Abstract

In this analytical study, we have presented a new type of solving procedure with the aim to obtain the coordinates of small mass m, which moves around primary M_Sun, referred to non-inertial frame of restricted two-body problem (R2BP) with a modified potential function (taking into account the variable velocity \(\vec{V}\) of central body M_Sun motion in a prescribed fixed direction) instead of a classical potential function for Kepler’s formulation of R2BP. Meanwhile, system of equations of motion has been successfully explored with respect to the existence of an analytical way of presenting the solution in polar coordinates {r(t), φ(t)}. We have obtained an analytical formula for function t = t(r) via an appropriate elliptic integral. Having obtained the inversed dependence r = r(t), we can obtain the time dependence φ = φ(t). Also, we have pointed out how to express components of solution (including initial conditions) from cartesian to polar coordinates as well.

中文翻译：

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研究中心体运动在指定固定方向上的变速 $$\vec{\mathbf{V}}$$ 情况下的非惯性 R2BP

摘要

在这项分析研究中，我们提出了一种新型的求解过程，旨在获得小质量m的坐标，该小质量 m 围绕初级M _Sun移动，称为限制二体问题 (R2BP) 的非惯性系，其中修改后的势函数（考虑到中心体M_{太阳在规定固定方向上运动的可变速度}\(\vec{V}\)）而不是开普勒R2BP 公式中的经典势函数。同时，关于极坐标{ r ( t )，φ ( t )}解的解析方法的存在性，已经成功地探索了运动方程组。我们通过适当的椭圆积分获得了函数t  =  t ( r ) 的解析公式。获得逆相关性r  =  r ( t ) 后，我们可以获得时间相关性φ  =  φ ( t )。此外，我们还指出了如何将解的分量（包括初始条件）从笛卡尔坐标表达为极坐标。