论文标题
具有重力以外力的行星系统
Planetary systems with forces other than gravitational forces
论文作者
论文摘要
最近的一篇文章（Eur。J.Plus 2022，137：99）得出了用于获得行星系统的离散算法。在这里，该算法用于获取具有与牛顿逆平方重力力不同的力的行星系统。 牛顿行星系统表现出规则的椭圆轨道，在这里证明，具有纯力的行星系统也很稳定并且具有常规轨道，而具有逆力的行星系统则不稳定并且没有常规轨道。但是，具有反向力的行星系统中的常规轨道偏离了通常的椭圆轨道，其旋转轨道的倾向倾向于具有三个或八个循环的轨道。牛顿的命题45在$ \ textit {principia {princionia} $中，这是由于对引力吸引力的附加吸引力引起的旋转轨道的，但是虽然额外的逆力稳定行星系统，但额外的反向力可以使行星系统具有足够的强度使行星系统稳定。
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square gravitational forces. A Newtonian planetary system exhibits regular elliptical orbits, and here it is demonstrated that a planetary system with pure inverse forces also is stable and with regular orbits, whereas a planetary system with inverse cubic forces is unstable and without regular orbits. The regular orbits in a planetary system with inverse forces deviate, however, from the usual elliptical orbits by having revolving orbits with tendency to orbits with three or eight loops. Newton's Proposition 45 in $\textit{Principia}$ for the Moon's revolving orbits caused by an additional attraction to the gravitational attraction is confirmed, but whereas the additional inverse forces stabilize the planetary system, the additional inverse cubic forces can destabilize the planetary system at a sufficient strength.
