Wake wazibuza ukuthi kwakungubani? UJohannes Kepler? Nokho, wayengusosayensi waseJalimane obaluleke kakhulu, owagqama ngolwazi lwakhe lwesayensi yezinkanyezi nefilosofi, weza ukuze adale futhi abonise ukuba khona kwemithetho emithathu yokunyakaza kwamaplanethi, namuhla ebizwa ngokuthi imithetho kaKepler. Sikumema ukuba ufunde lesi sihloko ukuze ufunde okwengeziwe ngokuphila nomsebenzi wakhe.
Biography of Johannes Kepler
Ngesikhathi sakhe UJohannes Kepler kwakubaluleke kakhulu ukuthi eze azosebenzisana noTycho Brahe, kamuva esikhundleni sakhe esikhundleni sokuba isazi sezibalo sasebukhosini sikaRudolf II. Ngenxa yempumelelo yakhe emangalisayo, i-International Astronomical Union yabhapathiza incwadi yezinkanyezi ebizwa ngokuthi u-Kepler ngo-1935. Ake sifunde okwengeziwe ngokuphila kwakhe.
Ubuntwana
Unyaka wokuzalwa kwakhe kwakungu-1571, edolobheni laseJalimane iWurttemberg, ngaleso sikhathi okwakuyi-dukedom. Kusukela esemncane wayengumuntu ohlushwa izifo eziningi, njenge-myopia, isisu futhi ehlushwa yikhanda elibuhlungu. Lapho eneminyaka emithathu ubudala, wangenwa isifo sengxibongo, imiphumela yaso eyayihlanganisa ukuwohloka kwamehlo kakhulu.
Nakuba ayehlale enezinkinga zempilo ezingathi sína, wayehlale eyingane ehlakaniphile, ehlakaniphe kakhulu, ejabulela ukuvela kubantu ababehlala ehostela likanina, esebenzisa izipho zakhe ezingavamile zezibalo. Ngonyaka ka-1584 wakwazi ukungena esikoleni sobufundisi samaProthestani edolobheni lase-Adelberg.
Izifundo
Ngenxa yokuhlakanipha kwakhe okuqinisekisiwe, ngonyaka ka-1589 waqala ukufundela imfundiso yenkolo eNyuvesi yaseTübingen. Lapho ezithola lapho, waba nethuba lokuba uMaestlin njengothisha wakhe wezibalo, owayesevele enolwazi lwethiyori ye-heliocentric kaCopernicus futhi wabelana ngayo kabanzi.
UKepler walandela izimfundiso zikaPythagoras, futhi wayekholelwa ukuthi uNkulunkulu uyi-geometer enkulu kunazo zonke, umdali wendawo yonke evumelanayo, eqaphela ngobulula benkolelo-mbono kaPythagoras isici sohlelo lukaNkulunkulu lokudala. Waqhubeka nokufunda eTübingen, ngisho nangemva kokuthola iziqu ze-master ngo-1591.
Matrimonio
UJohannes Kepler washada kabili. Umshado wakhe wokuqala, umphumela wokunethezeka okuphelele, waba ngo-April 27, 1597, noNkosazana Bárbara Müller. Lo mshado owahlelwa yizihlobo zakhe, wamenza umbhangqwana wowesifazane oyisidudla, onomoya ophansi, owayenesimilo esinengekayo.
umsebenzi wezemfundo
Ngonyaka ka-1594 wasuka eTübingen, waya eGraz, idolobha elise-Austria, lapho aphishekela khona umsebenzi wakhe wokuba uprofesa enyuvesi, efundisa i-Arithmetic, Geometry kanye ne-Rhetoric, ekwazi ukunikela isikhathi sakhe samahhala emsebenzini wokuzilibazisa owawuwumsebenzi wokufundisa. isayensi yezinkanyezi.
Sibhekisela esikhathini lapho umehluko phakathi kwenkolelo nesayensi wawungadonswa ngokugcwele, futhi imishini yendlela izindikimba zasemkhathini ezazihamba ngayo zazingaziwa. Eqinisweni, kwakuthiwe izinhlangano ezinjalo zaziyilalela imithetho yaphezulu.
Lapho eseGraz, wayeshicilele ama-almanacs aqukethe izibikezelo zezinkanyezi, aqanjwa uKepler, nakuba ayengavumelani nezinye zeziqondiso.
