LINEAR STABILITY IN THE RESTRICTED THREE-BODY PROBLEM WITH OBLATE PRIMARIES

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This is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.

Year : 2026 | Volume : 15 | 02 | Page :
    By

    SHYAM NANDAN KUMAR,

  1. LECTURER, DEPARTMENT OF ENGINEERING MATHEMATICS, AL-KABIR POLYTECHNIC, MANGO, JAMSHEDPUR,, JHARKHAND, INDIA

Abstract

We present a study of the linear stability which is based on numerically we find that the critical mass ratio  of the primaries forms a smooth surface and absence that  c decrease as oblate parameter increase. In the restricted three-body problem the collinear points are unstable and equilateral triangular points are stable for the mass ratio . The numerical calculations give a thorough explanation of how changes in oblateness affect the areas of stable motion and the stability limits. In order to comprehend the fundamental mechanisms controlling the stability transition, the dependency of the critical mass ratio on the physical characteristics of the primary is also investigated. The equilateral triangle points in the traditional limited three-body problem stay stable for certain values of the mass ratio μ, whereas the collinear equilibrium points are known to be unstable. By taking into account the consequences of oblateness, the current study expands and validates these traditional findings. The results show that the range of mass ratios for which stable motion is feasible around the triangle points decreases with increasing oblateness. These findings advance our knowledge of celestial mechanics and might be helpful in analysing the motion of manmade and natural entities in satellite and planetary systems where oblateness cannot be disregarded.

Keywords: Restricted Three-Body Problem; Oblate Primaries; Stability; Libration Points; Stability Analysis; Coriolis Force; Centrifugal Force

How to cite this article:
SHYAM NANDAN KUMAR. LINEAR STABILITY IN THE RESTRICTED THREE-BODY PROBLEM WITH OBLATE PRIMARIES. Research & Reviews : Journal of Space Science & Technology. 2026; 15(02):-.
How to cite this URL:
SHYAM NANDAN KUMAR. LINEAR STABILITY IN THE RESTRICTED THREE-BODY PROBLEM WITH OBLATE PRIMARIES. Research & Reviews : Journal of Space Science & Technology. 2026; 15(02):-. Available from: https://journals.stmjournals.com/rrjosst/article=2026/view=246976


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Ahead of Print Subscription Review Article
Volume 15
02
Received 13/06/2026
Accepted 17/06/2026
Published 18/06/2026
Publication Time 5 Days
9

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