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Stability of the Moons Orbits in Solar System in the Restricted Three-Body Problem

机译:受限制的三体问题中太阳系中月球轨道的稳定性

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摘要

We consider the equations of motion of three-body problem in aLagrange form(which means a consideration of relative motions of 3 bodies in regard to each other). Analyzing such a system of equations, we consider in detail the case of moon’s motion of negligible massm3around the 2nd of two giant-bodiesm1,m2(which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. Under assumptions of R3BP, we obtain the equations of motion which describe the relative mutual motion of the centre of mass of 2nd giant-bodym2(planet) and the centre of mass of 3rd body (moon) with additional effective massξ·m2placed in that centre of massξ·m2+m3, whereξis the dimensionless dynamical parameter. They should be rotating around their common centre of masses on Kepler’s elliptic orbits. For negligible effective massξ·m2+m3it gives the equations of motion which should describe aquasi-ellipticorbit of 3rd body (moon) around the 2nd bodym2(planet) for most of the moons of the planets in Solar System.
机译:我们以拉格朗日形式考虑三体问题的运动方程(这意味着要考虑三个体相对于彼此的相对运动)。通过分析这样的方程组,我们详细考虑了绕着两个巨型物体m1,m2(围绕开普勒轨迹的共同质心旋转)中的第二个绕着可忽略质量m3的月亮运动的情况。小于中心体的质量。在R3BP的假设下,我们获得了运动方程,该运动方程描述了第二大体m2(行星)的质心与第三体(月球)的质心的相对相互运动,并在该中心放置了附加有效质量ξ·m2的质量ξ·m2 + m3,其中ξ是无量纲的动力学参数。它们应该绕开普勒椭圆轨道上共同的重心旋转。对于可忽略不计的有效质量ξ·m2 + m3,它给出了运动方程,该方程应描述太阳系中大多数行星月球围绕第二体m2(行星)的第三体(月球)的准椭圆轨道。

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