Copyright: © the author(s), publisher and licensee Technoscience Academy. This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited International Journal of Scientific Research in Science and Technology Print ISSN: 2395-6011 | Online ISSN: 2395-602X (www.ijsrst.com) doi : https://doi.org/10.32628/IJSRST229658 395 Study of Stability of Equilibrium Points in The Pcr3bp on the Circumference of FEC Vikash Kumar 1 , Dr. K. B. Singh 2 , Dr. M. N. Haque 3 1 Research Scholar, University Department of Mathematics, B. R. A. Bihar University, Muzaffarpur, Bihar, India 2 P. G. Department of Physics, L. S. College, Muzaffarpur, B. R. A. Bihar University, Muzaffarpur, Bihar, India 3 P. G. Department of Mathematics, M. S. College, Motihari, B. R. A. Bihar University, Muzaffarpur, Bihar, India Article Info Volume 9, Issue 6 Page Number : 395-401 Publication Issue November-December-2022 Article History Accepted : 20 Nov 2022 Published : 07 Dec 2022 ABSTRACT The Three Body Problem The three body problem studies the motion of three masses whose gravitational attraction have an effect on each other. The dynamics of the three-body problem are essentially different from those of two bodies, because in the latter case, an analytical solution may be found that admits orbits in the form of conic sections. This problem has been studied at great length and is the basis of most of today’s orbit planning and trajectory design for satellites. However, the two-body problem is valid on close to a single massive body, compared to which the target body (the object whose motion is desired) is essentially a massless particle. In deep space, when there may be two or more massive bodies to affect the motion of our test particle, the two-body solution obviously fails. It then becomes essential to study the three- body problem. Keywords : RTBP, CRTBP, Three Body Problem. I. INTRODUCTION In the restricted three body problem (RTBP), the target mass/test particle is assumed to be of negligible mass when compared to the other two bodies (called primaries). The two primaries orbit around their common center of mass and their motion is unaffected by the test particle. Common examples of the RTBP are: a satellite in the Earth-Moon system, asteroids in the Sun-Jupiter system, etc. The most common alternative to the RTBP is the method of patched conics. Here, it is assumed that the test particle is only under the effect of one primary when in its vicinity, and under the effect of the other primary when close to it. This allows the solution in terms of two conic analytical solutions to the orbit, hence the name patched conics. Here we must introduce the concept of the sphere of influence - the sphere enclosing the second primary of comparatively less mass, in which the effects of the more massive primary can be “switched off”. At the point of entry into the sphere of influence, the position and velocity conditions of the two conic orbits are matched to ensure continuity. Obviously, it is less accurate than the three-body problem and only serves as a preliminary trajectory design tool. The RTBP has been the subject of constant study for the last few centuries. It has given rise to