Nā ʻāpana kala a me ka pō o ka lā

Hōʻike ka ʻatikala i kaʻu mau papa no nā haumāna kula waena - nā mea hoʻonaʻauao o ka National Children's Fund. Ke ʻimi nei ke kahua i nā keiki a me nā ʻōpio maikaʻi loa (mai ka papa XNUMX o ke kula haʻahaʻa a hiki i ke kula kiʻekiʻe) a hāʻawi i "nā haʻawina" i nā haumāna i koho ʻia. Eia naʻe, ʻaʻole lākou i komo i ka unuhi ʻana i ke kālā, akā i ka mālama piha ʻana i ka hoʻomohala ʻana i ke talena, ma ke ʻano he kānāwai, i nā makahiki he nui. ʻAʻole like me nā papahana ʻē aʻe o kēia ʻano, ʻo nā kānaka ʻepekema kaulana, nā kiʻi moʻomeheu, nā kānaka koʻikoʻi a me nā poʻe naʻauao ʻē aʻe, a me kekahi poʻe kālai'āina, e mālama koʻikoʻi i nā papa o ka Foundation.

Hoʻopili ʻia nā hana a ka Foundation i nā aʻo kumu a pau o ke kula kumu, koe naʻe nā haʻuki, me ka hana noʻeau. Ua hoʻokumu ʻia ke kālā ma 1983 ma ke ʻano he antidote i ka ʻoiaʻiʻo. Hiki i kekahi ke noi i ka waihona kālā (maʻamau ma o ke kula, ʻoi aku ka maikaʻi ma mua o ka hopena o ka makahiki kula), akā, ʻoiaʻiʻo, aia kekahi sieve, kahi kaʻina hana.

E like me kaʻu i haʻi mua ai, ua hoʻokumu ʻia ka ʻatikala ma kaʻu mau papa haku, ma Gdynia, ma Malaki 2016, ma ke kula kiʻekiʻe ʻo 24th ma ke kula kiʻekiʻe III. Navy. No nā makahiki he nui, ua hoʻonohonoho ʻia kēia mau seminar ma lalo o ka mana o ka Foundation e Wojciech Thomalczyk, he kumu o ka charisma kupaianaha a me ka pae naʻauao kiʻekiʻe. I ka makahiki 2008, ua komo ʻo ia i ka ʻumi kiʻekiʻe ma Polani, i hāʻawi ʻia i ka inoa ʻo Professor of Pedagogy (i hāʻawi ʻia e ke kānāwai i nā makahiki he nui aku nei). Aia kahi hoʻonui iki i ka ʻōlelo: "ʻO ka hoʻonaʻauao ka axis o ka honua".

a me ka mahina ʻoluʻolu mau - a laila hiki iā ʻoe ke manaʻo e noho nei mākou ma kahi honua liʻiliʻi ma kahi ākea nui, kahi e neʻe ai nā mea a pau, ana ʻia i ke kenimika a me kekona. Hoʻoweliweli iki iaʻu, ʻo ka hiʻohiʻona o ka manawa. Ua aʻo mākou ʻo ka huina eclipse aʻe, ʻike ʻia mai ka wahi o Warsaw i kēia lā, aia ma ... 2681. Manaʻo wau ʻo wai ka mea e ʻike? Aneane like ka nui o ka La a me ka mahina i ko kakou lewa - no laila pōkole loa a kupanaha loa ka eclipses. No nā kenekulia, pono e lawa kēlā mau minuke pōkole e ʻike i ka corona solar. He mea kupanaha ka hana ʻana i ʻelua manawa i ka makahiki ... akā ʻo ia wale nō ke ʻike ʻia ma kahi o ka Honua no kahi manawa pōkole. Ma muli o ka neʻe ʻana o ke kai, ke neʻe nei ka mahina mai ka Honua - i loko o 260 miliona mau makahiki e mamao loa ia e ʻike wale mākou (mākou???) i nā eclipses annular.

