Scholarlink

<p>Lunar artificial satellite theories differ in important aspects from analogous solutions for Earth satellites due to more uneven nature of the Moon’s gravity, pronounced third-body perturbations, and the absence of atmospheric drag. Existing lunar satellite theories typically incorporate only few gravity spherical harmonics and Hill’s approximation of the third-body disturbing function. Despite these simplifications, they provide semi-analytical solutions and require numerical propagation, thus limiting their applications. In this work, a fully analytic theory for lunar satellites is developed using generalized formulae that enable inclusion of spherical harmonics up to an arbitrary degree and order. The complete gravity and third-body disturbing functions are jointly treated as dominant perturbations to the Keplerian Hamiltonian, which is fully normalized to second order through a sequence of three canonical transformations. This formulation ensures broad applicability of the resulting theory across a wide range of lunar orbits, from low to high altitudes. The gravity harmonics are comprehensively addressed in Part-I of this study, with short- and medium-period terms developed up to first order, and long-period and secular terms up to second order. For third-body perturbations, secular terms are developed up to first order here and periodic effects (including those originating from the coupling between gravity and third-body terms) will be explicitly treated in Part-II. The original contributions of this work in Part-I include the derivation of novel formulae for first-order short-periodic variations induced by an arbitrary gravity harmonic with no singularities for resonant orbits, second-order secular and long-periodic variations that capture the coupling effects between any pair of gravity harmonics, and first-order secular variations resulting from the complete third-body disturbing function. The accuracy of this theory and the impact of coupling effects among gravity harmonics are evaluated by comparing analytically-propagated lunar satellite ephemerides with numerically integrated orbits.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Lunar Satellite Analytic Theory with Complete Gravity and Third-Body Perturbations

  • 期刊论文

  • 发表日期：

    2026年3月9日

查看全文
  • Bharat Mahajan

摘要

Lunar artificial satellite theories differ in important aspects from analogous solutions for Earth satellites due to more uneven nature of the Moon’s gravity, pronounced third-body perturbations, and the absence of atmospheric drag. Existing lunar satellite theories typically incorporate only few gravity spherical harmonics and Hill’s approximation of the third-body disturbing function. Despite these simplifications, they provide semi-analytical solutions and require numerical propagation, thus limiting their applications. In this work, a fully analytic theory for lunar satellites is developed using generalized formulae that enable inclusion of spherical harmonics up to an arbitrary degree and order. The complete gravity and third-body disturbing functions are jointly treated as dominant perturbations to the Keplerian Hamiltonian, which is fully normalized to second order through a sequence of three canonical transformations. This formulation ensures broad applicability of the resulting theory across a wide range of lunar orbits, from low to high altitudes. The gravity harmonics are comprehensively addressed in Part-I of this study, with short- and medium-period terms developed up to first order, and long-period and secular terms up to second order. For third-body perturbations, secular terms are developed up to first order here and periodic effects (including those originating from the coupling between gravity and third-body terms) will be explicitly treated in Part-II. The original contributions of this work in Part-I include the derivation of novel formulae for first-order short-periodic variations induced by an arbitrary gravity harmonic with no singularities for resonant orbits, second-order secular and long-periodic variations that capture the coupling effects between any pair of gravity harmonics, and first-order secular variations resulting from the complete third-body disturbing function. The accuracy of this theory and the impact of coupling effects among gravity harmonics are evaluated by comparing analytically-propagated lunar satellite ephemerides with numerically integrated orbits.