华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (1): 53-59.doi: 10.3969/j.issn.1000-5641.201922016

• 物理学与电子学 • 上一篇    下一篇

修正牛顿动力学中的平面圆形限制性三体问题

毕艳芳, 王焘*()   

  1. 华东师范大学 物理与电子科学学院, 上海　200241
  • 收稿日期:2019-10-08 出版日期:2021-01-25 发布日期:2021-01-28
  • 通讯作者: 王焘 E-mail:twang@phy.ecnu.edu.cn
  • 基金资助:
    国家自然科学基金(91536218)

Plane circular restricted three-body problem using modified Newtonian dynamics

Yanfang BI, Tao WANG*()   

  1. School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China
  • Received:2019-10-08 Online:2021-01-25 Published:2021-01-28
  • Contact: Tao WANG E-mail:twang@phy.ecnu.edu.cn

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摘要：

修正牛顿动力学理论是暗物质理论的一个主要竞争者. 该理论不仅含有万有引力常数, 还含有加速度常数. 基于二体问题的圆形轨道解, 研究了修正牛顿动力学理论中的平面圆形限制性三体问题, 得到了与牛顿动力学理论中类似的拉格朗日点和希尔曲线; 发现拉格朗日点的位置和数目、希尔域的分布都随加速度常数和主天体质量而变化. 这些结果为检验修正牛顿动力学理论提供了新的可能性.

关键词: 修正牛顿动力学, 拉格朗日点, 希尔曲线

Abstract:

Modified Newtonian dynamics is a major competitor of dark matter theory and contains not only a gravitational constant but also an acceleration constant. Based on a circular orbit solution for a two-body problem, this paper is devoted to studying a plane circular restricted three-body problem using modified Newtonian dynamics. We work out the Lagrangian points and the Hill curves akin to those observed in Newtonian dynamics. In contrast, however, the location and number of Lagrangian points, as well as the profile of the Hill region, are dependent on both the acceleration constant and the mass ratio of the main celestial bodies. These findings reveal a new avenue for testing modified Newtonian dynamics.

Key words: modified Newtonian dynamics, Lagrangian point, Hill curve

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