Nkhani yokhudza Lamulo la Kepler
Kodi mukukumbukirabe zokumbukira za kukwera galimoto koyamba? Mukakhala mgalimoto yoyenda, mumaona ngati mtengo kapena nyumba ikuyenda. Panthawiyo, mungaganize kuti mitengo kapena nyumba zikuyenda, pamene inu ndi galimoto muli kupuma. Ndipotu, inu ndi galimotoyo mumasuntha, pamene mitengo kapena nyumbazo mukupuma. Zochitika izi zoyenda zabodza zimachitika tsiku lililonse. M'mawa uliwonse, "dzuwa limatuluka" kum'mawa kenako limasunthira kumadzulo ndipo "limalowa" kumadzulo masana.
Mofananamo, usiku, nthawi zambiri mumawona mwezi ukuyenda kuchokera kum'mawa kupita kumadzulo. Kodi munayamba mwaganizapo kapena kuganiza kuti dzuwa ndi mwezi zimayendayenda padziko lapansi, pamene dziko lapansi linali bata?
Mbiri ya chitukuko cha zakuthambo
Anthu omwe anakhalapo kale (kumayambiriro kwa BC) ankaonanso dzuwa, mwezi, ndi zinthu zina zakuthambo zikuyendayenda padziko lapansi, pamene dziko lapansi linali kupuma. Mwa kuyankhula kwina, dziko lapansi limaonedwa kuti ndi pakati pa chilengedwe chonse (geocentric). Lingaliro limeneli limachokera pa zomwe anthu amamva pang'ono, omwe amaona dzuwa, mwezi, ndi nyenyezi zikuyenda tsiku ndi tsiku, pomwe dziko lapansi likumva ngati likupuma. Mofanana ndi kukhala m'galimoto yoyenda, mumaona ngati mitengo kapena nyumba zikuyenda. Lingaliro lakuti dziko lapansi ndi pakati pa chilengedwe chonse linafufuzidwa ndikupangidwa ndi katswiri wa zakuthambo wachigiriki. Klaudiyo Ptolemayo (100-170 AD) m'zaka za zana lachiwiri AD ndipo anakhulupirira zaka 1400 zotsatira.
Malinga ndi Ptolemy, dziko lapansi linali pakati pa dongosolo la dzuwa. Dzuwa ndi mapulaneti zimazungulira bwalo (kuzungulira) komwe pakati pa bwaloli zimazungulira dziko lapansi m'njira yozungulira (kusinthasintha).
Mu 1543, katswiri wa zakuthambo wa ku Poland Nicholas Copernicus (1473-1543) adapereka chitsanzo cha heliocentric, momwe dzuwa linali pakati pa dongosolo la dzuwa. Mapulaneti akuphatikizapo dziko lapansi mozungulira bwalo (kuzungulira) komwe pakati pa bwaloli amazungulira dzuwa munjira yozungulira (kusinthasintha). Copernicus anali ndi chidziwitso chapamwamba kuposa Ptolemy chifukwa adayika dzuwa pakati pa dongosolo la dzuwa. Komabe, Copernicus akadali kugwiritsa ntchito mabwalo ngati njira yoyendera mapulaneti.
Mikangano yosangalatsa yokhudza zitsanzo za geocentric ndi heliocentric imalimbikitsa akatswiri a zakuthambo kuti aziyang'ana mosamala kwambiri. Akatswiri a zakuthambo panthawiyo ankaona zinthu zakuthambo pogwiritsa ntchito maso okha, sankagwiritsa ntchito zida monga ma telescope kapena ma binocular a nyenyezi. Panthawiyo, telescope inali isanapangidwe. Telescope yomwe ingagwiritsidwe ntchito kuwona zinthu zakuthambo inapangidwa koyamba ndi wasayansi waku Italy, Galileo Galilei, mu 1609. Galileo anagwiritsa ntchito telescope yake yopangira kuti aone zinthu zakuthambo ndipo anagwiritsa ntchito deta yake yowonera kuti atsutsane ndi omwe ankachirikiza chitsanzo cha geocentric.
Katswiri wa zakuthambo wotchuka wa ku Denmark dzina lake Tycho Brahe (1546-1601) anali katswiri womaliza wa zakuthambo kuona zinthu zakuthambo pogwiritsa ntchito maso okha. Atayang'ana kuyambira 1576 mpaka 1599, Tycho Brahe anagwirizana ndi katswiri wa zakuthambo wa ku Germany, Johannes Kepler (1571-1630), yemwenso anali katswiri wa masamu. Kepler anali wothandizira Tycho Brahe. Mgwirizano pakati pa Tycho Brahe ndi Kepler unatenga nthawi yochepa chifukwa Tycho Brahe anamwalira. Tycho Brahe atamwalira, Kepler anagwiritsa ntchito deta ya zakuthambo yomwe mphunzitsi wake adapeza ndipo anakhala zaka pafupifupi makumi awiri za moyo wake popanga zitsanzo za masamu kuti afotokoze mayendedwe a mapulaneti.
Buku loyamba la Kepler pankhani ya zakuthambo lotchedwa The Mystery of the Universe linasindikizidwa mu 1596. M'bukuli, iye anafuna kuti pakhale kugwirizana pakati pa mapulaneti ozungulira malinga ndi Copernicus ndi Tycho brahezomwe adaziona. Koma Kepler adalephera kupeza mgwirizano pakati pa zitsanzo zomwe Copernicus ndi Ptolemy adapanga ndi zotsatira za zomwe Tycho Brahe adaziona. Chifukwa chake, adasiya zitsanzo za Ptolemaic ndi Copernican kenako adafunafuna zitsanzo zatsopano. Mu 1609, Kepler adapeza kuti ma ellipse anali oyenera kwambiri ndi zotsatira za zomwe Tycho Brahe adaziona. Kepler sagwiritsanso ntchito bwalo ngati njira yoyendera zinthu zakuthambo, koma ma ellipse.
Lamulo la Kepler
Lamulo limeneli linaperekedwa ndi Kepler, zaka makumi asanu Isaac Newton asanapereke malamulo ake atatu oyendetsera zinthu ndi lamulo la mphamvu yokoka ya chilengedwe chonse.
Lamulo loyamba la Kepler
Njira ya pulaneti iliyonse ikazungulira dzuwa imakhala ngati ellipse, pomwe dzuwa limakhala pamalo amodzi.
F1 ndi F2 ndi malo ozungulira. Dzuwa lili pa malo amodzi ozungulira (monga pachithunzi chosankhidwa F2), dziko lapansi lili patali ndi r2 kuchokera ku F2 kapena r1 kuchokera ku F1Ngati malo a dziko lapansi asintha, r2 ndi r1 kusinthanso.
Ngakhale zili choncho, r1 +r2 nthawi zonse imakhala yofanana. Mtunda a umatchedwa semimajor axis ndipo 2a umatchedwa major axis. Mtunda b umatchedwa semiminor axis ndipo 2b umatchedwa minor axis. Malo ofunikira a ellipse ali pa mtunda c kuchokera pakati pa ellipse, komwe c2 = a2 + b2.
Mawonekedwe a ellipse amatsimikiziridwa ndi kusiyana kwa (e) kwa ellipse, komwe e = c / a. Kusiyana kwa ellipse kumayambira pa 0 mpaka 1 (0).
Ngati dziko lapansi lili kumapeto kwa ellipse (kumanzere kwa F1) ndiye kuti mtunda wa dziko lapansi kupita ku dzuwa ndi a + c. Mfundo imeneyi imatchedwa aphelion. Dziko lapansi likakhala pa aphelion, dziko lapansili limakhala patali kwambiri ndi dzuwa. Ngati dziko lapansili lili kumapeto kwa ellipse (kumanja kwa F2) ndiye kuti mtunda wa dziko lapansi kupita ku dzuwa ndi ac. Mfundo imeneyi imatchedwa perihelion. Dziko lapansi likakhala pamalo a perihelion, dziko lapansi limakhala pa mtunda wapafupi kwambiri ndi dzuwa.
Lamulo lachiwiri la Kepler
Mzere wongopeka womwe umatengedwa kuchokera ku dzuwa kupita ku dziko lapansi, umachotsa madera ofanana, kwa nthawi yomweyo.
Mu chithunzi chomwe chili pansipa, pali zitsanzo ziwiri zokha za madera, omwe ndi dera la abc ndi dera la ade. Madera awiriwa ali ndi kukula kofanana. Munthawi yomweyi, mzere wongoyerekeza wolumikiza dziko lapansi ndi dzuwa umadutsa dera lomwe lili ndi kukula kofanana. Chifukwa chake, posuntha kuchokera ku b kupita ku c (dziko lapansi lili pa aphelion), liwiro la dziko laling'ono kapena dziko lapansi limayenda pang'onopang'ono. M'malo mwake, posuntha kuchokera ku d kupita ku e (dziko lapansi lili pa perihelion), liwiro la dziko lalikulu kapena dziko lapansi limayenda mofulumira. Chifukwa chake, liwiro lalikulu la mapulaneti likakhala pa perihelion ndi liwiro lochepera la mapulaneti likakhala pa aphelion.
Lamulo lachitatu la Kepler
Chiŵerengero cha mabwalo a kuzungulira nyengo ya dziko lapansi ku ku kyubu ya the mtunda wapakati wa dziko lapansi ndi dzuwa (T)2/r3) ndi yosasintha, ndipo mtengo wake ndi womwewo pa mapulaneti onse. Ngati T1 ndi T2 tchulani nthawi ya mapulaneti awiri, r1 ndi r2 ikuyimira mtunda wapakati wa pulaneti iliyonse kuchokera ku dzuwa:
