{"paper":{"title":"Hill approximation in a restricted four-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jaime Burgos-Garcia, Marian Gidea","submitted_at":"2014-12-11T19:43:25Z","abstract_excerpt":"We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very small compared with the other two, m1 and m2, and we study the Hamiltonian system describing the motion of the massless particle in a neighborhood of m3. In a similar way to Hill approximation of the lunar problem, we perform a symplectic scaling, sending the two massive bodies to infinity, expanding the potential as a power series in m3, and taking the limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3775","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"}