{"id":"https://openalex.org/W7204772963","doi":"https://doi.org/10.5281/zenodo.22206044","title":"The Stars' Differential Equations: A Narrative Review of Stellar Structure, from Eddington's Radiative Equilibrium to the Polytrope's Numerical Solutions","display_name":"The Stars' Differential Equations: A Narrative Review of Stellar Structure, from Eddington's Radiative Equilibrium to the Polytrope's Numerical Solutions","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204772963","doi":"https://doi.org/10.5281/zenodo.22206044"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22206044","doi":"https://doi.org/10.5281/zenodo.22206044","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22206044","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},"volume":null,"type":"review","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22206044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120933120","display_name":"Zen Revista","orcid":"https://orcid.org/0009-0007-6299-2008","observed_orcids":["https://orcid.org/0009-0007-6299-2008"]},"institutions":[{"id":"https://openalex.org/I4210124990","display_name":"Faculdades Guarulhos","ror":"https://ror.org/02s6maw65","country_code":"BR","type":"other","lineage":["https://openalex.org/I4210124990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Revista, Zen","raw_affiliation_strings":["Faculdade de Guarulhos (FG)"],"raw_orcid":"https://orcid.org/0009-0007-6299-2008","affiliations":[{"raw_affiliation_string":"Faculdade de Guarulhos (FG)","institution_ids":["https://openalex.org/I4210124990"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148798901","display_name":"10 ASTRO","orcid":"https://orcid.org/0009-0007-6299-2008","observed_orcids":["https://orcid.org/0009-0007-6299-2008"]},"institutions":[{"id":"https://openalex.org/I4210124990","display_name":"Faculdades Guarulhos","ror":"https://ror.org/02s6maw65","country_code":"BR","type":"other","lineage":["https://openalex.org/I4210124990"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"ASTRO, 10","raw_affiliation_strings":["Faculdade de Guarulhos (FG)"],"raw_orcid":"https://orcid.org/0009-0007-6299-2008","affiliations":[{"raw_affiliation_string":"Faculdade de Guarulhos (FG)","institution_ids":["https://openalex.org/I4210124990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210124990"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.7964000105857849,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.7964000105857849,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12836","display_name":"History and Developments in Astronomy","score":0.19580000638961792,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14475","display_name":"History of Science and Medicine","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stellar-structure","display_name":"stellar structure","score":0.996999979019165},{"id":"https://openalex.org/keywords/stellar-structure-equations","display_name":"stellar structure equations","score":0.640999972820282},{"id":"https://openalex.org/keywords/chandrasekhar","display_name":"Chandrasekhar","score":0.8149999976158142},{"id":"https://openalex.org/keywords/mass-luminosity-relation","display_name":"mass-luminosity relation","score":0.8960000276565552},{"id":"https://openalex.org/keywords/stellar-energy-production","display_name":"stellar energy generation","score":0.7319999933242798},{"id":"https://openalex.org/keywords/hansen","display_name":"Hansen","score":0.5590000152587891},{"id":"https://openalex.org/keywords/main-sequence-stars","display_name":"main-sequence stars","score":0.7639999985694885},{"id":"https://openalex.org/keywords/red-giants","display_name":"red giants","score":0.925000011920929},{"id":"https://openalex.org/keywords/stellar-evolutionary-tracks","display_name":"evolutionary tracks","score":0.8949999809265137},{"id":"https://openalex.org/keywords/history-of-computing","display_name":"history of computing","score":0.5860000252723694},{"id":"https://openalex.org/keywords/inverse-problems","display_name":"inverse problems","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.6560999751091003},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6132000088691711},{"id":"https://openalex.org/C101638190","wikidata":"https://www.wikidata.org/wiki/Q6311","display_name":"Stellar