Periodic orbits for Newtonian planar three-body problem with unequal mass

Xiaoming LI, Yipeng JING and Shijun LIAO

Shanghai Jiaotong University, China

On September 13th 2017, we presented 1349 families of Newtonian periodic planar three-body orbits with unequal mass and zero angular momentum and the initial conditions in case of isosceles collinear configurations. These 1349 families of the periodic collisionless orbits can be divided into seven classes according to their geometric and algebraic symmetries. Among these 1349 families, 1223 families are entirely new, to the best of our knowledge. For more detail, please refer to arXiv:1709.04775. It was accepted by Publications of the Astronomical Society of Japan on April 23th, 2018. It was published online on May 21th, 2018(dio:10.1093/pasj/psy057)[PDF].

For the detailed characteristic parameters (such as the periods, the scale-invariant averaged periods, initial velocities and so on), the definitions and lengths of the so-called free group element (word) of each orbit, and the movies of these periodic orbits, please visit the websites:

(A) The free group element (word);

(B) The movies of periodic orbits in real space and on the shape sphere.

In our prior work, we reported 695 families of planar periodic orbits of the three-body system with equal mass and zero angular momentum in case of initial conditions with isosceles collinear configuration. More than 600 among them have been never reported, to the best of our knowledge. For more detail, please refer to arXiv:1705.00527v4 and website. It was accepted by Science China-Physics, Mechanics & Astronomy for the publication on July 11th 2017. It was published online on September 11th 2017 (Science China Physics, Mechanics & Astronomy, 60(12),2017,dio:10.1007/s11433-017-9078-5) [PDF].

On May 21th 2018, we report 234 collisionless periodic free-fall three-body orbits with different mass ratios. Eexcept for three periodic orbits have benn found before, 231 collisionless periodic orbits are entirely new. For more detail, please refer to arXiv:1805.07980 and website.

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