Interplanetary interactions are the largest forces in our Solar System that disturb the planets from their elliptical orbits around the Sun, yet are weak (<10⁻³ Solar). Currently, these perturbations are computed in pairs using Hill’s model for steady-state, central forces between one circular and one elliptical ring of mass. However, forces between rings are not central. To represent interplanetary interactions, which are transient, time-dependent, and cyclical, we build upon Newton’s model of interacting point-mass pairs, focusing on circular orbits of the eight largest bodies. To probe general and evolutionary behavior, we present analytical and numerical models of the interplanetary forces and torques generated during the planetary interaction cycles. From symmetry, over a planetary interaction cycle, radial forces dominate while tangential forces average to zero. Our calculations show that orbital perturbations require millennia to quantify, but observations are only over ~165 years. Furthermore, these observations are compromised because they are predominantly made from Earth, whose geocenter occupies a complex, non-Keplerian orbit. Eccentricity and inclination data are reliable and suggest that interplanetary interactions have drawn orbital planes together while elongating the orbits of the two smallest planets. This finding is consistent with conservation principles governing the eight planets, which formed as a system and evolve as a system.

中文翻译：

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从其周期的对称性出发，对多分量系统中牛顿行星际点-质相互作用的约束

行星际相互作用是我们太阳系中最大的力，它们会干扰行星从其绕太阳的椭圆形轨道的运动，但作用力很弱（<10 ^-3太阳的）。目前，这些扰动是使用Hill模型成对计算的，该模型用于一个圆形质量环与一个椭圆形质量环之间的稳态，中心力。但是，环之间的力不是中心。为了表示瞬态，时间相关和周期性的行星际相互作用，我们建立在牛顿相互作用的点-质量对模型上，重点是八个最大天体的圆形轨道。为了探究一般和进化行为，我们提出了行星相互作用周期中产生的行星际力和转矩的分析和数值模型。从对称性来看，在行星相互作用周期中，径向力占主导，而切向力平均为零。我们的计算表明，轨道扰动需要数千年才能量化，但观测值仅约165年。此外，这些观测值之所以受到损害，是因为它们主要来自地球，地球的地球中心占据着一个复杂的非基普利耶轨道。偏心率和倾斜度数据可靠，表明行星际相互作用将轨道平面拉在一起，同时拉长了两个最小行星的轨道。这一发现与管理八个行星的守恒定律是一致的，八个行星形成为一个系统，然后演化为一个系统。