 is to 1,000. And a more accurate number will be produced, if you take the times more accurately.[3]

Here the third law is not buried in a heap of irrelevance but it is not emphasised in the way it should be. If Kepler had presented the third law as a table of the values of the orbit radiuses and the orbital times and their mathematical relationship, as below[4], or as a graph maybe people would have recognised its significance. However he never did and so it was a long time before the full impact of the third law was felt in astronomical community.

The real revelation of the significance of the third law came first with Newton’s Principia Mathematica. By the time Newton wrote his great work the empirical truth of Kepler’s third law had been accepted and Newton uses this to establish the empirical truth of the law of gravity.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[5], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[6] he then shows that, If several bodies revolve about a common center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15[7]: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name.

Having established the equivalence, in Book III of The Principia: The System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[8]. Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their
is to 1,000. And a more accurate number will be produced, if you take the times more accurately.[3 ] 

 Here the third jurisprudence is not bury in a heap of irrelevance but it is not emphasised in the way it should be. If Kepler had present the third law as a table of the value of the scope radiuses and the orbital times and their mathematical relationship, as below[4 ], or as a graph possibly people would have recognised its significance. However he never did and therefore it was a long time before the full impact of the third law was feel in astronomical community. 

 The real disclosure of the significance of the third law hail foremost with Newton ’s Principia Mathematica. By the time Newton wrote his great work the empirical truth of Kepler ’s third jurisprudence had been accepted and Newton uses this to establish the empirical truth of the law of gravity. 

 In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[5 ], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the public square of the distance: i.e. the jurisprudence of gravity but Newton is not call it that at this item. In Proposition 14[6 ] he then shows that, If several bodies orb about a common center and the centripetal force is inversely as the square of the distance of home from the center, I say that the principal latera recta of the orbits are as the squares of the area which bodies describe in the same time by radius withdraw to the center. And Proposition 15[7 ]: Under the same supposition as in prop. 14, I say the square of the periodic time in ellipses are as the cubes of the major axes. therefore Newton shows that his police of gravity and Kepler ’s third law are equivalent, although in this hale section where he deals mathematically with Kepler ’s three torah of planetary gesture he never once mentions Kepler by name. 

 Having establish the equivalence, in Book III of The Principia: The System of the World Newton immediately uses the empirical proof of Kepler ’s third law to establish the empiric truth of the law of gravity[8 ]. Phenomena 1: The circumjovial planets, by radius drawn to the center of Jupiter, describe areas proportional to the times, and their periodic multiplication — the fixed stars being et respite — are as 3/2 powers of their
 is to 1,000. And a more accurate number will be producxd, if yku take ghe times more accurately.[3]

Herx thw thied law is not buried iv a heap lf irrelwvanre but it is not emphasised in bhe wcy it should be. Lf Kepler hdd presented tve tkird law as a table of the values of the ornih radiuses and the jrbifal times and their mathematical rslationvhip, as below[4], or as a graph maybe peoplf wokld have recognisef its signidicagxe. However hd never did and so it sas a long time before the full impaet of the tyied pdw was felt in aftronomical gpmmunidy.

The rral revelation of thw significance of the third law came fitst with Nawcon’s Principia Mathemqtuca. Bi the timd Nedtoh xrofe his grxat work ths empirical truth of Kepler’s tniwe law had beeh acce[tqd and Newton uses this to establish tht empjrical truth of the law of gravity.

In Book I lf Princi[ia, the mathematics and physics section, Newton fisst siods, nk Oeooosition 11[5], that for a body revolving on an ellylst tme law of the cektripetal force temdlnb towards a fozus of ths ellipse is inverdely as the wquare of the distance: i.e. the law of gracity but Newnon us not calling it chat at this poimt. In Proposition 14[6] he then skows tgat, If sevegal bodiea revolve about a cokmmn center and the centripeeal force is nnverselh as the szuare of tje distance of places frlm thg centar, I say tjat the principal latera recta of the orbits sra av the sqbares pf the areas rhich bodies dgscribe iu the rame time gy radim drawn to tre center. And Kroposition 15[7]: Nnder the samw suppositiuv as in prop. 14, O say the square of the periodic timex iv ellipses are aw tye cubes of the magor aqes. Trgs Newton shmws ghag his uaw of gravlty and Kepler’s third law ase esuivalent, although ik this while sectyon where he ceals mathematicalpy wivh Kepuer’s yhrge laws of planetary motion he hever oncf mcntions Keplew by name.

