De Saedeleer Bernard, Henrard Jacques
Département de Mathématique, University of Namur, Rempart de la Vierge, 8, B-5000 Namur, Belgium.
Ann N Y Acad Sci. 2004 May;1017:434-49. doi: 10.1196/annals.1311.025.
The dynamics of an artificial satellite of the moon is quite different from the dynamics of an artificial satellite of the Earth. Indeed, the C(22) term is only 1/10 of the J(2) term, and the effect of the Earth on the lunar satellite is much larger than the effect of the Moon on a terrestrial satellite. The method used here is the Lie method for averaging the Hamiltonian of the problem, in canonical variables. The solution is developed in powers of the small factors linked to J(2) and C(22). Short period terms (linked to l, the mean anomaly) are eliminated first, and then the long period terms (linked to g, the mean argument of the periaster, and to h, the longitude of the ascending node), which finally gives the secular motion. The results are obtained in a closed form, without any series developments in eccentricity or inclination. Thus, the solution applies for a wide range of values, except for few isolated critical values. The results are only very preliminary. As a side result, we were able to check the solution given by Kozai for the effect of the J(2) term on an artificial satellite.
月球人造卫星的动力学与地球人造卫星的动力学截然不同。实际上，C(22)项仅为J(2)项的1/10，且地球对月球卫星的影响远大于月球对地球卫星的影响。这里使用的方法是在正则变量中对问题的哈密顿量进行平均的李方法。解是按照与J(2)和C(22)相关的小因子的幂次展开的。首先消除短周期项（与平近点角l相关），然后消除长周期项（与近心点平经度g和升交点经度h相关），最终得到长期运动。结果以封闭形式给出，无需在偏心率或倾角上进行任何级数展开。因此，该解适用于广泛的值范围，除了少数孤立的临界值。这些结果只是非常初步的。作为附带结果，我们能够检验科扎伊给出的J(2)项对人造卫星影响的解。
