Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits
We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon's periodic orbits with values of the topological exponent k ranging from k=3 to k=58 to plot the angular momentum L as a function of the period T, with both L and T rescaled to energy E=-0.5. Upon plotting L(T/k) we...
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| Veröffentlicht in: | Physical review letters 2016-02, Vol.116 (6), p.064301-064301, Article 064301 |
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| creator | Jankovic, Marija R Dmitrasinovic, V |
| description | We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon's periodic orbits with values of the topological exponent k ranging from k=3 to k=58 to plot the angular momentum L as a function of the period T, with both L and T rescaled to energy E=-0.5. Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. This regularity supports Hénon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable. |
| doi_str_mv | 10.1103/PhysRevLett.116.064301 |
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Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. 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Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. 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Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. This regularity supports Hénon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable.</abstract><cop>United States</cop><pmid>26918993</pmid><doi>10.1103/PhysRevLett.116.064301</doi><tpages>1</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Angular momentum Functions (mathematics) Orbits Plotting Polynomials Satellites Standard deviation Topology |
| title | Angular Momentum and Topological Dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-Hénon Family of Periodic Three-Body Orbits |
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