Ngā Ture a Kepler mō te Nekehanga Aorangi
Ko te nekehanga o ngā aorangi huri noa i te Rā tētahi o ngā panga nui rawa atu o te pūtaiao. Mō ngā rautau, kua mātakitaki te tangata i ngā tūranga hurihuri o ngā aorangi i te rangi pō, e ngana ana ki te mārama ki ngā tauira me ngā ture kei muri i a rātou. I puta tētahi tohu nui i roto i te hītori o te whetū i te wā i titoa ai e Johannes Kepler (1571–1630) ētahi ture e toru i whakaahua tika i te nekehanga o ngā aorangi i runga i ngā raraunga mātakitaki. Kāore i whakautua noa e ngā ture e toru a Kepler te "me pēhea" te nekehanga o ngā aorangi, engari i whakarato hoki i tētahi piriti ki te mārama ki te "take" o taua nekehanga, i whakamāramahia i muri mai e Isaac Newton mā te ture o te kaha ā-papa. Ka tirohia e tēnei tuhinga ngā ture a Kepler mō te nekehanga o ngā aorangi, ō rātou hiranga, me ō rātou pānga ki te pūtaiao hou.
Te Papamuri o te Putanga Mai o ngā Ture a Kepler
I mua i a Kepler, ko te tauira geocentric (te pokapū o te Ao) i rongonuihia e Ptolemy te mea i kaha ake. I whakamahia e tēnei tauira ngā porowhita iti (epicycles) hei whakamārama i te nekehanga whakamuri o ngā aorangi. Ahakoa he rite tonu ki ngā kitenga o taua wā, he uaua, he koretake hoki te tauira.
Nā te huarahi pōrohe a Nicolaus Copernicus (me te Rā i waenganui) i whakangawari ake ngā mea, engari i mau tonu a Copernicus i ngā porowhita porowhita, ā, kāore i tino tika ana hua. I te mahi tahi a Kepler me ngā raraunga tirotiro tino tika a Tycho Brahe, ka mōhio ia ko te whakaaro me tino porowhita ngā porowhita aorangi i whakararu i te tika. Nā tēnei i kitea ai e Kepler he tika ake te whakaahua i ngā porowhita aorangi hei porowhita.
Te Ture Tuatahi a Kepler: He Porowhita ngā Āmiomio Aorangi
E mea ana te ture tuatahi a Kepler:
"Ka huri haere ngā aorangi i te Rā i roto i ngā porowhita porowhita, ko te Rā kei te arotahi kotahi o te porowhita."
Ka taea te whakaaro he porowhita te porowhita he "porowhita papatahi pakupaku." Ahakoa he pokapū kotahi tō te porowhita, e rua ngā pūwāhi motuhake o te porowhita e kiia nei ko ngā arotahi. I kitea e Kepler kāore te Rā i te pokapū o te porowhita, engari kei tētahi o ngā arotahi. He mea nui tēnei nā te mea e whakamārama ana he aha i kore ai ngā aorangi e rite tonu te tawhiti mai i te Rā i ngā wā katoa.
I roto i te porowhita porowhita, e rua ngā tūranga tino tawhiti:
– Perihelion: te pūwāhi tata rawa atu o te aorangi ki te Rā.
– Aphelion: te pūwāhi tawhiti rawa atu o te aorangi mai i te Rā.
Hei tauira, he porowhita porowhita te porowhita o te Ao, nō reira kāore i te nui te rerekētanga o te tawhiti o te perihelion me te aphelion. Heoi, mō tētahi aorangi pērā i a Mercury, he "porowhita" ake te porowhita, nō reira he nui ake te rerekētanga o te tawhiti.
Ko te hiranga nui o tēnei ture he panonitanga tauira: kāore te taiao e hiahia ki te whai i te "tino pai" o ngā porowhita pāngarau, engari me whai i ngā ture e rite ana ki te mooni o ngā raraunga.
Te Ture Tuarua a Kepler: Ngā Horahanga ōrite i roto i ngā Wā ōrite
E mea ana te ture tuarua a Kepler:
"Ka horahia e te rārangi whakaaro e hono ana i te aorangi ki te Rā ngā horahanga ōrite i roto i ngā wā ōrite."
Ko te tikanga o tēnei, ki te tangohia e tātou ngā wā e rua he rite te roa—hei tauira, 30 ngā rā—kātahi ka rite tonu te horahanga e "whiwhihia ana" e te rārangi aorangi-Rā i roto i aua rā 30, ahakoa kei hea te aorangi i roto i tōna porowhita. Nō reira, kāore te tere o te aorangi i te pumau.
Ina tata te aorangi ki te perihelion, he iti ake tōna tawhiti mai i te Rā, nō reira, kia taea ai te hora i taua rohe, me tere ake te neke o te aorangi. I tetahi atu taha, ina tata ki te aphelion, ka pōturi ake te neke o te aorangi.
E whakamārama ana tēnei ture i te kitenga ko ētahi aorangi te āhua nei he tere ake, he puhoi ake rānei te neke i ngā whetū papamuri. I roto i te ahupūngao hou, e pā tata ana te ture tuarua ki te tiakitanga o te nekehanga koki: i te whakatata mai o te aorangi, ka piki ake tōna tere; i te neke atu, ka heke tōna tere, engari ka mau tonu tōna "rahinga o te nekehanga hurihuri".
Te Ture Tuatoru a Kepler: Te Hononga i waenga i te Wā me te Tawhiti Āmiomio
E mea ana te ture tuatoru a Kepler:
"He rite te tapawhā o te wā hurihanga o te aorangi ki te tapawhā o te tuaka haurua-matua o tōna porowhita."
I tuhia mā te pāngarau:
\[
T^2 \propto a^3
\]
kāore i te mana:
– Ko T te wā hurihanga o te aorangi (te wā e huri ai i te Rā kotahi te wā),
– ko a te tuaka haurua-matua o te porowhita (te tawhiti toharite o te aorangi mai i te Rā).
Ki te whakamahia e tātou ngā waeine whetū (AU) mō te tawhiti me ngā tau mō te wā, ka tino māmā noa iho tēnei whanaungatanga mō ngā aorangi o te Pūnaha Rā. Hei tauira:
– Papatūānuku: \(a = 1\) AU, \(T = 1\) tau → \(T^2 = a^3 = 1\)
– Māte: \(a \approx 1{,}52\) AU → \(a^3 \approx 3{,}51\), nō reira \(T \approx \sqrt{3{,}51} \approx 1{,}87\) tau, e ai ki ngā raraunga whetū.
He kaha te ture tuatoru nā te mea ka taea e ngā kaipūtaiao te whakatau tata i ngā wā porowhita mena e mōhiotia ana te tawhiti, me te ritenga kē. I roto i te ao whetū o ēnei rā, ka whakamahia he mātāpono rite ki te tatau i ngā papatipu o ngā tinana tiretiera i roto i ngā pūnaha whetu rua, me te whakatau tata i ngā tawhā porowhita o ngā aorangi o waho.
He aha te hiranga o ngā ture a Kepler?
I te tīmatanga, he ture ā-wheako ngā ture e toru a Kepler, arā, i titoa mai i ngā raraunga tirotiro, ehara i te ariā kaha. Heoi, he mea whakamiharo tō rātou tika. Ko ētahi o ō rātou pānga nui ko:
1. Te Whakangāwari i te Tauira Pūnaha Rā
Nā te mea he porowhita, ka ngaro te hiahia mō ngā huringa uaua. Nā reira, ka māmā ake te whakatauira me te matapae i te nekehanga o ngā aorangi.
2. Hei turanga mō ngā mahi hangarau o te rangi
Nā Kepler i whakatakoto te ara mō Newton. Kātahi ka whakakitea e Newton ko ngā ture a Kepler i ahu mai i te meka he rite whakamuri te kaha o te papatipu ki te tapawhā o te tawhiti.
3. Ngā tono i runga i ngā amiorangi me ngā misioni ātea
Ko te mātāpono o ngā ara porowhita e whakamahia ana i roto i te whakamahere ara porowhita amiorangi, te whakawhiti ara porowhita (hei tauira, te whakawhiti Hohmann), me te whakatere waka mokowhiti.
4. Whakatenatenahia te whānautanga o ngā tikanga pūtaiao hou
I whakaatu a Kepler i te mana o ngā raraunga me ngā pāngarau i roto i te whakatakoto i ngā ture o te taiao, ahakoa i whakahē ana hua i ngā whakaaro matatika o mua.
Ngā Here me ngā Whanaketanga Anō
Ahakoa he tino tika mō ngā kaupapa maha, ehara ngā ture a Kepler i te tauira "tino" kāore he rohe. Tērā ētahi rerekētanga iti e puta ake ana nā:
– ngā raruraru ā-papa i waenga i ngā aorangi,
– ngā āhua koretake o ngā tinana o te rangi,
– ā, i runga i ngā tauine tino tika, ngā pānga o te whanaungatanga whānui.
Ko tētahi tauira rongonui ko te perihelion precession a Mercury, kāore i tino whakamāramahia e ngā tikanga miihini Newtonian, ā, i te mutunga ka whakamāramahia e te ariā whānui a Einstein mō te whanaungatanga. Ahakoa rā, mō te nuinga o ngā tātaitanga ā-pōro i roto i te Pūnaha Rā me ngā tono hangarau, he tino whai hua tonu ngā ture a Kepler.
Whakamutunga
He tohu nui ngā ture a Kepler mō te nekehanga o ngā aorangi i roto i te hītori o te pūtaiao. E whakamārama ana te Ture I ko ngā porowhita aorangi he porowhita me te Rā i te arotahi kotahi. E whakaatu ana te Ture II ka tere ake te nekehanga o ngā aorangi ina tata atu ki te Rā, ā, ka pōturi ake ina tawhiti atu, e tohuhia ana e ngā horahanga porowhita ōrite i ngā wā ōrite. E hono ana te Ture III i te wā porowhita ki te tawhiti toharite o te aorangi, e āhei ai te matapae me te tatau whānui i roto i te whetū arorangi.
Ehara i te mea ko ngā ture mō te nekehanga o ngā aorangi anake, engari i whakamātauhia e ngā ture a Kepler ka taea te mārama ki te taiao mā te tirotiro me te whakatauira pāngarau. Tae noa ki tēnei rā, kei te whakaakona tonutia, kei te whakamahia tonutia ēnei ture, ā, he wāhi nui hei urunga mō te mārama ki te kaha ā-papatipu, ki ngā porowhita amiorangi, me ngā āhuatanga o ngā tinana o te rangi puta noa i te ao.
