Abstract

The influence of the planets of the Solar System on the precession of the orbit of Mercury is investigated in the framework of classical mechanics. The influence of each planet on the motion of Mercury is calculated in the context of a restricted problem of three bodies: the Sun, the planet in question, and Mercury. It is demonstrated that the average shift of the perihelion of the orbit of Mercury determined in the context of a planar circular restricted three-body problem is 556.5″ per century and agrees with the observed shift (570″) with a relative accuracy of 2.5%. It is also demonstrated that the observed perihelion shift of Mercury features oscillatory components with a total amplitude up to 20″ and periods from several years to several decades. Owing to the presence of these components, the perihelion shift rate calculated based on observations conducted for several tens or even hundreds of years may differ considerably from the true average rate. This is likely the reason why the calculated average perihelion shift rate is not completely consistent with observational data.

中文翻译：

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水星轨道的进动

摘要

在经典力学的框架内研究了太阳系行星对水星轨道进动的影响。每个行星对水星运动的影响是在三个物体的有限问题的背景下计算出来的：太阳，所讨论的行星和水星。结果表明，在平面圆形受限三体问题的背景下确定的水星轨道近日点的平均位移为每世纪556.5英寸，并且与观察到的位移（570英寸）相符，相对精度为2.5％ 。还表明，观察到的水星近日点偏移具有振荡成分，其总振幅高达20英寸，周期从几年到几十年不等。由于这些成分的存在，根据几十年甚至几百年的观测结果计算出的近日点偏移率可能与实际平均率有很大差异。这可能是计算出的平均近日平移率与观测数据不完全一致的原因。