Isihloko mayelana Umthetho kaKepler
Usazikhumbula yini izinkumbulo zokugibela imoto okokuqala? Uma usemotweni ehambayo, ubona sengathi isihlahla noma isakhiwo siyahamba. Ngaleso sikhathi, ungase ucabange ukuthi izihlahla noma izakhiwo ziyahamba, kuyilapho wena nemoto niphumule. Eqinisweni, wena nemoto niyahamba, kuyilapho izihlahla noma izakhiwo ziphumule. Lokhu okuhlangenwe nakho kokunyakaza kwamanga empeleni kwenzeka nsuku zonke. Njalo ekuseni, “ilanga liyaphuma” emkhathizwe osempumalanga bese liya entshonalanga bese “lishona” emkhathizwe osentshonalanga ntambama.
Ngokufanayo, ebusuku, uvame ukubona inyanga isuka empumalanga iye entshonalanga. Wake wacabanga noma waqagela ukuthi ilanga nenyanga kuhambahamba emhlabeni, kuyilapho umhlaba uphumule?
Umlando wentuthuko yesayensi yezinkanyezi
Abantu ababephila endulo (ekuqaleni kwe-BC) babecabanga futhi ngelanga, inyanga, nezinye izidalwa zasezulwini ezihambahamba emhlabeni, kuyilapho umhlaba uphumule. Ngamanye amazwi, umhlaba ubhekwa njengesikhungo sendawo yonke (geocentric). Lokhu kucabanga kusekelwe kokuhlangenwe nakho okulinganiselwe kwemizwa yabantu, ababuka ilanga, inyanga, nezinkanyezi nsuku zonke zihamba, kuyilapho umhlaba uzizwa sengathi uphumule. Ngokufana nokuba semotweni ehambayo, ubona sengathi izihlahla noma izakhiwo ziyahamba. Ukucabanga ukuthi umhlaba uyisikhungo sendawo yonke kwacwaningwa futhi kwathuthukiswa yisazi sezinkanyezi esingumGreki uClaudius Ptolemaeus (100-170 AD) ngekhulu lesibili AD futhi kwakholelwa eminyakeni engu-1400 eyalandela.
Ngokusho kukaPtolemy, umhlaba wawusenkabeni yesimiso selanga. Ilanga namaplanethi azungeze indilinga (ukunyakaza okujikelezayo) lapho isikhungo sale ndilinga sizungeze umhlaba ngendlela eyindilinga (ukunyakaza okuguqukayo).
Ngo-1543, isazi sezinkanyezi sasePoland uNicolaus Copernicus (1473-1543) waphakamisa imodeli ye-heliocentric, lapho ilanga laliphakathi nendawo yesimiso selanga. Amaplanethi afaka umhlaba ozungeze indilinga (ukunyakaza okujikelezayo) lapho isikhungo salesi siyingi sizungeze ilanga ngendlela eyindilinga (ukunyakaza okuguqukayo). UCopernicus wayenokuqonda okuthuthukile kunoPtolemy ngoba wabeka ilanga phakathi nendawo yesimiso selanga. Noma kunjalo, uCopernicus usasebenzisa indilinga njengendlela yokunyakaza kwamaplanethi.
Izingxoxo ezijabulisayo mayelana namamodeli e-geocentric kanye ne-heliocentric zikhuthaza izazi zezinkanyezi ukuba zenze ukuqaphela okucophelelayo. Izazi zezinkanyezi ngaleso sikhathi zazibuka izidalwa zasezulwini zisebenzisa amehlo kuphela, azizange zisebenzise izinsimbi ezifana nama-telescope noma ama-binocular ezinkanyezi. Ngaleso sikhathi, i-telescope yayingakakhiwa. I-telescope engasetshenziswa ukubuka izidalwa zasezulwini yenziwa okokuqala ngusosayensi wase-Italy, uGalileo Galilei, ngo-1609. UGalileo wasebenzisa i-telescope yakhe yokwenziwa ukubuka izidalwa zasezulwini futhi wasebenzisa idatha yakhe yokubuka ukuphikisana nabasekeli bemodeli ye-geocentric.
Isazi sezinkanyezi esidumile saseDenmark okuthiwa uTycho Brahe (1546-1601) saba yisazi sezinkanyezi sokugcina ukubuka izidalwa zasezulwini sisebenzisa amehlo kuphela. Ngemva kokubukela kusukela ngo-1576 kuya ku-1599, uTycho Brahe wabe esesebenzisana nesazi sezinkanyezi saseJalimane, uJohannes Kepler (1571-1630), naye owayengusosayensi wezibalo. UKepler wayengumsizi kaTycho Brahe. Ukubambisana phakathi kukaTycho Brahe noKepler kwahlala isikhathi esifushane ngoba uTycho Brahe washona. Ngemva kokushona kukaTycho Brahe, uKepler wasebenzisa idatha yezinkanyezi etholwe nguthisha wakhe futhi wachitha iminyaka engaba amashumi amabili yokuphila kwakhe edala amamodeli ezibalo ukuchaza ukunyakaza kwamaplanethi.