ʻO ka mea mua i wānana eclipseʻO Thales o Miletus (28-585 mau kenekulia BC). ʻAʻole paha mākou e ʻike inā ua hana maoli ia, ʻo ia hoʻi, inā ua wānana ʻo ia, no ka mea, ʻo ka ʻoiaʻiʻo o ka eclipse ma Asia Minor i hana ʻia ma Mei 567, 566 BC he mea i hōʻoia ʻia e nā helu hou. ʻOiaʻiʻo, haʻi wau i ka ʻikepili no ka moʻolelo o kēia lā. I koʻu wā kamaliʻi, noʻonoʻo wau i ka helu ʻana o nā kānaka i nā makahiki. No laila, ʻo kēia, no ka laʻana, XNUMX BC, e hiki mai ana ka makahiki hou a hauʻoli nā kānaka: XNUMX mau makahiki BC wale nō! Ua hauʻoli paha lākou i ka hiki ʻana mai o "ko mākou wā"! He aha ka huli ʻana o nā millennia a mākou i ʻike ai i kekahi mau makahiki i hala aku nei!

Ka Makemakika o ka helu ana i na la a me na pae nā pōʻalo, ʻaʻole paʻakikī loa, akā ua paʻa i nā ʻano mea like ʻole e pili ana i ka maʻamau a, ʻoi aku ka maikaʻi, me ka neʻe ʻole ʻana o ke kino i nā orbit. Makemake au e ʻike i kēia makemakika. Pehea e hiki ai ia Thales o Miletus ke helu pono? He maʻalahi ka pane. Pono kāu palapala honua. Pehea e hana ai i palapala ʻāina? ʻAʻole paʻakikī kēia, ʻike ka poʻe ʻAigupita kahiko i ka hana. I ke aumoe, puka mai na kahuna elua iluna o ka hale. Noho kēlā me kēia o lākou a huki i kāna mea e ʻike ai (e like me kāna hoa hana). Ma hope o ʻelua kaukani makahiki, ʻike mākou i nā mea āpau e pili ana i ka neʻe ʻana o ka honua ...

Geometry nani, a i ʻole leʻaleʻa ma ka "rug"

ʻAʻole makemake ka poʻe Helene i nā helu, ua huli lākou i ka geometry. ʻO kēia kā mākou e hana ai. ʻO kā mākou eclipse e maʻalahi, waihoʻoluʻu, akā e like me ka hoihoi a me ka maoli. ʻAe mākou i ka ʻaha kūkā o ka neʻe ʻana o ke kiʻi polū ma ke ʻano e uhi ai i ka ʻulaʻula. E kapa kākou i ke kiʻi uliuli ʻo ka mahina, a ʻo ke kiʻi ʻulaʻula ka lā. Ke nīnau nei mākou iā mākou iho i kēia mau nīnau:

1. pehea ka lōʻihi o ka pōʻeleʻele;
2. ke uhi ʻia ka hapalua o ka pahu hopu;

   Laiki. 1 ʻO ka "kāpena" he nui me ka lā a me ka mahina

3. he aha ka uhi nui loa;
4. hiki ke kālailai i ka hilinaʻi o ka uhi pale i ka manawa? Ma kēia 'atikala (ua kaupalena au i ka nui o ka kikokikona) e nānā au i ka nīnau lua. Ma hope o kēia he geometry maikaʻi, ʻaʻole paha me ka helu ʻole. E nana kakou i ka fig. 1. Hiki ke manaʻo ʻia e pili ana ia me ... ka pō o ka lā?

Pono wau e ʻōlelo ʻoiaʻiʻo e koho ʻia nā hana aʻu e kūkākūkā ai, i hoʻopili ʻia i ka ʻike a me nā mākau o nā haumāna kula waena a me ke kula kiʻekiʻe. Akā, hoʻomaʻamaʻa mākou i nā hana e like me ka pāʻani ʻana o nā mea mele i nā unahi, a hana nā mea pāʻani i nā hoʻomaʻamaʻa hoʻomohala maʻamau. Ma waho aʻe, ʻaʻole anei he moena nani wale nō (fig. 1)?

Laiki. 2 "Blue" Moon a me "Red" Sun

ʻO ko mākou kino lani, ma ka liʻiliʻi loa, he mau ʻāpana kala. Polū ka mahina, ʻulaʻula ka lā (maikaʻi no ke kala ʻana). me keia manawa eclipse Hahai ka mahina i ka lā ma ka lani, hopu ... a pani. Pela no kakou. ʻO ka hihia maʻalahi loa, ke neʻe ka mahina e pili ana i ka Lā, e like me ka mea i hōʻike ʻia ma ka Fig. 2. Hoʻomaka ka pōʻeleʻele i ka wā e pā ai ka ʻaoʻao o ka diski o ka Moon i ka ʻaoʻao o ka diski o ka Lā (Fig. 2) a pau i kona hele ʻana ma waho.

Laiki. 3 Hoʻokokoke ka mahina i ka lā ma ka diagonal

Manaʻo mākou e hoʻoneʻe ka "Moon" i hoʻokahi kelepona i kēlā me kēia ʻāpana o ka manawa, no ka laʻana, no ka minuke. ʻEwalu ʻāpana o ka manawa, e ʻōlelo i nā minuke. ʻO ka hapalua pōʻalo lā pohihihi loa Ua pani ʻia ka hapalua o ke kelepona ʻelua: ma hope o 2 a me 6 mau minuke. He maʻalahi ka pākēneka obscuration graph. I loko o nā minuke mua ʻelua, e pani like ka pale ma ka helu o ka zero a i ka 1, ʻo nā minuke ʻelua e hiki mai ana e hōʻike ʻia ma ka helu like.

Eia kekahi laʻana hoihoi loa (Fig. 3). Hoʻokokoke ka mahina i ka lā ma ka diagonal. E like me kā mākou ʻaelike uku no kēlā me kēia minuke, ʻo ka eclipse ka lōʻihi o 8√2 mau minuke - i ka waenakonu o kēia manawa, loaʻa iā mākou kahi eclipse piha. E helu kākou i ka ʻāpana o ka lā i uhi ʻia ma hope o ka manawa t (Fig. 3). Ina ua hala t mau minuke mai ka hoomaka ana o ka eclipse, a no ia mea, ua like ka mahina ma ke kii. 5, a laila (noʻonoʻo!) No laila, ua uhi ʻia (ka ʻāpana o ka huinahā APQR), e like me ka hapalua o ka pā lā, no laila, ua uhi ʻia i ka wā, ʻo ia. ma hope o 4 mau minuke (a laila 4 mau minuke ma mua o ka pau ʻana o ka pōʻeleʻele).

Laiki. 4 Kipi o ka hana "shading".

Huina hoʻokahi manawa (t = 4√2), a ʻo ka pakuhi o ka hana "ʻaoʻao malu" he ʻelua arc o parabolas (Fig. 4).

E hoʻopā ko mākou mahina polū i ke kihi me ka lā ʻulaʻula, akā uhi ʻia ia, ʻaʻole hele ma ka diagonal, akā he diagonal iki. ʻO ke kuhikuhi o ka neʻe ʻana i kēia manawa he vector [6], ʻo ia hoʻi, "ʻehā mau keena ma ka ʻākau, ʻekolu mau pū i luna." ʻO ke kūlana o ka Lā e hoʻomaka ai ka pō (kūlana A) i ka wā e hui ai nā ʻaoʻao o nā "kino lani" i ka hapahā o ko lākou lōʻihi. Ke neʻe ka mahina i kahi B, e pōʻeleʻele ʻo ia i ka hapaono o ka Lā, a ma ke kūlana C e uhi ʻia ka hapalua. Ma ke kūlana D, loaʻa iā mākou kahi eclipse piha, a laila hoʻi nā mea a pau, "e like me ia."

Laiki. 5 He hapa o ka La i hunaia i ka manawa t

Pau ka eclipse ke kū ka mahina ma ke kūlana G. Ua lōʻihi ka lōʻihi pauku lōʻihi AG. Inā, e like me ka wā ma mua, lawe mākou ma ke ʻano he ʻāpana o ka manawa i ka wā i hala ai ka mahina "hoʻokahi huinahā", a laila ua like ka lōʻihi o ka AG. Inā mākou e hoʻi i ka ʻaha kahiko he 4 me 4 ko mākou kino lani, ʻokoʻa ka hopena (he aha?). E like me ka maʻalahi o ka hōʻike ʻana, pani ka pahu hopu ma hope o ka t <15. Hiki ke ʻike ʻia ka pakuhi o ka hana "pakeneka o ka uhi pale" ma ka fig. 6.

