He tuhinga mō Te ture a Kepler
Kei te maumahara tonu koe ki ngā maharatanga o te ekenga tuatahi i tētahi motuka? I roto i tētahi motuka e neke ana, ka kite koe me te mea kei te neke tētahi rākau, tētahi whare rānei. I taua wā, tera pea ka whakaaro koe kei te neke ngā rākau, ngā whare rānei, i a koe e okioki ana me te motuka. Inaa, kei te neke koe me te motuka, i a koe e okioki ana me ngā rākau, ngā whare rānei. Ka wheakohia tēnei wheako o te nekehanga rūpahu i ia rā. I ia ata, ka "putanga o te rā" i te pae rawhiti, kātahi ka neke ki te hauauru, ā, ka "tō" ki te pae hauauru i te ahiahi.
Waihoki, i te pō, ka kite pinepine koe i te marama e neke ana mai i te rawhiti ki te hauauru. Kua whakaaro koe, kua whakapae rānei koe i te neke haere o te rā me te marama i te whenua, i te wā e okioki ana te whenua?
Te hītori o te whanaketanga o te whetū
I whakaaro anō hoki ngā tāngata i noho i ngā wā onamata (tīmatanga o BC) ko te rā, te marama, me ētahi atu tinana rangi e neke haere ana i te whenua, i te wā e okioki ana te whenua. Arā, ko te whenua te pokapū o te ao (geocentric). Ko tēnei whakaaro e ahu mai ana i te iti o ngā wheako pārongo o te tangata, e mātakitaki ana i ia rā i te rā, te marama, me ngā whetū e neke ana, i te wā e okioki ana te whenua. He rite ki te noho i roto i te motuka e neke ana, ka kite koe me te mea kei te neke ngā rākau, ngā whare rānei. Ko te whakaaro ko te whenua te pokapū o te ao i rangahauhia, ā, i whakawhanakehia e te tohunga whetū Kariki. Karauria Ptoremaeus (100-170 AD) i te rautau tuarua AD, ā, i whakaponohia mō ngā tau 1400 i muri mai.
E ai ki a Ptolemy, ko te whenua te pokapū o te pūnaha rā. E karapotia ana te whenua e te rā me ngā aorangi i tētahi porowhita (nekehanga hurihuri) ā, ko te pokapū o tēnei porowhita e karapoti ana i te whenua i roto i tētahi ara porowhita (nekehanga hurihuri).
I te tau 1543, he tohunga whetū Pōrana Nicholas Copernicus (1473-1543) i whakaaro i tētahi tauira heliocentric, arā, ko te rā kei waenganui o te pūnaha rā. Kei roto i ngā aorangi ko te whenua e karapoti ana i tētahi porowhita (nekehanga hurihuri) kei reira te pokapū o tēnei porowhita e karapoti ana i te rā i roto i tētahi ara porowhita (nekehanga hurihuri). He matatau ake te māramatanga o Copernicus i a Ptolemy nā te mea i whakanohoia e ia te rā ki waenganui o te pūnaha rā. Ahakoa rā, kei te whakamahi tonu a Copernicus i ngā porowhita hei momo nekehanga aorangi.
Ko ngā tautohetohe whakahihiri mō ngā tauira geocentric me te heliocentric e akiaki ana i ngā kaitātari whetū ki te tirotiro āta haere. I taua wā, i tirotirohia e ngā kaitātari whetū ngā tinana o te rangi mā te whakamahi i ngā kanohi anake, kāore i whakamahia ngā taputapu pēnei i ngā karu tiro, i ngā karu tiro whetū rānei. I taua wā, kāore anō kia hangaia te karu tiro. Ko te karu tiro ka taea te whakamahi hei tirotiro i ngā tinana o te rangi i hangaia tuatahitia e te kaipūtaiao Itari, a Galileo Galilei, i te tau 1609. I whakamahia e Galileo tana karu tiro horihori hei tirotiro i ngā tinana o te rangi, ā, i whakamahia e ia ana raraunga tirotiro hei tautohetohe ki ngā kaitautoko o te tauira geocentric.
Ko tētahi tohunga whetū rongonui o Tenemāka ko Tycho Brahe (1546-1601) te tohunga whetū whakamutunga i mātakitaki i ngā tinana o te rangi mā te whakamahi i ngā kanohi anake. Whai muri i te mātakitaki mai i te tau 1576 ki te 1599, ka mahi tahi a Tycho Brahe me tētahi tohunga whetū Tiamana, a Johannes Kepler (1571-1630), he tohunga pāngarau anō hoki. Ko Kepler te kaiawhina a Tycho Brahe. Kāore i roa te mahi tahi a Tycho Brahe rāua ko Kepler nā te mea i mate a Tycho Brahe. I muri i te matenga o Tycho Brahe, i whakamahia e Kepler ngā raraunga whetū i riro mai i tana kaiako, ā, e rua tekau tau te roa o tōna oranga e hanga ana i ngā tauira pāngarau hei whakamārama i ngā nekehanga o ngā aorangi.
Ko te mahi tuatahi a Kepler i roto i te ao whetū, ko Te Mea Ngaro o te Ao Whānui te taitara, i whakaputaina i te tau 1596. I roto i te pukapuka, i rapu ia i tētahi hononga i waenga i ngā porowhita o ngā aorangi e ai ki a Copernicus rāua ko Tycho brahengā kitenga a Kepler. Engari kāore i kitea e Kepler te ōritetanga i waenga i ngā tauira i whakawhanakehia e Copernicus rāua ko Ptolemy me ngā hua o ngā kitenga a Tycho Brahe. Nō reira, i whakarērea e ia ngā tauira Ptolemy me Copernican, kātahi ka rapu tauira hou. I te tau 1609, i kitea e Kepler he tino pai ngā porowhita ki ngā hua o ngā kitenga a Tycho Brahe. Kāore a Kepler e whakamahi ana i te porowhita hei momo ara o ngā tinana o te rangi, engari ko ngā porowhita.
Te ture a Kepler
I whakatakotoria tēnei ture e Kepler, i te haurua rautau i mua i te whakaaro o Isaac Newton ki ana ture e toru mō te nekehanga me te ture o te kaha ā-papatipu.
Te ture tuatahi a Kepler
He porowhita te ara o ia aorangi ina karapoti i te rā, arā, kei te arotahi kotahi te rā.
F1 me F2 he pūwāhi arotahi porowhita. Kei tētahi o ngā pūwāhi arotahi te rā (hei tauira, i roto i te ahua i tīpakohia ko F2), kei te tawhiti o r te aorangi2 mai i te F2 r ranei1 mai i te F1. Ki te rerekē te tūnga o te aorangi, r2 me r1 huri hoki.
Ahakoa rā, r1 +r2 he rite tonu. Ko te tawhiti a ka kiia ko te tuaka haurua-matua, ā, ko te 2a ka kiia ko te tuaka matua. Ko te tawhiti b ka kiia ko te tuaka haurua-iti, ā, ko te 2b ka kiia ko te tuaka iti. Kei te tawhiti c mai i te pokapū o te ellipse te pūwāhi arotahi o te porowhita, ko c2 = a2 + b2.
Ko te āhua o te porowhita ka whakatauhia e te āhua rerekē (e) o te porowhita, ko e = c / a. Ko te āhua rerekē o te porowhita kei waenga i te 0 ki te 1 (0
Mena kei te pito maui o te porowhita te aorangi (ki te taha maui o F1) kātahi ko te tawhiti o te aorangi ki te rā ko a + c. Ka kiia tēnei pūwāhi ko te aphelion. Ina kei te aphelion te aorangi, kei tōna tawhiti rawa atu te aorangi mai i te rā. Mena kei te pito matau o te porowhita te aorangi (ki te taha matau o F2) kātahi ko te tawhiti o te aorangi ki te rā ko ac. Ka kiia tēnei pūwāhi ko te perihelion. Ina tae te aorangi ki te pūwāhi perihelion, kei te tawhiti tata rawa atu te aorangi mai i te rā.
Te ture tuarua a Kepler
Ko te rārangi pohewa e tuhia ana mai i te rā ki te aorangi, e horapa ana i ngā horahanga ōrite, mō te wā kotahi.
I te pikitia i raro nei, e rua noa ngā tauira o ngā horahanga, arā, ko te horahanga abc me te horahanga ade. He rite te rahi o ēnei horahanga e rua. I roto i te wā kotahi, ka horahia e te rārangi whakaaro e hono ana i te aorangi me te rā te horahanga he rite te rahi. Nō reira, ina neke mai i b ki c (kei te aphelion te aorangi), ka puhoi ake te tere o te aorangi iti, o te aorangi rānei. Engari, ina neke mai i d ki e (kei te perihelion te aorangi), ka tere ake te tere o te aorangi nui, o te aorangi rānei. Nō reira, ko te tere aorangi mōrahi ina kei te pūwāhi perihelion me te tere aorangi iti rawa ina kei te pūwāhi aphelion.
Te ture tuatoru a Kepler
Ko te ōwehenga o ngā tapawhā o te orbital wā o tētahi aorangi ki te kupiki o te the ngā tawhiti toharite o te aorangi mā te te rā (T2/r3) he pumau, ā, he rite tonu te uara mō ngā aorangi katoa. Mena ko T1 a T2 tuhia te wā o ngā aorangi e rua, r1 me r2 e tohu ana i te tawhiti toharite o ia aorangi mai i te rā:
