Mitemo yaKepler yeKufamba Kwepasi
Kufamba kwemapuraneti akatenderedza Zuva kwagara kuri chimwe chezvinhu zvikuru zvesainzi. Kwemazana emakore, vanhu vakatarisa kuchinja kwemapuraneti mudenga rehusiku, vachiedza kunzwisisa mapatani nemitemo iri shure kwawo. Chiitiko chakakosha munhoroondo yekuongorora nyeredzi chakauya apo Johannes Kepler (1571–1630) akagadzira mitemo mitatu yaitsanangura kufamba kwemapuraneti nenzira yakarurama zvichibva padata rekucherechedza. Mitemo mitatu yaKepler haina kungopindura "kuti" mapuraneti anofamba sei, asiwo yakapa zambuko rekunzwisisa "nei" kufamba ikoko kuchiitika, izvo zvakazotsanangurwa zvakare naIsaac Newton kuburikidza nemutemo wegiravhiti. Chinyorwa chino chinoongorora mitemo yaKepler yekufamba kwemapuraneti, kukosha kwayo, uye simba rayo pasainzi yemazuva ano.
Nhoroondo yeKubuda kweMitemo yaKepler
Kepler asati asvika, muenzaniso we geocentric (wepakati peNyika) waifarirwa naPtolemy. Muenzaniso uyu waishandisa madenderedzwa madiki (epicycles) kutsanangura kufamba kwemapuraneti kunooneka. Kunyange zvazvo waienderana nekucherechedza kwenguva iyoyo, muenzaniso uyu waive wakaoma uye usina kunaka.
Maitiro aNicolaus Copernicus ekutarisa denga (neZuva riri pakati) akarerutsa zvinhu, asi Copernicus akaramba achitenderera denderedzwa, zvichiita kuti mhedzisiro yake isanyatsojeka. Kepler, achishanda neruzivo rwaTycho Brahe rwekutarisa, akazoona kuti fungidziro yekuti denderedzwa remapuraneti rinofanira kunge rakatenderera zvakakwana yakavhiringidza kururama. Izvi zvakaita kuti Kepler aone kuti denderedzwa remapuraneti raitsanangurwa nemazvo se ellipses.
Mutemo wekutanga waKepler: Mapoka epasi anotenderera denderedzwa
Mutemo wekutanga waKepler unoti:
"Mapuraneti anofamba-famba achitenderedza Zuva mudenderedzwa rakaita denderedzwa, Zuva riri panzvimbo imwe chete padenderedzwa rakaita denderedzwa."
Dura redenderedzwa rinogona kufungidzirwa se "denderedzwa rakati sandara zvishoma." Kunyange zvazvo denderedzwa riine pakati peimwe, dura redenderedzwa rine nzvimbo mbiri dzakakosha dzinonzi foci. Kepler akaona kuti Zuva harisi pakati pedura redenderedzwa, asi pane imwe yenzvimbo dzakapoteredza. Izvi zvakakosha nekuti zvinotsanangura kuti sei mapuraneti asiri nguva dzose ari kure neZuva.
Munzira ye elliptical orbit, pane nzvimbo mbiri dzakanyanya:
– Perihelion: nzvimbo iri pedyo zvikuru neZuva pasi rose.
– Aphelion: nzvimbo iri kure zvikuru neZuva pasi rose.
Semuenzaniso, Nyika ine orbit inenge yakatenderera yakaita denderedzwa, saka musiyano uripo pakati pemadaro eperihelion neeaphelion hauna kukosha. Zvisinei, kune planet yakaita seMercury, ellipse "inotenderera" zvakanyanya, saka musiyano wedaro unoonekwa zvakanyanya.
Kukosha kukuru kwemutemo uyu kuchinja kwemaonero: zvakasikwa hazvifanirwe kutevedzera "kukwana" kwemasvomhu, asi zvinotevedzera mitemo inoenderana nechokwadi chedata.
Mutemo wechipiri waKepler: Nzvimbo dzakaenzana munguva dzakaenzana
Mutemo wechipiri waKepler unoti:
"Mutsetse wekufungidzira unobatanidza nyika neZuva unobvisa nzvimbo dzakaenzana panguva imwe chete."
Izvi zvinoreva kuti kana tikatora nguva mbiri dzakareba zvakaenzana—semuenzaniso, mazuva makumi matatu—ipapo nzvimbo "yakatsvairwa" nepasi-mutsetse weZuva mumazuva iwayo makumi matatu ichave yakafanana, zvisinei nekuti pasi riri kupi mudenderedzwa rayo. Nekuda kweizvozvo, kumhanya kwepasi hakusi kuchinjika.
Kana puraneti iri pedyo neperihelion, daro rayo kubva kuZuva rinenge riri diki, saka kuti iparadze nzvimbo imwe chete, puraneti inofanira kufamba nekukurumidza. Kusiyana neizvi, kana iri pedyo neaphelion, puraneti inofamba zvishoma nezvishoma.
Mutemo uyu unotsanangura zvakaonekwa kuti mapuraneti dzimwe nguva anoita seanofamba nekukurumidza kana kuti zvishoma nezvishoma kupfuura nyeredzi dziri kumashure. Mufizikisi yemazuva ano, mutemo wechipiri wakabatana zvakanyanya nekuchengetedzwa kwe angular momentum: sezvo puraneti iri kuswedera pedyo, kumhanya kwayo kunowedzera; sezvainofamba, kumhanya kwayo kunoderera, asi "huwandu hwekufamba kwayo" hunoramba hwakafanana.
