{"paper":{"title":"On the dynamics of the three dimensional planetary systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"George Voyatzis, John D. Hadjidemetriou, Kyriaki I. Antoniadou","submitted_at":"2013-11-18T14:31:33Z","abstract_excerpt":"Over the last decades, there has been a tremendous increase in research on extrasolar planets. Many exosolar systems, which consist of a Star and two inclined Planets, seem to be locked in 4/3, 3/2, 2/1, 5/2, 3/1 and 4/1 mean motion resonance (MMR). We herewith present the model used to simulate three dimensional planetary systems and provide planar families of periodic orbits (PO), which belong to all possible configurations that each MMR has, along with their linear horizontal and vertical stability. We focus on depicting stable spatial families (most of them up to mutual inclination of $60^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4396","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"}