论文标题
修改动力学中的三体问题
Three-Body Problem in Modified Dynamics
论文作者
论文摘要
在修改动力学模型中，三体问题的一般特性进行了研究。结果表明，该模型中的三体问题与牛顿动力学中的类似问题共享了一些字符。此外，对于这种类型的扩展重力，通过分析解决了平面限制的三体问题，并且证明在某些条件下，通常发生在银河系和外层面尺度上，轨道大约$ l_ {4} $和$ l_ {5} $ lagrange点稳定。此外，还提供了一个代码来比较牛顿和修改的动力学下的受限三体问题中轨道的行为。基于此代码的轨道集成在这两个动力学下显示出对比鲜明的轨道行为，并以定性方式表现出，与牛顿重力相比，修饰动力学的弹性速率较小。这些结果可以帮助我们搜索延长重力的观察性特征。
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar restricted three-body problem is solved analytically for this type of extended gravity and it is proved that under certain conditions, which generally happen at galactic and extragalactic scales, the orbits around $L_{4}$ and $L_{5}$ Lagrange points are stable. Furthermore, a code is provided to compare the behavior of orbits in the restricted three-body problem under Newtonian and modified dynamics. Orbit integrations based on this code show contrasting orbital behavior under the two dynamics and specially exhibit in a qualitative way that the rate of ejections is smaller in the modified dynamics compared to Newtonian gravity. These results could help us to search for observational signatures of extended gravities.
