Labari game da Dokar Kepler
Shin har yanzu kuna tuna da abubuwan da suka faru lokacin da kuka fara hawa mota? Lokacin da kuke cikin mota mai motsi, kuna gani kamar itace ko gini yana motsi. A wannan lokacin, kuna iya tunanin bishiyoyi ko gine-gine suna motsawa, yayin da ku da motar kuna hutawa. A gaskiya ma, ku da motar kuna motsawa, yayin da bishiyoyi ko gine-gine ke hutawa. Wannan yanayin motsi na karya ana samunsa kowace rana. Kowace safiya, "fitowar rana" a sararin sama na gabas sannan ya koma yamma ya "faɗi" a sararin sama na yamma da rana.
Haka nan, da daddare, sau da yawa za ka ga wata yana tafiya daga gabas zuwa yamma. Shin ka taɓa tunanin ko ka yi tunanin cewa rana da wata suna tafiya a duniya, yayin da duniya ke hutawa?
Tarihin ci gaban ilmin taurari
Mutane da suka rayu a zamanin da (farkon BC) sun kuma yi la'akari da rana, wata, da sauran halittun sama da ke motsawa a duniya, yayin da duniya ke hutawa. A wata ma'anar, ana ɗaukar duniya a matsayin cibiyar sararin samaniya (geocentric). Wannan zato ya dogara ne akan ƙarancin ƙwarewar jin daɗin mutane, waɗanda ke kallon rana, wata, da taurari suna motsi kowace rana, yayin da duniya ke jin kamar tana hutawa. Kamar kasancewa a cikin mota mai motsi, kuna gani kamar bishiyoyi ko gine-gine suna motsawa. An yi bincike kuma an ƙirƙiro zato cewa duniya ita ce cibiyar sararin samaniya ta wani masanin ilmin taurari ɗan Girka Claudius Ptolemaeus (100-170 AD) a ƙarni na biyu AD kuma ya yi imani da shi tsawon shekaru 1400 masu zuwa.
A cewar Ptolemy, duniya tana tsakiyar tsarin hasken rana. Rana da taurari suna kewaye da da'ira (motsin juyawa) inda tsakiyar wannan da'irar ke kewaye duniya a cikin hanyar da'ira (motsin juyin juya hali).
A shekara ta 1543, masanin ilmin taurari ɗan ƙasar Poland Nicolaus Copernicus (1473-1543) ya gabatar da samfurin da ke tsakiyar sararin samaniya, wanda rana take tsakiyar tsarin hasken rana. Duniyoyin sun haɗa da duniya a kusa da da'ira (motsin juyawa) inda tsakiyar wannan da'irar ke kewaye da rana a cikin hanyar da'ira (motsin juyin juya hali). Copernicus yana da fahimta mafi zurfi fiye da Ptolemy saboda ya sanya rana a tsakiyar tsarin hasken rana. Duk da haka, Copernicus har yanzu yana amfani da da'ira a matsayin nau'in motsi na duniyoyi.
Muhawara mai kayatarwa game da samfuran geocentric da heliocentric suna ƙarfafa masana ilmin taurari su yi lura sosai. Masana ilmin taurari a wancan lokacin sun kalli halittun sama ta amfani da idanu kawai, ba sa amfani da kayan aiki kamar na'urorin hangen nesa ko na taurari. A wancan lokacin, ba a yi na'urar hangen nesa ba. Wani masanin kimiyyar Italiya, Galileo Galilei, ne ya fara yin na'urar hangen nesa ta wucin gadi a shekarar 1609. Galileo ya yi amfani da na'urar hangen nesa ta wucin gadi don lura da halittun sama kuma ya yi amfani da bayanan lurarsa don yin jayayya da magoya bayan samfurin geocentric.
Wani fitaccen masanin ilmin taurari ɗan Denmark mai suna Tycho Brahe (1546-1601) shi ne masanin ilmin taurari na ƙarshe da ya kalli gawarwakin sama ta amfani da idanu kawai. Bayan ya lura daga 1576 zuwa 1599, sai Tycho Brahe ya yi aiki tare da wani masanin ilmin taurari ɗan Jamus, Johannes Kepler (1571-1630), wanda shi ma masanin lissafi ne. Kepler shi ne mataimakin Tycho Brahe. Haɗin gwiwar da ke tsakanin Tycho Brahe da Kepler bai daɗe ba saboda Tycho Brahe ya mutu. Bayan Tycho Brahe ya mutu, Kepler ya yi amfani da bayanan ilmin taurari da malaminsa ya samu kuma ya shafe kimanin shekaru ashirin na rayuwarsa yana ƙirƙirar samfuran lissafi don bayyana motsin duniyoyi.
