%0 Generic %1 dmitrasinovic2015topological %A Dmitrašinović, V. %A Šuvakov, Milovan %D 2015 %K arxiv class-ph %R 10.1016/j.physleta.2015.06.026 %T Topological Dependence of Kepler's Third Law for Collisionless Periodic Three-Body Orbits with Vanishing Angular Momentum and Equal Masses %U http://arxiv.org/abs/1507.08096 %X We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical law. This is the first known relation between topological and kinematical properties of three-body systems. We have used these results to predict the periods of several sets of as yet undiscovered orbits, but the relation also indicates that the number of periodic three-body orbits with periods shorter than any finite number is countable.

@misc{dmitrasinovic2015topological, abstract = {We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical law. This is the first known relation between topological and kinematical properties of three-body systems. We have used these results to predict the periods of several sets of as yet undiscovered orbits, but the relation also indicates that the number of periodic three-body orbits with periods shorter than any finite number is countable.}, added-at = {2015-08-04T13:36:13.000+0200}, author = {Dmitrašinović, V. and Šuvakov, Milovan}, biburl = {https://www.bibsonomy.org/bibtex/28c18c3284bd0af1d63baf23e2c12be51/vch}, description = {Topological Dependence of Kepler's Third Law for Collisionless Periodic Three-Body Orbits with Vanishing Angular Momentum and Equal Masses}, doi = {10.1016/j.physleta.2015.06.026}, interhash = {60c579669c2a70d18e63c54abd82e039}, intrahash = {8c18c3284bd0af1d63baf23e2c12be51}, keywords = {arxiv class-ph}, note = {cite arxiv:1507.08096Comment: 9 pages, 4 figures}, timestamp = {2015-08-04T13:36:13.000+0200}, title = {Topological Dependence of Kepler's Third Law for Collisionless Periodic Three-Body Orbits with Vanishing Angular Momentum and Equal Masses}, url = {http://arxiv.org/abs/1507.08096}, year = 2015 }