Abstract

The outer version of the restricted elliptic three-body problem, where a perturbed body of negligible mass is far from two bodies of finite masses (the main and perturbing ones) close to one another and its orbit is located entirely outside the orbit of the perturbing body, is considered. The terms up to the fourth order inclusive in the ratio of the orbital semimajor axes of the perturbing and perturbed bodies are retained in the expansion of the perturbing function for the problem. Explicit analytical expressions for the doubly averaged perturbing function and its derivatives with respect to the orbital elements on the right-hand sides of the evolution equations are presented. The integrable cases of the doubly averaged elliptic problem are investigated: planar and orthogonal apsidal orbits. Qualitative differences compared to the inner (satellite) version are pointed out. The evolution system is numerically integrated in the general (nonintegrable) case for a number of special initial conditions that hypothetically correspond to the orbital evolution of low-mass bodies (planetesimals, low-mass planets) in the exoplanetary system GJ 3512.

中文翻译：

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受限椭圆双平均三体问题外版本中轨道的演化

摘要

约束椭圆三体问题的外部形式，其中一个可忽略质量的受扰物体远离两个彼此接近的有限质量的物体（主质量和受扰质量）彼此接近，并且其轨道完全位于扰动轨道之外身体，被认为。在该问题的摄动函数的扩展中，保留了摄动体和被摄动体的轨道半长轴之比的直至四阶的项。给出了双平均扰动函数及其导数相对于演化方程右侧轨道元素的显式解析表达式。研究了双平均椭圆问题的可积情况：平面和正交的两栖轨道。指出了与内部（卫星）版本相比的质量差异。在一般（不可积）的情况下，对于许多特殊的初始条件，该进化系统在数值上进行了积分，这些初始条件假设对应于系外行星系统GJ 3512中低质量物体（行星，低质量行星）的轨道演化。