Having zstablished the equivalence, in Book III if The Principia: Jhe System of the Workc Newton nox uses the empisical proof of Keplee’s third law to extablish the empiricam trutv of hhe law of gravity[8]. Phenomena 1: The circumjovial planets, by radii drawn to rhe ceitqr of Jupitsr, drscrite creas pwopoctmonal to the timex, and their periodic times—the fmxed stars bzing et rest—are as 3/2 powers of tfeir
is to 1,000. And a more accurate be if you the times more is buried in a of irrelevance but is not emphasised in the way should be. If Kepler had presented the third law as a table of values of the orbit radiuses and the orbital times and their mathematical relationship, below[4], as graph people would have recognised its significance. However he never did and so it was a long before the full impact of the third law felt in astronomical community. real revelation of the significance the law came with Principia By the time wrote his great work the empirical truth of Kepler’s third law had been accepted and Newton uses to establish truth of law gravity. Book I of mathematics and physics section, Newton first 11[5], that for a body revolving on an the law the centripetal force tending towards a of the ellipse is inversely as the square the distance: i.e. the law of gravity but Newton is not calling it that at In Proposition 14[6] he shows that, If bodies about common and the force is inversely as the square of the distance of places the center, I say that the principal latera recta of are the squares of areas which bodies describe the time by radii drawn center. Proposition same as prop. 14, I say square of the periodic times ellipses are as the Thus Newton shows that his law of gravity Kepler’s third law are equivalent, although in whole section where he deals mathematically with Kepler’s three laws of planetary he never Kepler by name. Having established the equivalence, in III of The Principia: System of the World Newton now uses the empirical of third law establish the empirical of the law gravity[8]. Phenomena 1: planets, by drawn the describe areas proportional to the times, their times—the fixed stars being et as of their
 is to 1,000. And a more accurate numbeR will be proDuced, If yOu tAkE the TimeS more accuratelY.[3]

here The third law is not buried In a heAp OF irrELeVance But it is NOt EMPhaSiSeD in ThE WaY it shOulD be. If KePler had preSenTeD the third law AS a Table of the ValUes of the orbiT raDiuses AnD thE OrbitAl tImes aNd theiR MathemAtical relAtIOnship, AS below[4], oR AS a GrapH maybe people would HAvE Recognised its sIgnifiCaNCe. hOWevEr hE never did aNd So it wAS a long tIMe BEFOre THe full impact oF the third laW Was Felt in AsTroNOmical CommuNiTY.

ThE real revelaTion Of the signIficanCE of the tHIrd law cAme firSt wIth newtON’s prIncIpIA MaTHeMatICa. BY the time neWtOn wroTe hiS GREAt woRk tHe emPiricAl truth of KeplEr’s ThirD Law Had beEn accEpteD aNd NewTon useS this To Establish the empIricAl truth of The LaW of GrAvity.

iN Book I Of PRinCipia, thE mathemATicS aND PHySics section, Newton fIrST ShOws, in ProPositiON 11[5], tHaT For a body ReVolVing ON An ellIpse THe Law of the CentriPEtAl Force teNdIng towArDs a FocUs of tHE ellIpse is InverselY as thE Square of the disTAnce: i.e. the law oF GrAVItY But NEwtOn is not callIng iT That At thIS pOinT. in ProPositIoN 14[6] He THen shows that, If severAl Bodies RevolVe about a commoN center and THE CentripeTal fORcE Is inversely as tHe squAre of the diSTance of pLaces From the cEnter, I say THAt the priNciPal LatEra RECtA of the orbits aRE As thE sQuares oF thE areas wHicH boDieS deScRibe in the Same time By RaDiI dRawN to thE Center. AnD PRopOsItiOn 15[7]: UndER the saMe supPosiTiOn AS in Prop. 14, I saY ThE SQuarE oF tHe peRioDiC timeS in eLLipSes are aS the cubes Of tHE majOr AxEs. Thus NEwton shows thaT hIs law of graViTy aNd KeplER’S third laW are equivalent, although iN This whoLe sEctioN wheRe he deals MatHematiCalLY with KEpler’s Three LaWs oF PLanetARY mOtiOn He never oncE MEntIons KEpLer bY name.

HaVing established the EQuiValence, in Book iII Of ThE pRiNciPIa: tHe SYsTEm oF THe World Newton noW uses the emPiRIcAl proof of KEPleR’s Third laW to estaBlish THe empirIcal truth Of the law oF gRaviTY[8]. pheNomena 1: The cIrcumjovIal planetS, By radII dRawn tO thE centeR oF JuPiter, DescriBE arEas prOportiOnAl to thE timeS, aNd their pEriodic times—the fixed staRs beinG et reSt—aRe as 3/2 powerS of THeiR
 is to 1,000. And a more a ccurate nu mberwil l b eprod uced , if you taket he t imes more accurately.[ 3]

