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<p>Lunar gravitation is one of the primary perturbative forces affecting Earth-centered objects, such as satellites and space debris. Accurately modeling these perturbations is critical for precise orbit propagation, especially for high-altitude orbit objects. Besides stronger perturbation, the mean motion of high-altitude orbit object becomes comparable to lunar mean motion, calling for the need to treat the lunar mean motion as a second fast-varying argument. Analytically processing the perturbation function with two fast-varying arguments can be handled by elliptical expansion, which may lead to limited accuracy. To address this, we propose a double-averaged analytical solution for lunar gravitational perturbation, by expanding the perturbation function using a general form and therefore can be truncated up to any order at the user’s discretion. Numerical tests show that our model, when applied to highly eccentric <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((e\in [0.1, 0.6])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>e</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.6</mn> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> orbits, outperforms traditional single-averaged methods and low-order Legendre expansions. This solution is especially useful for analytical orbit propagation of space debris, with a propagation error of about 1–100&#xa0;m and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({10}^{-4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> degree in ten days.</p>

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General form of double-averaged solution of lunar gravitational perturbation on highly eccentric orbits

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • ShuLei Zhang,
  • Jingshi Tang

摘要

Lunar gravitation is one of the primary perturbative forces affecting Earth-centered objects, such as satellites and space debris. Accurately modeling these perturbations is critical for precise orbit propagation, especially for high-altitude orbit objects. Besides stronger perturbation, the mean motion of high-altitude orbit object becomes comparable to lunar mean motion, calling for the need to treat the lunar mean motion as a second fast-varying argument. Analytically processing the perturbation function with two fast-varying arguments can be handled by elliptical expansion, which may lead to limited accuracy. To address this, we propose a double-averaged analytical solution for lunar gravitational perturbation, by expanding the perturbation function using a general form and therefore can be truncated up to any order at the user’s discretion. Numerical tests show that our model, when applied to highly eccentric \((e\in [0.1, 0.6])\) ( e ∈ [ 0.1 , 0.6 ] ) orbits, outperforms traditional single-averaged methods and low-order Legendre expansions. This solution is especially useful for analytical orbit propagation of space debris, with a propagation error of about 1–100 m and \({10}^{-4}\) 10 - 4 degree in ten days.