Khona-ke, ngonyaka ka-1600, waya kohlala edolobheni lasePrague, namuhla eliyinhloko-dolobha yaseCzech Republic, ecelwe isazi sezinkanyezi esaziwayo uTycho Brahe, owaxhumana noKepler, ngemva kokufunda izincwadi zakhe. UProfesa Brahe washona ngonyaka olandelayo futhi uKepler wathatha isikhundla sakhe njengesazi sezibalo nesazi sezinkanyezi sasegcekeni lombusi.
Isikhathi eside UJohannes Kepler Wagcina inkolelo-mbono ehlanganisa i-geocentrism ne-heliocentrism, ukuze kamuva aguqule imiklamo yakhe ye-geocentric ibheke ku-heliocentrism. Nakuba ayewufezile umgomo wakhe, waqhubeka ethola ukungqubuzana okukhulu phakathi kwendlela, ngokwezibalo zakhe, okwakufanele ngabe izidalwa zasemkhathini ziye zayenza naleyo ezayenza ngempela.
Lesi siphetho samholela ekucabangeni ukuthi, ukuhlanganisa ILanga umzimba ophuma kuwo amandla okwenza amaplanethi ajikeleze endaweni yawo, lapho indlela phakathi kweplanethi neLanga yanda, isivinini okwenziwa ngaso ukunyakaza kwadingeka sincishiswe. Ukuze akwazi ukwenza lesi sitatimende, kwadingeka asuse umbono owamukelekayo ezinkulungwaneni zeminyaka edlule, ukuthi umzila owenziwe yindikimba yasezulwini wenziwa ngokuzungeza okuyisiyingi.
Ngonyaka ka-1612, wathola isikhundla esihloniphekile sokuba isazi sezibalo sase-Upper Austria, eyakha isifunda saseLinz. Naphezu kokuhlonishwa okutholiwe kanye nokutholwa kwakhe, UJohannes Kepler akazange aneliseke.
Wayeqiniseka ukuthi ukuvumelana nokulula kwakuyimithetho elawula i-Universe, yingakho wayehlala efuna ubuhlobo obulula, lapho izikhathi zokuguquguquka kwamaplanethi, namuhla eyaziwa ngokuthi i-orbital periods, kanye nebanga lokuya kumaplanethi. Ilanga.
UJohannes Kepler Kwamthatha iminyaka engaphezu kweyisishiyagalolunye ukuthola lobu budlelwano obulula futhi aqhubeke nokwenza umthetho wesithathu wokunyakaza kwamaplanethi, ngokusho ukuthi isikhathi sokujikeleza kweplanethi silingana ne-semi-major axis ye-ellipse ephakanyiswe emandleni 3/2.
Ngonyaka ka-1628, wangena ukuze enze izinkonzo zakhe ku-oda lika-A. von Wallenstein, edolobheni laseSagan, ngaleso sikhathi esifundazweni saseSilesia, owamnika izwi lakhe lokwesula isikweletu uMbusi owawunenkontileka naye. iminyaka eyayidlulile, kodwa akazange ayigcwalise. Cishe inyanga ngaphambi kokuba afe, ngenxa yomkhuhlane, UJohannes Kepler wayesemshiyile uSilesia efuna isikhundla esisha.
Ukufa
UJohannes Kepler Washona ngonyaka ka-1630, edolobheni laseRegensburg, ehamba nomkhaya wakhe besuka eLinz beya eSagan. Etsheni lakhe lethuna kwakuqoshwe i-epitaph elandelayo, eyadalwa nguye:
“Ngalinganisa amazulu, manje ngilinganisa ithunzi.
Esibhakabhakeni kwakhanya umoya.
Emhlabeni kuphumule umzimba. "
umsebenzi wesayensi
Ngonyaka ka-1594, lapho UJohannes Kepler Washiya idolobha laseTübingen waya eGraz, e-Austria, wenza inkolelo-mbono ye-geometry eyinkimbinkimbi ukuze azame ukuchaza ukuhlukana phakathi kokujikeleza kwamaplanethi, okwakucatshangwa ngokungalungile ukuthi ayisiyingi ngaleso sikhathi.
Ehlaziya i-hypothesis yakhe, uKepler wathola ukuthi I-Orbit amaplanethi ayeyi-elliptical. Kodwa lezo mali ezibanjwayo zokuqala ziqondane kuphela no-5% neqiniso. Uphinde wathi iLanga yilona elinamandla amakhulu ancipha ngokuphambene nebanga futhi abangele ukuthi amaplanethi ahambe emzileni wawo.
Ngonyaka we-1596, wakwazi ukushicilela incwadi ebizwa ngokuthi i-Mysterium Cosmographicum. Ukubaluleka kwalo msebenzi kuvela eqinisweni lokuthi kwakuwukubonakaliswa kokuqala okubanzi nokuzwakalayo kwesayensi yezinzuzo zejometri zethiyori kaCopernican.
Ngonyaka olandelayo, ngo-1597, wanyathelisa i-Mysterium Cosmographicum, lapho eshiya khona ubufakazi obucacile bezinzuzo, kusukela esikhundleni sesayensi yejometri, etholakala kumbono we-heliocentrism.
UJohannes Kepler Wayenguprofesa wesayensi yezinkanyezi kanye nezibalo eNyuvesi yaseGraz kusukela ngo-1954 kuya ku-1600, lapho enikezwa isikhundla sokuba umsizi wesazi sezinkanyezi saseDenmark uTycho Brahe endaweni yokuhlola iPrague. Ngesikhathi uBrahe efa ngo-1601, uKepler wayesethathe isikhundla sakhe njengesazi sezibalo nesazi sezinkanyezi sasenkantolo kuMbusi uRudolf II.
Emisebenzini yakhe eyakhiqizwa ngaleso sikhathi, enye ebaluleke kakhulu i-Astronomia Nova, eyanyatheliswa ngonyaka ka-1609. Kwakuwukuhlanganiswa okukhulu kwemizamo yakhe enzima yokubala ukuzungeza kweplanethi i-Mars, azama ngayo cishe kuphela ukuyithwebula. yizibalo zakhe emzileni walo mhlaba.
Ku-Astronomia Nova wethula imithetho yakhe emithathu kwezintathu eyaziwa kakhulu yokuhamba kwamaplanethi, namuhla ebizwa ngokuthi imithetho kaKepler. Ngonyaka ka-1610 wanyathelisa i-Dissertatio cum Nuncio Sidereo, eyayikhuluma ngokuphawulwa uGalileo Galilei.
Ngonyaka olandelayo, wakwazi ukwenza okwakhe ukuphawula mayelana neziphuphutheki ezachazwa usosayensi wase-Italy, ngenxa yosizo lwesibonakude, enyathelisa imiphumela yalokhu kubuka emsebenzini wakhe othi Narratio de Observatis Quatuor Jovis Satellitibus.
Wamiswa njengesazi sezibalo ezifundazweni zase-Austrian ngonyaka ka-1612. Ngesikhathi ekuleso sikhundla wahlala eLinz, lapho abhala khona incwadi yakhe ethi Harmonices Mundi, Libri (1619), lapho abeka khona umthetho wakhe wesithathu, ukuze abonise ubuhlobo obuseduze. yebanga elimaphakathi ukusuka eplanethini kuya eLangeni.
ngesikhathi esifanayo UJohannes Kepler inyathelisa i-Epitome Astronomiae Copernicanae (1618-1621), lapho ekwazi khona ukuqoqa konke akutholile ngencwadi eyodwa.
Ukuhlobana okufanayo kwaba nencwadi yakhe yokuqala yesayensi yezinkanyezi, eyayisekelwe ezimisweni zikaCopernicus, futhi okwathi emashumini amathathu eminyaka alandela yaba nethonya elimangalisayo, yadonsa izazi zezinkanyezi eziningi ku-Keplerian Copernicanism.
Umsebenzi wokugcina ofanelekile owashicilelwa ngenkathi u-Kepler esaphila, kwakuyi-Rudolphine Tables, ngonyaka we-1625. Ngokusekelwe olwazini olwahlanganiswa ngu-Brahe, amatafula amasha okunyakaza kwamaplanethi akwazi ukunciphisa amaphutha aphakathi nendawo yangempela ye-a. iplanethi kusuka ku-5 ° kuya ku-10′.
Kamuva, isazi sezibalo nefiziksi saseNgilandi, uSir Isaac Newton, sathatha njengesisekelo izinkolelo-mbono kanye nokuphawulwa kwesayensi. Johannes Kepler, njengesisekelo sethiyori sokwakhiwa komthetho wakhe wamandla adonsela phansi endaweni yonke.
Uma unentshisekelo, ungabona futhi Isaac Newton Biography.
U-Kepler uphinde wenza iminikelo ebalulekile kuma-optics, ekwazi ukwenza lokhu okulandelayo:
- Umthetho Oyisisekelo Wezithombe
- Ukuzindla Okugcwele
- I-First Theory of Modern Vision
- Wakha i-Infinitesimal System, eyandulela i-Infinitesimal Calculus yase-Leibnitz ne-Newton.
Imithetho emithathu kaKepler
Isazi sezinkanyezi saseJalimane sakha imithetho emithathu eyaziwayo enegama laso, ngemva kokuhlaziya idatha yenani elikhulu lokubhekwa okwenziwa nguTycho Brahe (1546-1601) mayelana nokunyakaza kwamaplanethi, ikakhulukazi kuplanethi i-Mars.
UJohannes Kepler, esebenzisa izibalo eziyinkimbinkimbi kakhulu, ukwazile ukuphetha ngokuthi kunomehluko ofanelekile phakathi komzila owawubalwe ukuthi iplanethi i-Mars yayizoyithatha kanye nombono kaBrahe, umehluko kwezinye izimo owawufinyelela kumaminithi angu-8 we-arc, empeleni okubonwa nguBrahe ukunemba cishe kwemizuzu emi-2 ye-arc.
Lokhu kwathola umehluko kwamsiza ukuba athole ukuthi wawuyini umjikelezo wangempela weplanethi i-Mars namanye amaplanethi eSistimu Solar.
Umthetho woku-1. Imizila eyi-elliptical
U-Kepler wayebambe, ngokuphambene nenkolelo-mbono eyindilinga, ukuthi imizungezo yamaplanethi iyizimbotshana ezine-eccentricity encane futhi lapho iLanga litholakala kwenye ye-foci yalo. Uma uyibhekisisa kahle, isinika umbono wokuthi i-ellipse ekuqaleni iyindilinga eye yacabana kancane.
Ngokombono, igama elithi ellipse linikezwa ijika eliyisicaba nelivaliwe lapho isamba sebanga ukuya ku-foci (amaphoyinti agxilile, F1 kanye no-F2) ukusuka kunoma yimaphi amaphuzu angu-M awakhekayo ahlala njalo futhi alingana nobude i-eksisi enkulu ye-ellipse (ingxenye AB). I-axis encane ye-ellipse iyisegimenti ye-CD, i-perpendicular ku-segment AB futhi iyinqamule phakathi.
I-eccentricity imelela izinga lokuguqulwa kwe-ellipse. I-eccentricity ye-zero ayikho, ngakho-ke kungaba umbuthano ophelele. Uma kukhulu ukuguqulwa kwe-eccentricity, likhulu inani lama-engeli we-ellipse.
Ama-engeli anama-engeli alingana neyodwa abizwa ngokuthi ama-parabolic orbits, futhi lawo amakhulu kunowodwa abizwa ngokuthi ama-hyperbolic orbits.
Uma ibanga phakathi kwe-foci F1F2 lilingana no-zero, njengoba kwenzeka kumbuthano, i-eccentricity izophinde ibangele zero.
Isiphetho esifinyelelwe u-Kepler siwukuthi ukuzungeza kweplanethi kune-elliptical, nokuguqulwa okuncane noma ukungaboni kahle. Endabeni yeplanethi enguMhlaba, inani le-sinusity ngu-0.017, iplanethi enezinga elikhulu kakhulu lokuguqulwa ku-ellipse yayo i-Pluto eno-0.248, ilandelwa eduze ne-Mercury, ngo-0.206.
Okwesibili umthetho wemizila
I-radius vector ehlanganisa amaplanethi nendawo yeLanga ingamboza izindawo ezifanayo ngesikhathi esifanayo. Ijubane le-orbital leplanethi, okuyijubane elihamba ngalo emzileni walo, liyaguquguquka, ngokuphambene nebanga ukusuka eLangeni, ngenxa yalesi sizathu, kuphethwa ngokuthi ebangeni elikhulu, ijubane le-orbital lizoba ngaphansi. , ngenkathi kumabanga amafushane, isivinini se-orbital sizoba phezulu.
Ijubane le-orbital lamaplanethi lizoba yinani eliphakeme kakhulu, lapho eseqophelweni lokuzungeza kwawo eliseduze neLanga, elibizwa ngokuthi i-perihelion, futhi ayoba nejubane elincane endaweni yawo ekude kakhulu neLanga, ebizwa ngokuthi i-aphelion.