An buga aikin Kepler na farko a fannin ilmin taurari mai suna The Mystery of the Universe a shekarar 1596. A cikin littafin, ya nemi daidaitawa tsakanin kewayar taurari bisa ga lurar Copernicus da Tycho Brahe . Amma Kepler ya kasa samun jituwa tsakanin samfuran da Copernicus da Ptolemy suka ƙirƙira tare da sakamakon lurar Tycho Brahe. Saboda haka, ya yi watsi da samfuran Ptolemaic da Copernican sannan ya nemi sabbin samfura. A shekarar 1609, Kepler ya gano cewa ellipses sun dace sosai da sakamakon lurar Tycho Brahe. Kepler ba ya amfani da da'ira a matsayin nau'in hanyar jikin sama, sai dai ellipses.
Dokar Kepler
Kepler ne ya gabatar da wannan doka, rabin ƙarni kafin Isaac Newton ya gabatar da dokokinsa guda uku na motsi da kuma dokar nauyi ta duniya.
Dokar farko ta Kepler
Hanyar kowace duniya idan ta kewaye rana ita ce ellipse, inda rana take a hankali ɗaya.
F1 da F2 Rana tana ɗaya daga cikin wuraren da aka fi mayar da hankali (misali a cikin hoton da aka zaɓa F)2), duniyar tana da nisan r2 daga F2 ko r1 daga F1Idan yanayin duniyar ya canza, r2 da r1 kuma canza.
Duk da haka, r 1 + r 2 koyaushe iri ɗaya ne. Nisa a ana kiranta da rabin babban axis kuma 2a ana kiranta babban axis. Nisa b ana kiranta rabin ƙaramin axis kuma 2b ana kiranta ƙaramin axis. Wurin mai da hankali na ellipse yana nan a nisan c daga tsakiyar ellipse, inda c 2 = a 2 + b 2.
Siffar ellipse ana tantance ta ne ta hanyar rashin daidaituwar (e) na ellipse, inda e = c / a. Rashin daidaituwar ellipse yana tsakanin 0 zuwa 1 (0)
Idan duniyar tana gefen hagu na ellipse (a gefen hagu na F 1 ) to nisan da duniyar ke da shi zuwa rana shine + c. Wannan wurin ana kiransa aphelion. Idan duniyar tana aphelion, duniyar tana a mafi nisanta daga rana. Idan duniyar tana a ƙarshen dama na ellipse (dama na F 2 ) to nisan da duniyar ke da shi zuwa rana shine ac. Wannan wurin ana kiransa perihelion. Idan duniyar tana a wurin perihelion, duniyar tana a mafi kusa da rana.
Dokar Kepler ta biyu
Layin tunani da aka zana daga rana zuwa duniya, yana share yankuna daidai gwargwado, na tsawon lokaci ɗaya.
A cikin hoton da ke ƙasa, akwai misalai biyu kawai na yankuna, wato yankin abc da yankin ade. Waɗannan yankuna biyu suna da girma iri ɗaya. A lokacin lokaci ɗaya, layin tunani da ke haɗa duniyar da rana yana share yankin da ke da girma iri ɗaya. Don haka, lokacin da ake motsawa daga b zuwa c (duniyar tana aphelion), saurin ƙaramin duniya ko duniya yana motsawa a hankali. Akasin haka, lokacin da ake motsawa daga d zuwa e (duniyar tana a perihelion), saurin babban duniya ko duniya yana motsawa da sauri. Don haka, matsakaicin ƙimar duniya lokacin da yake a wurin perihelion da mafi ƙarancin ƙimar duniya lokacin da yake a wurin aphelion.
Dokar Kepler ta uku
Rabon murabba'ai na orbital zamani na duniya zuwa kumburi na the matsakaicin nisan duniya tare da rana (T)2/r3) yana da daidaito, kuma ƙimar iri ɗaya ce ga dukkan duniyoyi. Idan T1 da kuma T2 bayyana lokacin duniyoyi biyu, r1 da r2 yana wakiltar matsakaicin nisan kowace duniya daga rana:
