http://arxiv.org/abs/1705.00527
The famous three-body problem can be traced back to Isaac Newton in 1680s. In the 300 years since this “three-body problem” was first recognized, just three families of solutions had been found, until 2013 when \v{S}uvakov and Dmitra\v{s}inovi\’c [Phys. Rev. Lett. 110, 114301 (2013)] made a breakthrough to find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. In this letter, we numerically obtained 164 families of Newtonian planar periodic three-body orbits with equal mass and zero angular momentum, including the well-known Figure-eight family found by Moore in 1993, the 11 families found by \v{S}uvakov and Dmitra\v{s}inovi\’c in 2013, and 152 completely new families that have been never reported. With the definition of the average period $\bar{T} = T/k$, where $k$ is the length of the so-called free group element, these 164 families of the periodic three-body orbits suggest that there should exist the quasi Kepler’s third law $\bar{R}\propto |E|^{-1}= 0.56 \, \bar{T}^{2/3}$, where $\bar{R}$ is the mean of hyper-radius of the three-body system and $E$ is its total kinetic and potential energy, respectively. The movies and pictures of the periodic three-body orbits in the real space and the corresponding close curves in the “shape sphere” can be found via the website: this http URL
X. Li and S. Liao
Mon, 8 May 17
38/54
Comments: 16 pages, 11 tables, 2 figures