Laiki. 6 Kipi o ka hana "palekana pākēneka".

Eclipse a lele like

Laiki. 7 Ke ālai ʻia o ka pā o ka lā i ka wā o ka pō i hōʻike ʻia ma ka fig. 6

ʻAʻole paʻa ka pilikia o nā pōʻai inā ʻaʻole mākou e noʻonoʻo i ka hihia o nā pōʻai. ʻOi aku ka paʻakikī o kēia, akā e hoʻāʻo kākou e noʻonoʻo i ka wā e uhi ai kekahi pōʻai i ka hapalua o kekahi - a ma ka hihia maʻalahi, ke neʻe kekahi o lākou ma ke anawaena e hoʻopili ai iā lāua ʻelua. Ua kamaʻāina ke kaha kiʻi i ka poʻe paʻa i kekahi kāleka hōʻaiʻē.

He paʻakikī ka helu ʻana i ke kūlana o nā māla, no ka mea, ʻo ka mea mua, ʻo ia ka ʻike o ke kumu no ka wahi o kahi ʻāpana pōʻai, ʻo ka lua, ka ʻike o ke arc o ke kihi, a ʻo ke kolu (a ʻoi aku ka maikaʻi o nā mea āpau), ka hiki. e hoopau i kekahi hoohalike lele. ʻAʻole wau e wehewehe i ke ʻano o ka "equation transitive", e nānā i kahi laʻana (Fig. 8).

Laiki. 8 "Spherical" eclipse

ʻO ka ʻāpana pōʻai ʻo ia ka "puʻu" i koe ma hope o ka ʻoki ʻana i ka pōʻai me kahi laina pololei. ʻO ka ʻāpana o ia ʻāpana he S = 1/2r²(φ-sinφ), kahi r ka radius o ka pōʻai, a ʻo φ ka huina waena i kau ai ka ʻāpana (Fig. 8). Loaʻa maʻalahi kēia ma ka unuhi ʻana i ka ʻāpana o ka triangle mai kahi o ka ʻāpana pōʻai.

Mokuna O₁O₂ (ka mamao ma waena o nā kikowaena o nā pōʻai) a laila ua like me 2rcosφ/2, a me ke kiʻekiʻe (ākea, “waistline”) h = 2rsinφ/2. No laila, inā makemake mākou e helu i ka wā e uhi ai ka mahina i ka hapalua o ka pā o ka lā, pono mākou e hoʻoponopono i ka hoohalike: a ma hope o ka hoʻomaʻamaʻa ʻana, lilo ia:

Laiki. 9 Nā kiʻi o nā hana ʻelua

ʻOi aku ka hoʻonā o ia mau hoohalike ma mua o ka algebra maʻalahi - aia nā ʻāpana ʻelua a me kā lākou mau hana trigonometric i ka hoohalike. ʻAʻole hiki ke hoʻohālikelike ʻia i nā ʻano kuʻuna. ʻO ia ke kumu i kapa ʻia ai lele. E nānā mua kākou i nā pakuhi o nā hana ʻelua, ʻo ia hoʻi nā hana a me nā hana. Eia nō naʻe, hiki iā mākou ke loaʻa i kahi mea hoʻohālikelike a i ʻole… hoʻohana i ka koho Solver i ka pāpalapala Excel. Hiki i kēlā me kēia haumāna kula kiʻekiʻe ke hana i kēia, no ka mea, ʻo ia ke kenekulia 20. Ua hoʻohana au i kahi mea hana Mathematica ʻoi aku ka maʻalahi a eia kā mākou hopena me ka XNUMX mau wahi decimal o ka pololei ʻole:

SetPrecision[FindRoot[x==Sin[x]+Pi/2,{x,2}],20] {x⇒2.3098814600100574523}.

Laiki. 10 Animation o ka eclipse ma matematica

Hoʻololi mākou i kēia i nā degere ma ka hoʻonui ʻana me 180/π. Loaʻa iā mākou he 132 degere, 20 mau minuke, 45 a me ka hapahā o ka arc kekona. E helu mākou ʻo ka mamao i ke kikowaena o ka pōʻai ʻo O₁O₂ = 0,808 radius, a me "pūhaka" 2,310.