{"id":"https://openalex.org/W3189809107","doi":"https://doi.org/10.1109/access.2021.3103750","title":"General Formulas of Effective Earth Radius and Modified Refractive Index","display_name":"General Formulas of Effective Earth Radius and Modified Refractive Index","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3189809107","doi":"https://doi.org/10.1109/access.2021.3103750","mag":"3189809107"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3103750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3103750","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09509503.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09509503.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005515979","display_name":"G. Feng","orcid":"https://orcid.org/0000-0002-5473-1998"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoxu Feng","raw_affiliation_strings":["School of Aeronautic Science and Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002107900","display_name":"Jun Huang","orcid":"https://orcid.org/0000-0002-2827-8990"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Huang","raw_affiliation_strings":["School of Aeronautic Science and Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103011235","display_name":"Mingxu Yi","orcid":"https://orcid.org/0000-0001-6228-457X"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingxu Yi","raw_affiliation_strings":["School of Aeronautic Science and Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautic Science and Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.1972,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92772725,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"9","issue":null,"first_page":"115068","last_page":"115076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13121","display_name":"Radio Wave Propagation Studies","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13121","display_name":"Radio Wave Propagation Studies","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.6718224287033081},{"id":"https://openalex.org/keywords/refractive-index","display_name":"Refractive index","score":0.6431798338890076},{"id":"https://openalex.org/keywords/geometrical-optics","display_name":"Geometrical optics","score":0.5273761749267578},{"id":"https://openalex.org/keywords/electromagnetic-radiation","display_name":"Electromagnetic radiation","score":0.4914902448654175},{"id":"https://openalex.org/keywords/figure-of-the-earth","display_name":"Figure of the Earth","score":0.48619168996810913},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"Wave propagation","score":0.47342851758003235},{"id":"https://openalex.org/keywords/earth-radius","display_name":"Earth radius","score":0.4272559881210327},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.4139631390571594},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3974141776561737},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3453372120857239},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3201625347137451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21616080403327942},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06838056445121765}],"concepts":[{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6718224287033081},{"id":"https://openalex.org/C42067758","wikidata":"https://www.wikidata.org/wiki/Q174102","display_name":"Refractive index","level":2,"score":0.6431798338890076},{"id":"https://openalex.org/C110277352","wikidata":"https://www.wikidata.org/wiki/Q467980","display_name":"Geometrical optics","level":2,"score":0.5273761749267578},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.4914902448654175},{"id":"https://openalex.org/C122224866","wikidata":"https://www.wikidata.org/wiki/Q437882","display_name":"Figure of the Earth","level":2,"score":0.48619168996810913},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.47342851758003235},{"id":"https://openalex.org/C75211307","wikidata":"https://www.wikidata.org/wiki/Q1155470","display_name":"Earth radius","level":4,"score":0.4272559881210327},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.4139631390571594},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3974141776561737},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3453372120857239},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3201625347137451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21616080403327942},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06838056445121765},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C130443932","wikidata":"https://www.wikidata.org/wiki/Q6915","display_name":"Magnetosphere","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3103750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3103750","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09509503.