I-Vector yeplanethi umugqa ocatshangwayo ohlanganisa inkaba yeplanethi neLanga ngesikhathi esithile. Ngakolunye uhlangothi, leyo vector ye-orbital izolingana nesamba sezikhathi ezithathwa iplanethi ukusuka kwenye ivekhtha ukuya kwenye, kuze kube yilapho kuqedwa ukuzungeza okukodwa.
Ngeziphetho ezafinyelelwa uKepler ekuhlaziyeni kwakhe ama-obits ayi-elliptical, wathola ukuthi njengoba isitshalo siseduze nelanga, kufanele sihambe ngokushesha, sithola ukuthi isikhathi lapho iplanethi isuka kwenye i-vector iye kwenye, kufanele ifane kubo bonke. ukudluliselwa ngamavekhtha alandelayo.
3rd. Umthetho we-Harmonic kanye nenkanyezi kaKepler
Ngenyanga ka-Okthoba wonyaka ka-1604, UJohannes Kepler yakwazi ukubona i-supernova ku-Galaxy yethu, kamuva eyayizobizwa ngokuthi inkanyezi ka-Kepler. Yona leyo supernova yayingabonwa abanye ososayensi baseYurophu, njengoBrunowski ePrague, owabhalelana noKepler, u-Altobelli eVerona, noClavius eRoma, noCapra noMarius ePadua.
U-Kepler, esekelwe encwadini kaBrahe, wenza ukuhlaziya okuningiliziwe kwalokhu kubonakala kuyi-supernova, encwadini yakhe ethi, De Stella Nova in Pede Serpentarii, ngokuhunyushwa kwayo, i-New Star in the Foot of Ophiuchus, ebeka izisekelo zenkolelo-mbono yakhe yokuthi Umkhathi. ihlala inyakaza, nokuthi ithonywa ukuguqulwa okubalulekile.
Ukuqina kwalenkanyezi kwakungangoba yayikwazi ukubonakala ngeso lenyama phakathi nezinyanga ezingu-18 ibonakale. Le nkanyezi ye-supernova itholakala kuphela eminyakeni engu-13.000 yokukhanya ukusuka kuplanethi enguMhlaba.
Kamuva, akwenzekanga ukubona enye i-supernova emthaleni wethu siqu. Ngenxa yokuvela kokukhanya kwenkanyezi okuye kwalinganiswa futhi kwabhekwa, namuhla kukholakala ukuthi iwuhlobo lwe-I supernova.
Isifinyezo Semisebenzi Ka-Kepler
Ngenxa yocwaningo lwakhe, olwenziwa empilweni yakhe yonke, UJohannes Kepler Ushicilele le misebenzi elandelayo, ehlelwe ngokulandelana kwezikhathi:
- I-Mysterium cosmographicum (Imfihlakalo ye-cosmic, 1596).
- I-Astronomiae Pars Optica (Ingxenye ye-optical ye-astronomy, 1604).
- U-De Stella nova uhamba no-Serpentarii (Inkanyezi entsha onyaweni luka-Ophiuchus, 1604). Ngo-Okthoba 17, 1604, uKepler wabona ukubonakala kwenkanyezi entsha. Lokhu kubuka, okwaqinisekiswa ezinye izazi zezinkanyezi zaseYurophu, kwavusa ilukuluku lakhe ngokujulile. Ngaphezu kokuthakazelisa ngokombono wesayensi yezinkanyezi, kwakuwumbuzo obalulekile wefilosofi, njengoba uKepler wayehlale eyivikela inkolelo-mbono yokuthi indawo yonke ayiyona into emile. Manje sekuyaziwa ukuthi i-Kepler's Star kwakuyikilasi I supernova.
- isayensi yezinkanyezi entsha (Isayensi yezinkanyezi entsha, 1609).
- I-Diopter (Diopter, 1611). Ngokusekelwe ku-myopia ayephethwe yiyo, u-Kepler wayehlale enesithakazelo kuma-optics. Iziphetho ezingokoqobo zalo msebenzi zabangela izibuko noma amalensi asiza abantu abane-myopic ne-presbyopic ukuba babone kangcono, futhi kwaba nesandla ekwakhiweni kwesibonakude esisha, esasetshenziselwa ukuhlola izinkanyezi iminyaka eminingi, esathola igama lesibonakude i-Kepler. .
