{"paper":{"title":"The perihelion of Mercury advance calculated in Newton's theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.EP","authors_text":"Marek A. Abramowicz","submitted_at":"2012-11-22T13:57:46Z","abstract_excerpt":"Three radii are associated with a circle: the \"geodesic radius\" R_1 which is the distance from circle's center to its perimeter, the \"circumferential radius\" R_2 which is the length of the perimeter divided by 2 pi and the \"curvature radius\" R_3 which is circle's curvature radius in the Frenet sense. In the flat Euclidean geometry it is R_1 = R_2 = R_3, but in a curved space these three radii are different. I show that although Newton's dynamics uses Euclidean geometry, its equations that describe circular motion in spherical gravity always unambiguously refer to one particular radius of the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0264","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"}