{"paper":{"title":"Angular momentum and topological dependence of Kepler's Third Law in the Broucke-Hadjidemetriou-H\\'enon family of periodic three-body orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Marija R. Jankovi\\'c, Veljko Dmitra\\v{s}inovi\\'c","submitted_at":"2016-04-28T09:42:27Z","abstract_excerpt":"We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Henon'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 $E=-\\frac12$. Upon plotting $L(T/k)$ we find that all our solutions fall on a curve that is virtually indiscernible by naked eye from the $L(T)$ curve for non-satellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is $\\sigma = 0.13$. This regularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08358","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}