- UDe Vero Anno quo Aeternus Dei Filius Humanam Naturam ku-Utero Benedictae Virginis Mariae Assumpsit (1613). Ngenxa yolwazi olukhethekile ayelutholile, uJohannes Kepler wabhala le ncwadi enelukuluku nemfishane abonisa kuyo ngokwaziswa okungokwesayensi ukuthi uJesu wazalwa ngonyaka ka-4 BC.
- I-Epitome astronomiae Copernicanae (yanyatheliswa ngezingxenye ezintathu, 1618-1621).
- Harmonize Umhlaba (Ukuvumelana kwemihlaba, 1619).
- Tabulae Rudolphinae (1627).
- I-Somnium (Iphupho, 1634), liyindaba engelona iqiniso, lapho abalingisi bengabona ngokumangalisayo umbukwane woMhlaba uziphendukela wona. Ngenxa yalo msebenzi, kube nokwenzeka ukuqinisekisa ukuthi u-Kepler wayengumbhali wokuqala wezinganekwane zesayensi emlandweni.
Ngaphandle komsebenzi wakhe njengesazi sezinkanyezi nezibalo, UJohannes Kepler Waba isazi sezinkanyezi esibaluleke kakhulu. Izibikezelo ezimbili ezazifaneleka kakhulu, esokuqala sihlobene nezitshalo, kanti esesibili sihlobene nokuthi ubani ozonqoba impi ngokumelene namaTurkey, zamnika udumo, ebhekwa njengengcweti kwezobuciko bokuhumusha izibikezelo zezulu. Izinkanyezi.
Lo msebenzi, u-Kepler ayengaziqhenyi ngawo ikakhulukazi, wakwazi ukumnika imali engenayo yezomnotho ngesikhathi lapho iholo lakhe libhekene nezikhathi ezinzima.
Ukungavumelani kwakhe kwaba kanjalo kangangokuthi kuthiwa uJohannes Kepler waze wathi isifebe sokufunda izinkanyezi kufanele sisekele unina, isayensi yezinkanyezi, ngoba iholo lezazi zezibalo liphansi kangangokuthi, nakanjani, umama wayeyolamba, uma indodakazi ingayitholi. okokuziphilisa. La mazwi ashiya kungangabazeki ngombono kaKepler ngezinkanyezi.
- I-Rudolphine Tables. Akuwona umsebenzi kaJohannes Kepler odume njengemithetho yakhe eyaziwa kakhulu yokuhamba kweplanethi, futhi naphezu kwalokhu, bakha omunye wemisebenzi ebaluleke kakhulu ephakeme ye-Kepler, ngoba iyingxenye ebalulekile ekuqaleni kwesayensi yezinkanyezi entsha.
Lawo matafula ekuqaleni ayewumsebenzi owathunywa iNkosi uRodolfo II, yingakho ebizwa ngegama likaRudolfinas. Ekuqaleni babephathiswe uTycho Brahe, kodwa ngenxa yokushona kwakhe, umsebenzi wabe usuphathiswa uKepler, owasebenzisa imibono yakhe emisha ekuchazeni kwawo, ukuze agcwalise izibalo zezikhundla zeLanga neNyanga.
Lokhu kwamsiza ukuba akwazi ukubala izikhathi lapho ukusitheka kwakuyokwenzeka ngaso, hhayi ngaleso sikhathi kuphela, kodwa nganoma yiluphi usuku, kungakhathaliseki ukuthi ngaphambi noma ngemva kwenkathi yobuKristu.
Uma siyihlaziya, kungaphethwa ngokuthi Amathebula kwakuwumsebenzi omuhle ngempela, onikeza ukuboniswa kwamakhasi angamakhulu anezinkulungwane zezibalo uKepler okwakudingeka azenze phakathi neminyaka engu-22 ende. Ngenhlanhla yakhe, ekwenzeni izibalo eziningi, u-Kepler wakwazi ukuzisebenzisa, ngoba base bengenile kakade kwisayensi yezibalo, i-logarithms ye-Napier, umkhuba u-Kepler awenza aphelele.
Ukuhambisana kwe-Las Tablas Rudolfinas kwaba nomthelela obalulekile ekulungiseleleni amakhalenda e-ephemeris nasekuzulazuleni iminyaka engaphezu kuka-200.