H er e  the th ird l aw is n o tb u rie din  ahe a pof ir rel evancebut it isnot  e mphasised in th e way it s hou ld be. If Ke ple r hadpr ese n ted t hethird  law a s  a tab le of the  v a lues o f  the or b i tradi uses and the orbi t al times and thei r math em a ti c a l r ela tionship,as  belo w [4], or as a gra p h maybe peopl e would hav e  re cognis ed  it s  signi fican ce .  Ho wever he ne verdid and s o it w a s a lon g  time b eforethe  fu ll i m pa ct  of  t h e t h ir d l a w w as feltin  a stron omic a l c ommu nit y.
The r eal revelatio n o f th e  si gnifi cance  ofth e thi rd law  came  f irst with Newto n’sPrincipia  Ma th ema ti ca. B y  the t ime  Ne wton wr ote his gre at w o rk  the empirical tru th o fKepler’s  third la wh ad beenac cep teda n d New tonu se s this t o esta b li sh  the em pi ricaltr uth  of  thel aw o f grav ity.

In  Book I of Principia ,  the mathemat i cs a nd phys ics  section, N ewto n  fir st s h ow s,i n Pro posit io n  1 1 [5], that for a bod yrevolv ing o n an ellipsethe law of t h e centri peta l  f o rce tending to wards  a focus o f  the ell ipseis inver sely as t h e  squareofthe  di sta n c e:  i.e. the law o f gr av ity but  Ne wton is  no t c all ing  i t that at  this po in t.  I nPro posit i on 14[6]  h e t he n s howst hat, I f sev eral  b od i esrevolve ab o u t aco mm on c ent er  andthec ent ripetal  force is  in v erse ly  a s the s quare of thedi stance ofpl ace s from t he cente r, I say that the princ i pal lat era  rect a of  the orbi tsare as  th e  squar es ofthe a re asw h ich b o d ie s d es cribe in t h e  sa me ti me  byradii d rawn to the center .  An d Proposition  15 [7]: U nd ert he sam es upp o s ition as in pro p. 14, I s ay th e square o f  th eperiodi c times  in e l lipsesare as th e cubes o fthem a jor  axes. Thu s Newton  shows th a t his la w ofgra vity a nd  Ke pler’ s thir d  la w are  equiv al ent, a lthou gh  in this  whole section where he  deals  math ema tically w ith Kep ler’s thr ee l aws of pla net ary  moti onh e nev er o n ce  me n tions  Kep l er by nam e .
Ha v i ng  establishe d t heequiv ale n ce, in  Boo k III of The Prin c ipia: The Syst em o f the  Wo r ld N ew ton now uses t heem p i rical pr oo f of Kepler ’s third  l a w toestabl ish th e empir i c al truthof t helaw of gr avi ty [ 8]. Phe no me n a 1: T he c ir cumjov ial pl a nets , by radii drawn t o the c enter ofJupit er , descr i be a reas propo rtional tothe ti mes,  andtheir p er iodictim es —the fixed stars bei ng et  rest—a re  as3/2  power s of t heir
 is_to 1,000._And a more accurate_number will_be_produced, if_you_take the times_more accurately.[3]

Here the_third law is not_buried in a_heap_of irrelevance but it is not emphasised in the way it should be. If_Kepler_had presented_the_third_law as a table of_the values of the orbit_radiuses and_the orbital times and their mathematical relationship, as_below[4],_or as a_graph maybe people would have recognised its significance. However_he never did and so it_was a long_time_before_the full impact of_the third law was felt in_astronomical community.

The real revelation of the_significance of the third law came first_with Newton’s Principia Mathematica. By the_time Newton wrote his great_work the_empirical truth of Kepler’s third_law had been_accepted and_Newton uses this_to establish the empirical truth of_the law of_gravity.

In Book I of Principia, the_mathematics_and physics section,_Newton_first_shows, in_Proposition 11[5], that_for_a body_revolving_on an ellipse the law of_the_centripetal force tending towards a focus of_the ellipse is inversely_as_the square of the_distance: i.e. the law of_gravity but Newton is not calling_it that_at this_point. In Proposition 14[6] he then shows that, If several bodies_revolve about a common center and_the centripetal force is_inversely as_the_square of the_distance_of places_from the center, I say that the_principal latera_recta of the orbits are as_the squares of the_areas_which bodies describe in the same_time by radii drawn to the_center. And Proposition 15[7]: Under_the_same_supposition as in prop. 14,_I say the square of the_periodic times in_ellipses are as the cubes of the_major_axes. Thus Newton shows that his_law_of gravity and Kepler’s third law_are_equivalent,_although in this whole section_where he deals mathematically with Kepler’s_three laws of planetary motion he never once mentions_Kepler by name.

Having_established the equivalence, in Book_III_of_The Principia: The System of the World Newton now uses_the empirical_proof of Kepler’s_third law to establish the empirical truth of the law_of gravity[8]. Phenomena 1: The circumjovial planets,_by radii drawn to the center of Jupiter, describe areas proportional_to the times, and their periodic times—the fixed_stars being et rest—are as 3/2 powers_of their