准双椭圆三体模型

Quasi-bielliptic three-body problem

本文我们提出了日地月准双椭圆三体问题(Quasi-Bielliptic Problem,QBEP)模型.该模型假设月球绕地球的轨道为受太阳引力摄动影响的准椭圆轨道,而地月质心绕太阳的轨道为严格的椭圆.此外我们认为日地月三个天体运行在同一轨道平面内.我们推导了月球准椭圆轨道的一阶展开解析表达式需要满足的微分方程,并利用我们提出的计算方法,将微分方程问题转化为线性方程组问题来进行求解.通过比较数值积分结果,我们方法的有效性得到了验证.而后我们详细比较了该解析结果与准双圆模型的差异,同时讨论了两个基准椭圆轨道偏心率对解析结果的影响.

In this paper,we first proposed the Quasi-Bielliptic Problem(QBEP)in the Sun-Earth-Moon three-body problem.In this model,we assume that the Moon revolves around the Earth in a quasi-elliptic orbit perturbed by the solar gravity,whereas the orbit of the Earth-Moon barycenter around the Sun has been known to be strictly elliptic.In addition,we assumed that these three celestial bodies move in the same orbital plane.The differential equations for the first-order analytical expansion of the lunar quasi-elliptic orbit were derived.Using a computational approach,these differential equations were transformed into a system of linear equations and then solved numerically.The validity of our semianalytical result was testified by comparing with the results of numerical integration.The differences between analytical results of the QBEP and the QBEP have been discussed in detail.The influences of these two eccentricities on analytical results were also investigated.