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<p>Maintaining stable low-altitude lunar orbits (LLO) is crucial for long-term missions, but this remains a significant challenge due to complex dynamical perturbations. Previous studies have largely concentrated on identifying lunar frozen orbits, whereas this research presents a generalized framework for lunar orbiters that combines third-body gravitational effects from Earth, accounting for its elliptical and inclined orbit, with the Moon’s obliquity and gravitational harmonics, specifically the zonal (J₂) and TESSERAL (C₂₂) coefficients. Unlike well-known double-averaged approaches, where short-period oscillations must be later reconstructed using generating functions, the current non-simplified dynamical model considers them directly in the dynamics. This reveals that these oscillations produce a measurable secular drift in eccentricity and inclination. Numerical simulations confirm that the Moon’s axial tilt and the C₂₂ tesseral harmonic produce considerable secular drift in both eccentricity and inclination, effects that traditional models tend to underestimate. The results underscore the necessity of including the Moon’s unique gravitational signature (J<sub>2</sub> and C<sub>22</sub>) and short-period phenomena in mission design for low-altitude lunar satellites, such as navigation constellations and infrastructure-supporting orbiters. By addressing current gaps in lunar orbiter dynamics modeling, this comprehensive framework ensures accurate orbital longevity predictions and provides a solid foundation for sustainable operations in the cislunar environment.</p>

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Orbital evaluation of low lunar orbits with considering zonal J2 and tesseral C22 harmonics, moon’s obliquity, and earth gravity perturbations

  • 期刊论文

  • 发表日期：

    2026年7月4日

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  • Hamed Soleymani,
  • Majid Bakhtiari

摘要

Maintaining stable low-altitude lunar orbits (LLO) is crucial for long-term missions, but this remains a significant challenge due to complex dynamical perturbations. Previous studies have largely concentrated on identifying lunar frozen orbits, whereas this research presents a generalized framework for lunar orbiters that combines third-body gravitational effects from Earth, accounting for its elliptical and inclined orbit, with the Moon’s obliquity and gravitational harmonics, specifically the zonal (J₂) and TESSERAL (C₂₂) coefficients. Unlike well-known double-averaged approaches, where short-period oscillations must be later reconstructed using generating functions, the current non-simplified dynamical model considers them directly in the dynamics. This reveals that these oscillations produce a measurable secular drift in eccentricity and inclination. Numerical simulations confirm that the Moon’s axial tilt and the C₂₂ tesseral harmonic produce considerable secular drift in both eccentricity and inclination, effects that traditional models tend to underestimate. The results underscore the necessity of including the Moon’s unique gravitational signature (J2 and C22) and short-period phenomena in mission design for low-altitude lunar satellites, such as navigation constellations and infrastructure-supporting orbiters. By addressing current gaps in lunar orbiter dynamics modeling, this comprehensive framework ensures accurate orbital longevity predictions and provides a solid foundation for sustainable operations in the cislunar environment.