The influence of zonal harmonics on the location and stability of the CEPs of a Nigerian satellite in the generalized R3BP for EQ Pegasi system

Abstract

In this study, the generalized restricted three-body problem (R3BP) is applied to the EQ Pegasi binary system to investigate the effects of zonal harmonics on the motion of a satellite. Building on previous research, it enhances the standard potential function to represent the oblateness of the primaries by adding higher-order zonal harmonic terms  and  for both the primary and secondary bodies. After establishing the equations regulating motion, the collinear equilibrium points (CEPs) are found numerically using the Newton-Raphson technique. The Lyapunov stability theorem is used to assess their stability. According to the results, the addition of zonal harmonics somewhat changes the locations of the CEPs, with the equatorial bulge  having the most significant impact. The Jacobian constants indicate the energy levels at these moments, showing slightvariations across different scenarios. Even after adding higher-order zonal harmonics, stability evaluations show that the CEPs are still unstable, which aligns with classical R3BP findings. The necessity of active station-keeping in satellite mission planning, particularly close to these locations, is highlighted by this ongoing volatility. The study highlights the importance of considering higher-order gravitational effects while designing missions and analyzing stability, particularly for Nigerian spacecraft operating in complicated gravitational fields. The findings underscore the importance of advanced modeling in addressing the complex dynamics of binary star systems, thereby supporting earlier studies and offering valuable insights for future space missions.