E-ISSN 1658-7073 | ISSN 1658-6638
 

Original Research 


The Photogravitational Circular Restricted Four-body Problem with Variable Masses

Abdullah A. Ansari.

Abstract
In this paper, we examine the stability of the equilibrium points in the photogravitational circular restricted four-body problem by considering all the masses are varying with time, one of the three masses are taken as source of radiation pressure and all the masses are placed at the vertices of an equilateral triangle. We derive the equations of motion under the effect of solar radiation pressure by using the Meshcherskii transformations. We have plotted the equilibrium points, time series, surfaces of motion of infinitesimal body, Poincare surface of sections and Newton-Raphson basin of attraction. Here five equilibrium points are found but it is ten in the classical case. From the time series, it is observed that the orbit will not be periodic. The surfaces of motion of the infinitesimal body are studied in the space. The Poincare surface of section is in the discrete type of pattern. The convergence of the equilibrium points is studied by the Newton-Raphson basin of attraction. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

Key words: Radiation Pressure; variable masses; equilateral triangle; Poincare surface of sections; Newton-Raphson basin of attraction.


 
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Pubmed Style

Abdullah A. Ansari. The Photogravitational Circular Restricted Four-body Problem with Variable Masses. JEAS. 2016; 3(2): 30-38. doi:10.5455/jeas.2016110105


Web Style

Abdullah A. Ansari. The Photogravitational Circular Restricted Four-body Problem with Variable Masses. http://jecasmu.org/?mno=91826 [Access: January 06, 2021]. doi:10.5455/jeas.2016110105


AMA (American Medical Association) Style

Abdullah A. Ansari. The Photogravitational Circular Restricted Four-body Problem with Variable Masses. JEAS. 2016; 3(2): 30-38. doi:10.5455/jeas.2016110105



Vancouver/ICMJE Style

Abdullah A. Ansari. The Photogravitational Circular Restricted Four-body Problem with Variable Masses. JEAS. (2016), [cited January 06, 2021]; 3(2): 30-38. doi:10.5455/jeas.2016110105



Harvard Style

Abdullah A. Ansari (2016) The Photogravitational Circular Restricted Four-body Problem with Variable Masses. JEAS, 3 (2), 30-38. doi:10.5455/jeas.2016110105



Turabian Style

Abdullah A. Ansari. 2016. The Photogravitational Circular Restricted Four-body Problem with Variable Masses. Journal of Engineering and Applied Sciences, 3 (2), 30-38. doi:10.5455/jeas.2016110105



Chicago Style

Abdullah A. Ansari. "The Photogravitational Circular Restricted Four-body Problem with Variable Masses." Journal of Engineering and Applied Sciences 3 (2016), 30-38. doi:10.5455/jeas.2016110105



MLA (The Modern Language Association) Style

Abdullah A. Ansari. "The Photogravitational Circular Restricted Four-body Problem with Variable Masses." Journal of Engineering and Applied Sciences 3.2 (2016), 30-38. Print. doi:10.5455/jeas.2016110105



APA (American Psychological Association) Style

Abdullah A. Ansari (2016) The Photogravitational Circular Restricted Four-body Problem with Variable Masses. Journal of Engineering and Applied Sciences, 3 (2), 30-38. doi:10.5455/jeas.2016110105