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:61533a4b62934a79873fbd3f1264b3a8","is_oa":true,"landing_page_url":"https://doaj.org/article/61533a4b62934a79873fbd3f1264b3a8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 9, Pp 115068-115076 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3103750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3103750","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09509503.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G145527907","display_name":null,"funder_award_id":"KH54210201","funder_id":"https://openalex.org/F4320321125","funder_display_name":"Beihang University"},{"id":"https://openalex.org/G6881604563","display_name":null,"funder_award_id":"KZ01005001","funder_id":"https://openalex.org/F4320321125","funder_display_name":"Beihang University"}],"funders":[{"id":"https://openalex.org/F4320321125","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3189809107.pdf","grobid_xml":"https://content.openalex.org/works/W3189809107.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W162802794","https://openalex.org/W621162152","https://openalex.org/W1578602021","https://openalex.org/W1652685704","https://openalex.org/W1763852523","https://openalex.org/W1971382442","https://openalex.org/W1975204975","https://openalex.org/W1977189307","https://openalex.org/W1978469820","https://openalex.org/W1984204197","https://openalex.org/W1996979095","https://openalex.org/W2011835721","https://openalex.org/W2017266367","https://openalex.org/W2021912909","https://openalex.org/W2055127775","https://openalex.org/W2078040506","https://openalex.org/W2104025125","https://openalex.org/W2111820179","https://openalex.org/W2155285018","https://openalex.org/W2307375521","https://openalex.org/W2339929407","https://openalex.org/W2504274537","https://openalex.org/W2559536409","https://openalex.org/W2573969901","https://openalex.org/W2601579138","https://openalex.org/W2753916741","https://openalex.org/W2804671975","https://openalex.org/W2811296994","https://openalex.org/W2830481125","https://openalex.org/W2904815078","https://openalex.org/W2911874218","https://openalex.org/W2949029582","https://openalex.org/W2951744008","https://openalex.org/W2953735919","https://openalex.org/W2962597833","https://openalex.org/W2981568947","https://openalex.org/W2987446267","https://openalex.org/W2999821449","https://openalex.org/W3000322136","https://openalex.org/W3103997002","https://openalex.org/W4211148763","https://openalex.org/W4242389273","https://openalex.org/W4247143882","https://openalex.org/W4300473455","https://openalex.org/W6703767893","https://openalex.org/W6765350965"],"related_works":["https://openalex.org/W2360070932","https://openalex.org/W2015290165","https://openalex.org/W4405795879","https://openalex.org/W1511688997","https://openalex.org/W4296748042","https://openalex.org/W2391373359","https://openalex.org/W4239009090","https://openalex.org/W2306393077","https://openalex.org/W1996038109","https://openalex.org/W71028157"],"abstract_inverted_index":{"The":[0],"effective":[1,78,139],"earth":[2,79,140,161],"radius":[3,80,141],"can":[4,19,29],"transform":[5,20],"the":[6,15,21,31,38,46,57,61,77,82,93,106,110,114,121,136,148,154,160,165],"curved":[7],"ray":[8],"path":[9],"into":[10,24],"a":[11,25,131],"straight":[12],"line,":[13],"and":[14,54,60,81,113,142,146],"modified":[16,83,143],"refractive":[17,84,144],"index":[18],"spherical":[22],"ground":[23],"plane.":[26],"Using":[27],"them":[28],"simplify":[30],"propagation":[32,50,155,166],"modeling":[33],"of":[34,48,51,95,120,138,156,167,170],"electromagnetic":[35,52,157],"waves":[36,158,171],"in":[37,45,109,125,159,172],"atmosphere,":[39,162],"so":[40],"they":[41,89],"are":[42,117],"widely":[43],"used":[44],"calculation":[47],"long-range":[49],"wave,":[53],"adopted":[55],"by":[56],"ITU":[58,111],"Recommendations":[59,112],"IEEE":[62,115],"Standards.":[63],"In":[64,98],"this":[65,126],"paper,":[66],"upon":[67],"employing":[68],"simple":[69],"geometric":[70],"methods,":[71],"we":[72,100],"provide":[73,130],"general":[74,122],"formulas":[75,107,123],"for":[76,103,150],"index,":[85,145],"pointing":[86],"out":[87],"that":[88,102],"both":[90,104],"originate":[91],"from":[92],"use":[94,152],"conformal":[96],"transformations.":[97],"turn,":[99],"prove":[101],"quantities":[105],"contained":[108],"Standards":[116],"special":[118],"cases":[119],"given":[124],"paper.":[127],"Our":[128],"results":[129],"solid":[132],"mathematical":[133],"background":[134],"to":[135,164],"concepts":[137],"pave":[147],"way":[149],"their":[151],"beyond":[153],"e.g.":[163],"other":[168],"types":[169],"generic":[173],"media.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}