கேள்வி: கெப்லரின் கோள் இயக்க விதிகள் பற்றி நீங்கள் என்ன அறிந்துள்ளீர்கள்?
பதில்: படிமம்:Johannes Kepler.jpg]] வானியல், ஜொஹான்னெஸ் கெப்லர் முதன்மையான பங்களிப்பு கெப்லரின் கோள் இயக்க விதிகள் எனப்படும் மூன்று விதிகளாகும். கண்பார்வைக் குறைவுள்ளவராக இருந்தும், மிகவும் திறமையுள்ளவராக விளங்கிய ஜெர்மானியக் கணிதவியலாளர் கெப்லரின் விதிகளின் உருவாக்கத்துக்கு டென்மார்க்கைச் சேர்ந்த வானியலாளர் டைக்கோ பிரா (Tycho Brahe) என்பவரது துல்லிய வானியல் குறிப்புகள் (அவதானிப்புகள்) மிகவும் துணை புரிந்தன.In his ''Astronomia nova'', Kepler presented only a proof that Mars' orbit is elliptical. Evidence that the other known planets' orbits are elliptical was presented only in 1621. See: Johannes Kepler, ''Astronomia nova'' … (1609), [https://archive.org/stream/Astronomianovaa00Kepl#page/284/mode/2up p. 285.] After having rejected circular and oval orbits, Kepler concluded that Mars' orbit must be elliptical. From the top of page 285: ''"Ergo ellipsis est Planetæ iter; … "'' (Thus, an ellipse is the planet's [i.e., Mars'] path; … ) Later on the same page: ''" … ut sequenti capite patescet: ubi simul etiam demonstrabitur, nullam Planetæ relinqui figuram Orbitæ, præterquam perfecte ellipticam; … "'' ( … as will be revealed in the next chapter: where it will also then be proved that any figure of the planet's orbit must be relinquished, except a perfect ellipse; … ) And then: ''"Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … "'' (Chapter 59. Proof that Mars' orbit, … , is a perfect ellipse: … ) The geometric proof that Mars' orbit is an ellipse appears as Protheorema XI on pages 289–290. Kepler stated that every planet travels in elliptical orbits having the Sun at one focus in: Johannes Kepler, ''Epitome Astronomiae Copernicanae'' [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, part 1, III. De Figura Orbitæ (III. On the figure [i.e., shape] of orbits), [https://books.google.com/books?id=wa2SE_6ZL7YC&pg=PA658#v=onepage&q&f=false pages 658–665.] From p. 658: ''"Ellipsin fieri orbitam planetæ … "'' (Of an ellipse is made a planet's orbit … ). From p. 659: ''" … Sole (Foco altero huius ellipsis) … "'' ( … the Sun (the other focus of this ellipse) … ).In his ''Astronomia nova'' ... (1609), Kepler did not present his second law in its modern form. He did that only in his ''Epitome'' of 1621. Furthermore, in 1609, he presented his second law in two different forms, which scholars call the "distance law" and the "area law". * His "distance law" is presented in: ''"Caput XXXII. Virtutem quam Planetam movet in circulum attenuari cum discessu a fonte."'' (Chapter 32. The force that moves a planet circularly weakens with distance from the source.) See: Johannes Kepler, ''Astronomia nova'' … (1609), [https://archive.org/stream/Astronomianovaa00Kepl#page/164/mode/2up pp. 165–167.] [https://archive.org/stream/Astronomianovaa00Kepl#page/166/mode/2up On page 167], Kepler states: ''" … , quanto longior est αδ quam αε, tanto diutius moratur Planeta in certo aliquo arcui excentrici apud δ, quam in æquali arcu excentrici apud ε."'' ( … , as αδ is longer than αε, so much longer will a planet remain on a certain arc of the eccentric near δ than on an equal arc of the eccentric near ε.) That is, the farther a planet is from the Sun (at the point α), the slower it moves along its orbit, so a radius from the Sun to a planet passes through equal areas in equal times. However, as Kepler presented it, his argument is accurate only for circles, not ellipses. * His "area law" is presented in: ''"Caput LIX. Demonstratio, quod orbita Martis, … , fiat perfecta ellipsis: … "'' (Chapter 59. Proof that Mars' orbit, … , is a perfect ellipse: … ), Protheorema XIV and XV, [https://archive.org/stream/Astronomianovaa00Kepl#page/284/mode/2up pp. 291–295.] On the top p. 294, it reads: ''"Arcum ellipseos, cujus moras metitur area AKN, debere terminari in LK, ut sit AM."'' (The arc of the ellipse, of which the duration is delimited [i.e., measured] by the area AKM, should be terminated in LK, so that it [i.e., the arc] is AM.) In other words, the time that Mars requires to move along an arc AM of its elliptical orbit is measured by the area of the segment AMN of the ellipse (where N is the position of the Sun), which in turn is proportional to the section AKN of the circle that encircles the ellipse and that is tangent to it. Therefore, the area that is swept out by a radius from the Sun to Mars as Mars moves along an arc of its elliptical orbit is proportional to the time that Mars requires to move along that arc. Thus, a radius from the Sun to Mars sweeps out equal areas in equal times. In 1621, Kepler restated his second law for any planet: Johannes Kepler, ''Epitome Astronomiae Copernicanae'' [Summary of Copernican Astronomy] (Linz ("Lentiis ad Danubium"), (Austria): Johann Planck, 1622), book 5, [https://books.google.com/books?id=wa2SE_6ZL7YC&pg=PA668#v=onepage&q&f=true page 668]. From page 668: ''"Dictum quidem est in superioribus, divisa orbita in particulas minutissimas æquales: accrescete iis moras planetæ per eas, in proportione intervallorum inter eas & Solem."'' (It has been said above that, if the orbit of the planet is divided into the smallest equal parts, the times of the planet in them increase in the ratio of the distances between them and the sun.) That is, a planet's speed along its orbit is inversely proportional to its distance from the Sun. (The remainder of the paragraph makes clear that Kepler was referring to what is now called angular velocity.) ஐசாக் நியூட்டன் பின்னாளைய கண்டுபிடிப்புகளான, நியூட்டனின் இயக்கவிதி மற்றும் புவியீர்ப்பு தொடர்பான விதிகள் என்பவற்றின் உருவாக்கத்துக்குக் கெப்லரின் கண்டுபிடிப்பு அடிக்களமாக (ஆதாரமாக) அமைந்தது எனலாம். தற்கால நோக்கில், கெப்லரின் விதிகள், நியூட்டனின் விதிகளின் விளைவுகளாக இருந்தாலும், வரலாற்றின்படி, கெப்லரின் விதிகளே முதலில் வெளியானவை.