{"paper":{"title":"Envelopes for orbits around axially symmetric sources with spheroidal shape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Javier Ramos-Caro, Ronaldo S. S. Vieira","submitted_at":"2023-02-06T12:34:23Z","abstract_excerpt":"We introduce a method to obtain the envelopes of eccentric orbits in axially symmetric potentials, $\\Phi(R,z)$, endowed with $z$-symmetry of reflection. By making the transformation $z\\rightarrow a+\\sqrt{a^{2}+ z^{2}}$, with $a>0$, we compute the resulting mass density, referred here as the \\emph{effective density} $\\rho_{\\rm ef}(R,z;a)$, in order to calculate the envelopes $Z(R)$ of orbits in the meridional plane $(R,z)$. We find that they obey the approximated formula $Z(R)\\propto [\\Sigma_{\\rm ef}(R;a\\approx 0)]^{-1/3}$, where $\\Sigma_{\\rm ef}(R;a)$ is the integrated surface density associat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.02739","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.02739/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}