atmosphere","level":3,"score":0.4381999969482422},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3903999924659729},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C199033989","wikidata":"https://www.wikidata.org/wiki/Q1318295","display_name":"Narrative","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3675000071525574},{"id":"https://openalex.org/C110472602","wikidata":"https://www.wikidata.org/wiki/Q6472","display_name":"Stellar evolution","level":3,"score":0.3668000102043152},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.3506999909877777},{"id":"https://openalex.org/C137650753","wikidata":"https://www.wikidata.org/wiki/Q6495","display_name":"Stellar structure","level":4,"score":0.3452000021934509},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C60056205","wikidata":"https://www.wikidata.org/wiki/Q691914","display_name":"Opacity","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3140000104904175},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C56956389","wikidata":"https://www.wikidata.org/wiki/Q3450","display_name":"Main sequence","level":3,"score":0.31200000643730164},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22206044","doi":"https://doi.org/10.5281/zenodo.22206044","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22206044","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.5281/zenodo.22206045","doi":"https://doi.org/10.5281/zenodo.22206045","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22206045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22206044","doi":"https://doi.org/10.5281/zenodo.22206044","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22206044","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"JournalArticle"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204664395","https://openalex.org/W2558544441","https://openalex.org/W1497063784","https://openalex.org/W1538231679","https://openalex.org/W2020200697","https://openalex.org/W3011621017","https://openalex.org/W4376866326","https://openalex.org/W2340023929","https://openalex.org/W7028347316","https://openalex.org/W3004330187"],"abstract_inverted_index":{"Stellar":[0],"structure":[1],"is":[2,31,120,126,152],"physics'":[3],"oldest":[4],"inverse":[5],"problem:":[6],"given":[7],"a":[8,19,139],"star's":[9],"light,":[10],"recover":[11],"the":[12,23,36,52,60,69,81,84,99,108,112,116,127,153],"gas":[13],"ball's":[14],"equations.":[15],"This":[16],"article":[17],"presents":[18],"narrative":[20],"review":[21],"of":[22,26,98,129,136,155],"primary":[24],"literature":[25,125],"that":[27,122],"recovery.":[28],"The":[29],"synthesis":[30],"organized":[32],"around":[33],"three":[34],"themes:":[35],"founding":[37],"equations,":[38,133],"in":[39,64,89],"which":[40,65,90],"Eddington's":[41,66],"radiative":[42],"equilibrium,":[43],"Lane's":[44],"and":[45,48,56,74,76,83,86,96,101,103,115,138],"Emden's":[46],"polytropes,":[47],"Chandrasekhar's":[49],"treatise":[50],"fixed":[51],"four":[53,132],"differential":[54],"equations":[55],"their":[57],"gaseous":[58],"solutions;":[59],"energy":[61,72],"problem's":[62],"resolution,":[63],"mass-luminosity":[67],"argument,":[68],"Bethe":[70],"cycles'":[71],"generation,":[73],"Schwarzschild's":[75,94],"H\"arm's":[77],"convective":[78],"criteria":[79],"completed":[80],"physics;":[82],"numerical":[85],"structural":[87],"maturity,":[88],"Henyey's":[91,150],"relaxation":[92],"methods,":[93],"extit{Structure":[95],"Evolution":[97],"Stars},":[100],"Kippenhahn's":[102],"Hansen's":[104],"modern":[105],"treatments":[106],"delivered":[107],"computed":[109],"main":[110],"sequence,":[111],"red":[113],"giants,":[114],"evolutionary":[117],"tracks.":[118],"It":[119],"concluded":[121],"stellar":[123],"structure's":[124],"exemplar":[128],"theoretical":[130],"astrophysics:":[131],"one":[134],"equation":[135],"state,":[137],"nuclear":[140],"source---solved":[141],"first":[142],"by":[143],"approximations":[144],"whose":[145],"sequence":[146],"(Lane--Emden's":[147],"polytropes":[148],"to":[149],"computers)":[151],"history":[154],"computation":[156],"itself.":[157]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-01T00:00:00"}