{"paper":{"title":"Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.class-ph","authors_text":"Ana Hudomal, Ayumu Sugita, Mitsuru Shibayama, V. Dmitra\\v{s}inovi\\'c","submitted_at":"2017-05-10T12:36:02Z","abstract_excerpt":"We test numerically the recently proposed linear relationship between the scale-invariant period $T_{\\rm s.i.} = T |E|^{3/2}$, and the topology of an orbit, on several hundred planar Newtonian periodic three-body orbits. Here $T$ is the period of an orbit, $E$ is its energy, so that $T_{\\rm s.i.}$ is the scale-invariant (s.i.) period, or, equivalently, the period at unit energy $|E| = 1$. All of these orbits have vanishing angular momentum and pass through a linear, equidistant configuration at least once. Such orbits are classified in ten algebraically well-defined sequences. Orbits in each s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03728","kind":"arxiv","version":3},"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"}