Mutemo wechitatu waKepler: Hukama huripo pakati penguva nedaro remuchadenga
Mutemo wechitatu waKepler unoti:
"Sikweya yenguva yekuchinja kwenyika inoenderana necube ye semi-major axis yekutenderera kwayo."
Zvakanyorwa nemasvomhu:
\[
T^2 \propto a^3
\]
di mana:
– T inguva yekuchinja kwenyika (nguva inotora kutenderera Zuva kamwe chete),
– a ndiyo semi-major axis yeellipse (avhareji yedaro repasi kubva kuZuva).
Kana tikashandisa mayuniti emuchadenga (AU) kureva daro uye makore kureva nguva, hukama uhwu hunova nyore kwazvo kumapuraneti ari muSolar System. Semuenzaniso:
– Nyika: \(a = 1\) AU, \(T = 1\) gore → \(T^2 = a^3 = 1\)
– Mars: \(a \approx 1{,}52\) AU → \(a^3 \approx 3{,}51\), saka \(T \approx \sqrt{3{,}51} \approx 1{,}87\) makore, zvichienderana nedata remuchadenga.
Mutemo wechitatu une simba nekuti unobvumira masayendisiti kufungidzira nguva dzemuchadenga kana daro richizivikanwa, uye zvinopesana. Mukuongorora nyeredzi dzemazuva ano, musimboti wakafanana unoshandiswa kuverenga huwandu hwezvinhu zvemudenga muhurongwa hwenyeredzi mbiri uye kufungidzira maparamita emuchadenga emapuraneti.
Nei Mitemo yaKepler Yakakosha Kwazvo?
Mitemo mitatu yaKepler pakutanga yaive yekuongorora, zvichireva kuti yakagadzirwa kubva padata rekucherechedza, kwete kubva padzidziso yesimba. Zvisinei, kururama kwayo kunoshamisa. Zvimwe zvezvakakosha zvayakaita zvinosanganisira:
1. Kurerutsa modhi yeSolar System
Nema "ellipses", kudiwa kwema "epicycles" akaomarara kwakapera. Kufamba kwemapuraneti kwakava nyore kutevedzera uye kufanotaura.
2. Iva hwaro hwemakanika ekudenga
Kepler akagadzirira Newton nzira. Newton akabva aratidza kuti mitemo yaKepler inongoerekana yavapo nekuti simba regiravhiti rinoenderana nechikamu chedaro.
3. Mashandisirwo emasetiraiti nemabasa emuchadenga
Nheyo yekufamba kwe elliptical inoshandiswa mukuronga satellite orbit, kutamiswa kwe orbit (semuenzaniso, kutamiswa kweHohmann), uye kufamba kwespacecraft.
4. Kurudzira kuberekwa kwenzira dzesainzi dzemazuva ano
Kepler akaratidza simba redata nemasvomhu mukugadzira mitemo yechisikigo, kunyangwe mhedzisiro yake yakaramba fungidziro dzeuzivi dzenguva refu.
Zvipingamupinyi uye Zvimwe Zvichiitika
Kunyange zvazvo iri chaiyo kune zvakawanda, mitemo yaKepler haisi muenzaniso "wakazara" usina miganhu. Pane zvimwe zvinhu zvidiki zvinokanganisa zvinokonzerwa ne:
- kukanganiswa kwesimba regiravhiti pakati pemapuraneti,
- maumbirwo asina kukwana emitumbi yekudenga,
- uye pazviyero zvakanyatsojeka, mhedzisiro yehukama hwese.
Muenzaniso wakakurumbira ndeweMercury's perihelion precession, iyo isina kutsanangurwa zvizere neNewtonian mechanics uye yakazotsanangurwa nedzidziso yaEinstein ye relativity. Kunyange zvakadaro, pakuverenga kwakawanda kwe orbital muSolar System uye mashandisirwo einjiniya, mitemo yaKepler inoramba iri hwaro hunobatsira zvikuru.
Mhedziso
Mitemo yaKepler yekufamba kwemapuraneti inhanho huru munhoroondo yesainzi. Mutemo wekutanga unotsanangura kuti madenderedzwa emapuraneti akafanana neZuva riri panzvimbo imwe chete. Mutemo wechipiri unoratidza kuti mapuraneti anofamba nekukurumidza kana ari pedyo neZuva uye anononoka kana ari kure, zvichiratidzwa nenzvimbo dzakaenzana dzekutenderera munguva dzakaenzana. Mutemo wechitatu unobatanidza nguva yekutenderera neavhareji yedaro repuraneti, zvichiita kuti kufanotaura kwakawanda uye kuverenga mukuongorora nyeredzi.
Kupfuura kungova mitemo yekufamba kwemapuraneti, mitemo yaKepler yakaratidza kuti zvisikwa zvinogona kunzwisiswa kuburikidza nekucherechedza nekungwarira uye kutevedzera masvomhu. Nanhasi, mitemo iyi ichiri kudzidziswa, kushandiswa, uye inoshanda senzvimbo inokosha yekunzwisisa simba rinokwevera pasi, marongero esatellite, uye mashandiro emitumbi yekudenga muchadenga.
