Plane circular restricted three-body problem using modified Newtonian dynamics
-
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.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
-
表 1 拉格朗日点与主天体的距离
Tab. 1 The distances between the Lagrangian points and the main celestial bodies
Li(a0 = 0) ρALi ρBLi Li(a0 = 0) ρALi ρBLi L1 0.85 0.15 L1 0.99 0.01 L2 1.17 0.17 L2 1.01 0.01 L3 0.99 1.99 L3 1.00 2.00 L4 1.00 1.00 L4 1.00 1.00 L5 1.00 1.00 L3 1.00 1.00 Li(a0 = 0.001) ρALi ρBLi Li(a0 = 0.001) ρALi ρBLi L1 0.85 0.150 L1 0.992 0.008 L2 1.17 0.170 L2 1.020 0.02 L3 0.99 1.990 L3 1.010 2.010 L4 1.011 1.095 L4 1.010 4.300 L3 1.011 1.095 L5 1.010 4.300 Li(a0 = 1) ρALi ρBLi Li(a0 = 1) ρALi ρBLi L1 0.87 0.13 L1 0.997 0.003 L2 1.46 0.46 L2 1.330 0.330 L3 1.34 2.34 L3 1.330 2.330 L4 1.33 3.06 L4 1.320 24.040 L3 1.33 3.06 L5 1.320 24.040 Li(a0 = 1 000) ρALi ρBLi Li(a0 = 1 000) ρALi ρBLi L1 0.898 0.102 L1 0.998 0.002 L2 5.989 4.989 L2 5.650 4.650 L3 5.870 5.870 L3 5.640 6.640 L4 5.660 16.900 L4 5.640 135.200 L3 5.660 16.900 L5 5.640 135.200 
下载: 导出CSV
-
[1] MILGROM M. A modification of the Newtonian dynamics: Implications for galaxies [J]. The Astrophysical Journal, 1983, 270: 371-383. [2] ARMANO M, AUDLEY H, BAIRD J, et al. LISA pathfinder performance confirmed in an open-loop configuration: Results from the free-fall actuation mode [J]. Physical Review Letters, 2019, 123: 111101. DOI: 10.1103/PhysRevLett.123.111101. [3] MCGAUGH S S, LELLI F, SCHOMBERT J M. Radial acceleration relation in rotationally supported galaxies [J]. Physical Review Letters, 2016, 117: 201101. DOI: 10.1103/PhysRevLett.117.201101. [4] BEVILS N, MAGUEIJO J, TRENKEL C, et al. MONDian three-body predictions for LISA Pathfinder [J]. Classical and Quantum Gravity, 2010, 27(21): 215014. [5] MILGROM M. Modified dynamics predictions agree with observations of the HI kinematics in faint dwarf galaxies contrary to the conclusions of Lo, Sargent and Young [J]. The Astrophysical Journal, 1994, 429: 540-544. [6] ZHAO H S, LI B J, BIENAYMÉ O. Modified Kepler’s law, escape speed, and two-body problem in modified Newtonian dynamics-like theories [J]. Physical Review D, 2010, 82: 103001. DOI: 10.1103/PhysRevD.82.103001. [7] 孙义燧, 周济林. 现代天体力学导论 [M]. 北京: 高等教育出版社, 2013. -
点击查看大图
图(2) / 表(1)
计量
- 文章访问数: 141
- HTML全文浏览量: 41
- PDF下载量: 4
- 被引次数: 0