Medical Imaging Procedures at Private Medical Radiography Centres in Ogun State, Nigeria — shares topic coverage
- Assessment of Cancer Risk from Fluorscopic Bile Duct Examinations at Sanjiwani Hospital, Gianyar — shares topic coverage
- Gastrointestinal Microflora in Radiation Injury and Countermeasure — shares topic coverage
- Photoprotection Comprising Oil Derived from Dromedary Camel Hump Fat — shares topic coverage
- Comparing and Modifying Eight Empirical Models of Snowmelt Using Data from Harp Experimental Station in Central Ontario — shares topic coverage
Article metrics
Real usage data collected on this platform.
0
Page views
0
PDF downloads
0
Outbound clicks
7
Citations
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
No views recorded yet.
Traffic sources
Referring site, by host.
No traffic recorded yet.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.