Umsebenzi wokuqala kaKepler emkhakheni wezinkanyezi onesihloko esithi The Mystery of the Universe wanyatheliswa ngo-1596. Encwadini, wafuna ukuhambisana phakathi kwemizila yamaplanethi ngokusho kokubona kukaCopernicus noTycho Brahe . Kodwa uKepler wehluleka ukuthola ukuvumelana phakathi kwamamodeli athuthukiswe nguCopernicus noPtolemy nemiphumela yokubona kukaTycho Brahe. Ngakho-ke, washiya amamodeli kaPtolemaic noCopernican wabe esefuna amamodeli amasha. Ngo-1609, uKepler wathola ukuthi ama-ellipse ayefaneleka kakhulu nemiphumela yokubona kukaTycho Brahe. UKepler akasasebenzisi indilinga njengendlela yomzila wezidalwa zasezulwini, kodwa ama-ellipse.
Umthetho kaKepler
Lo mthetho wabekwa phambili nguKepler, eminyakeni engamashumi amahlanu ngaphambi kokuba u-Isaac Newton aphakamise imithetho yakhe emithathu yokuhamba kanye nomthetho wamandla adonsela phansi wendawo yonke.
Umthetho wokuqala kaKepler
Indlela yeplanethi ngayinye uma izungeza ilanga ifana ne-ellipse, lapho ilanga ligxile khona.
F1 noF2 kuyizindawo ezigxile ku-elliptical. Ilanga likwenye yezindawo ezigxile ku-focus (isibonelo esithombeni esikhethiwe u-F2), iplanethi ikude kakhulu ne-r2 kusukela ku-F2 noma r1 kusukela ku-F1Uma indawo yeplanethi ishintsha, r2 futhi r1 futhi shintsha.
Noma kunjalo, u-r 1 + r 2 uhlala ufana. Ibanga u-a libizwa ngokuthi i-semimajor axis kanti u-2a ubizwa ngokuthi i-major axis. Ibanga u-b libizwa ngokuthi i-semiminor axis kanti u-2b ubizwa ngokuthi i-minor axis. Indawo yokugxila ye-ellipse itholakala ebangeni u-c ukusuka enkabeni ye-ellipse, lapho u-c 2 = a 2 + b 2.
Ukuma kwe-ellipse kunqunywa ubunjalo be-ellipse (e), lapho u-e = c / a. Ubunjalo be-ellipse buqala ku-0 kuya ku-1 (0).
Uma iplanethi isemaphethelweni esobunxele e-ellipse (ngakwesobunxele se-F 1 ) khona-ke ibanga leplanethi elangeni lingu-+ c. Leli phuzu libizwa ngokuthi i-aphelion. Uma iplanethi isemaphethelweni e-aphelion, iplanethi isemaphethelweni ayo akude kakhulu elangeni. Uma iplanethi isemaphethelweni engakwesokudla e-ellipse (ngakwesokudla se-F 2 ) khona-ke ibanga leplanethi elangeni lingu-ac. Leli phuzu libizwa ngokuthi i-perihelion. Uma iplanethi isemaphethelweni e-perihelion, iplanethi isemaphethelweni aseduze kakhulu elangeni.
Umthetho wesibili kaKepler
Umugqa ocatshangwayo odwetshwe kusukela elangeni uye eplanethini, ususa izindawo ezilinganayo, isikhathi esifanayo.
Esifanekisweni esingezansi, kunezibonelo ezimbili kuphela zezindawo, okungukuthi indawo ye-abc nendawo ye-ade. Lezi zindawo ezimbili zinobukhulu obufanayo. Ngesikhathi esifanayo, umugqa ocatshangwayo oxhumanisa iplanethi nelanga ushanela indawo enobukhulu obufanayo. Ngakho-ke, lapho usuka ku-b uye ku-c (iplanethi ise-aphelion), ijubane leplanethi encane noma iplanethi lihamba kancane kakhulu. Ngokuphambene nalokho, lapho usuka ku-d uye ku-e (iplanethi ise-perihelion), ijubane leplanethi enkulu noma iplanethi lihamba ngokushesha. Ngakho-ke, izinga eliphezulu kakhulu leplanethi uma lise-perihelion kanye nezinga eliphansi kakhulu leplanethi uma lise-aphelion.
Umthetho wesithathu kaKepler
Isilinganiso sezikwele ze i-orbital Isikhathi yeplanethi kuya ikhiyubhu ka the amabanga aphakathi kweplanethi nge ilanga (T)2/r3) ayiguquki, futhi inani liyafana kuwo wonke amaplanethi. Uma u-T1 no-T2 chaza isikhathi samaplanethi amabili, r1 futhi r2 imelela ibanga elimaphakathi leplanethi ngayinye ukusuka elangeni:
