ʻatikala e pili ana Ke kānāwai o Kepler
Ke hoʻomanaʻo nei ʻoe i nā hoʻomanaʻo o ka holo mua ʻana i kahi kaʻa? Ke noho ʻoe i loko o kahi kaʻa e neʻe ana, ʻike ʻoe me he mea lā e neʻe ana kahi lāʻau a hale paha. I kēlā manawa, manaʻo paha ʻoe e neʻe ana nā lāʻau a hale paha, ʻoiai ʻoe a me ke kaʻa e hoʻomaha ana. ʻOiaʻiʻo, neʻe ʻoe a me ke kaʻa, ʻoiai e hoʻomaha ana nā lāʻau a hale paha. ʻIke maoli ʻia kēia ʻike o ka neʻe hoʻopunipuni i kēlā me kēia lā. I kēlā me kēia kakahiaka, "puka ka lā" ma ka ʻaoʻao hikina a laila neʻe i ke komohana a "napoʻo" ma ka ʻaoʻao komohana i ke awakea.
Pēlā nō, i ka pō, ʻike pinepine ʻoe i ka mahina e neʻe ana mai ka hikina a i ke komohana. Ua manaʻo paha ʻoe a kuhi paha ua neʻe ka lā a me ka mahina a puni ka honua, ʻoiai ua hoʻomaha ka honua?
Ka mōʻaukala o ka hoʻomohala ʻana o ka ʻike hōkū
Ua manaʻo pū nā kānaka i noho i ka wā kahiko (mua o BC) i ka neʻe ʻana o ka lā, ka mahina, a me nā kino lani ʻē aʻe a puni ka honua, ʻoiai ua hoʻomaha ka honua. I nā huaʻōlelo ʻē aʻe, ua manaʻo ʻia ka honua ʻo ia ke kikowaena o ke ao holoʻokoʻa (geocentric). Hoʻokumu ʻia kēia kuhiakau ma luna o ka ʻike sensory palena o nā kānaka, ka poʻe e nānā ana i kēlā me kēia lā i ka neʻe ʻana o ka lā, ka mahina, a me nā hōkū, ʻoiai ua manaʻo ka honua ua hoʻomaha. E like me ke noho ʻana i loko o kahi kaʻa e neʻe ana, ʻike ʻoe me he mea lā e neʻe ana nā lāʻau a i ʻole nā hale. Ua noiʻi ʻia a hoʻomohala ʻia ke kuhiakau ʻana ʻo ka honua ke kikowaena o ke ao holoʻokoʻa e ka mea kilo hōkū Helene ʻo Claudius Ptolemaeus (100-170 AD) i ke kenekulia ʻelua AD a ua manaʻoʻiʻo ʻia no nā makahiki 1400 e hiki mai ana.
Wahi a Ptolemy, aia ka honua ma ke kikowaena o ka ʻōnaehana lā. Hoʻopuni ka lā a me nā hōkūhele i kahi pōʻai (neʻe rotational) kahi e hoʻopuni ai ke kikowaena o kēia pōʻai i ka honua ma ke ala pōʻai (neʻe revolutionary).
I ka makahiki 1543, ua hāpai ka mea kilo hōkū Polani ʻo Nicolaus Copernicus (1473-1543) i kahi kumu hoʻohālike heliocentric, kahi i kū ai ka lā ma ke kikowaena o ka ʻōnaehana lā. ʻO nā hōkūhele e pili ana i ka honua a puni kahi pōʻai (neʻe rotational) kahi e hoʻopuni ai ke kikowaena o kēia pōʻai i ka lā ma ke ala pōʻai (neʻe revolutionary). Ua ʻoi aku ka ʻike o Copernicus ma mua o Ptolemy no ka mea ua kau ʻo ia i ka lā ma ke kikowaena o ka ʻōnaehana lā. Eia naʻe, hoʻohana mau ʻo Copernicus i nā pōʻai ma ke ʻano he ʻano neʻe honua.
ʻO nā hoʻopaʻapaʻa hoihoi e pili ana i nā hiʻohiʻona geocentric a me heliocentric e paipai i nā mea kilo hōkū e hana i nā nānā akahele. Ua nānā nā mea kilo hōkū i kēlā manawa i nā kino lani me ka hoʻohana ʻana i nā maka wale nō, ʻaʻole i hoʻohana i nā mea hana e like me nā telescope a i ʻole nā binoculars hōkū. I kēlā manawa, ʻaʻole i hana ʻia ka telescope. ʻO ka telescope hiki ke hoʻohana ʻia e nānā i nā kino lani ua hana mua ʻia e kahi ʻepekema Italia, ʻo Galileo Galilei, i ka makahiki 1609. Ua hoʻohana ʻo Galileo i kāna telescope hana e nānā i nā kino lani a hoʻohana i kāna ʻikepili nānā e hoʻopaʻapaʻa me nā mea kākoʻo o ke kumu hoʻohālike geocentric.
ʻO kekahi mea kilo hōkū kaulana Denemaka i kapa ʻia ʻo Tycho Brahe (1546-1601) ka mea kilo hōkū hope loa i nānā i nā kino lani me ka hoʻohana ʻana i nā maka wale nō. Ma hope o ka nānā ʻana mai 1576 a i 1599, a laila ua hui pū ʻo Tycho Brahe me kekahi mea kilo hōkū Kelemania, ʻo Johannes Kepler (1571-1630), he kanaka makemakika hoʻi. ʻO Kepler ke kōkua o Tycho Brahe. ʻAʻole i lōʻihi ka hui pū ʻana ma waena o Tycho Brahe lāua ʻo Kepler no ka mea ua make ʻo Tycho Brahe. Ma hope o ka make ʻana o Tycho Brahe, ua hoʻohana ʻo Kepler i ka ʻikepili kilo hōkū i loaʻa i kāna kumu a ua hoʻolilo i kahi iwakālua mau makahiki o kona ola e hana ana i nā kumu hoʻohālike makemakika e wehewehe i ka neʻe ʻana o nā hōkūhele.
Ua paʻi ʻia ka hana mua a Kepler ma ke kahua o ka ʻike hōkū i kapa ʻia ʻo The Mystery of the Universe i ka makahiki 1596. Ma ka puke, ua ʻimi ʻo ia i kahi kūlike ma waena o nā kaapuni honua e like me nā nānā ʻana a Copernicus lāua ʻo Tycho Brahe . Akā, ʻaʻole i loaʻa iā Kepler ka launa pū ʻana ma waena o nā kumu hoʻohālike i hoʻomohala ʻia e Copernicus lāua ʻo Ptolemy me nā hopena o nā nānā ʻana a Tycho Brahe. No laila, ua haʻalele ʻo ia i nā kumu hoʻohālike Ptolemaic lāua ʻo Copernican a laila ʻimi i nā kumu hoʻohālike hou. I ka makahiki 1609, ua ʻike ʻo Kepler he kūpono loa nā ellipses me nā hopena o nā nānā ʻana a Tycho Brahe. ʻAʻole hoʻohana hou ʻo Kepler i kahi pōʻai ma ke ʻano he ʻano o ke ala o nā kino lani, akā ʻo nā ellipses.
Ke kānāwai o Kepler
Ua kau ʻia kēia kānāwai e Kepler, he hapalua kenekulia ma mua o ka hāpai ʻana o Isaac Newton i kāna mau kānāwai ʻekolu o ka neʻe ʻana a me ke kānāwai o ka umekaumaha honua.
Ke kānāwai mua o Kepler
ʻO ke ala o kēlā me kēia hōkūhele ke hoʻopuni i ka lā he ellipse ia, kahi i kū ai ka lā ma kekahi kiko.
F1 a me F2 he mau kiko kikowaena elliptical. Aia ka lā ma kekahi o nā kiko kikowaena (no ka laʻana ma ke kiʻi i koho ʻia ʻo F2), aia ka honua ma kahi mamao o r2 mai F2 a i ʻole r1 mai F1Inā loli ke kūlana o ka honua, r2 a r1 hoʻi e loli.
ʻOiai pēlā, ua like mau ʻo r 1 + r 2. Ua kapa ʻia ka mamao ʻo a ʻo ka axis semimajor a ua kapa ʻia ʻo 2a ʻo ka axis major. Ua kapa ʻia ka mamao ʻo b ʻo ka axis semiminor a ua kapa ʻia ʻo 2b ʻo ka axis minor. Aia ke kiko waena o ka ellipse ma ka mamao c mai ke kikowaena o ka ellipse, kahi c 2 = a 2 + b 2.
Hoʻoholo ʻia ke ʻano ellipse e ka eccentricity (e) o ka ellipse, kahi e = c / a. Loaʻa ka eccentricity o kahi ellipse mai 0 a 1 (0
Inā aia ka honua ma ka ʻaoʻao hema o ka ellipse (ma ka hema o F 1 ) a laila ʻo ka mamao o ka honua i ka lā he a + c. Ua kapa ʻia kēia kiko he aphelion. Ke aia ka honua ma ka aphelion, aia ka honua ma kona mamao loa mai ka lā. Inā aia ka honua ma ka ʻaoʻao ʻākau o ka ellipse (ʻākau o F 2 ) a laila ʻo ka mamao o ka honua i ka lā he ac. Ua kapa ʻia kēia kiko he perihelion. Ke aia ka honua ma ke kiko o ka perihelion, aia ka honua ma ka mamao kokoke loa mai ka lā.
Ke kānāwai ʻelua o Kepler
ʻO ka laina hoʻokalakupua i kaha ʻia mai ka lā a i ka honua, e hoʻopili ana i nā wahi like, no ka manawa like.
Ma ke kiʻi ma lalo nei, ʻelua wale nō laʻana o nā wahi, ʻo ia hoʻi ka wahi abc a me ka wahi ade. Ua like ka nui o kēia mau wahi ʻelua. I ka manawa like, ua uhi ka laina hoʻokalakupua e hoʻohui ana i ka honua a me ka lā i ka wahi i like ka nui. No laila, i ka neʻe ʻana mai b a i c (aia ka honua ma ka aphelion), neʻe lohi ka wikiwiki o ka honua liʻiliʻi a i ʻole ka honua. I ka ʻaoʻao ʻē aʻe, i ka neʻe ʻana mai d a i e (aia ka honua ma ka perihelion), neʻe wikiwiki ka wikiwiki o ka honua nui a i ʻole ka honua. No laila, ʻo ka wikiwiki honua kiʻekiʻe loa i ka wā ma ka wahi perihelion a me ka wikiwiki honua haʻahaʻa loa i ka wā ma ka wahi aphelion.
Ke kānāwai ʻekolu o Kepler
ʻO ka lakio o nā huinahā o ka orbital manawa o kahi honua i ka kupa o the nā mamao awelika o ka honua me ka lā (T2/r3) he paʻa, a ua like ka waiwai no nā hōkūhele āpau. Inā ʻo T1 a me T2 e hōʻike i ka wā o ʻelua mau hōkūhele, r1 a r2 hōʻike i ka mamao awelika o kēlā me kēia hōkūhele mai ka lā:
