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   Message 15,965 of 17,516   
   qripet@gmail.com to All   
   Newton's Principia Book III Propositions   
   19 Jan 18 11:23:18   
   
   Newton's Principia Book III Propositions 1 to 8   
      
   In Propositions 1, 2, 3 and 8 Newton does not mention the mass of   
   solar objects but only the square of their distance from the sun   
   or from each other.   
      
   Proposition IV   
   In the Scholium to Prop IV Newton says "--the periodic times of   
   these (fictitious) moons (of the earth)  would observe the same law   
   which Kepler found to obtain among the planets; and therefore their   
   centripetal forces would be reciprocally as the squares of the   
   distances from the centre of the earth, by Prop. I, of this Book."   
      
   Proposition V   
   Cor 2. The force of gravity which tends to any one planet is   
   re=C2=ACciprocally as the square of the distance of places from   
   that planet's centre.   
      
   Proposition VI   
   That all bodies gravitate towards every planet ; and that the weights   
   of bodies towards any the same planet, at equal distances from the   
   centre of the planet, are proportional to the quantities of matter   
   which they severally contain.   
      
   Proposition VII   
   That there is a power of gravity tending to all bodies, proportional   
   to the several quantities of matter which they contain.   
   That all the planets mutually gravitate one towards another, we   
   have proved before ; as well as that the force of gravity towards   
   every one of there, considered apart, is reciprocally as the square   
   of the distance of places from the centre of the planet. And thence   
   (by Prop. LXIX, Book I, and its Corollaries) it follows, that the   
   gravity tending towards all the planets is proportional to the   
   matter which they contain. (Scholium to Prop LXIX: These Propositions   
   naturally lead us to the analogy there is between centripetal forces,   
   and the central bodies to which those forces used to be directed;   
   for it is reasonable to suppose that forces which are directed to   
   bodies should depend upon the nature and quantity of those bodies,   
   as we see they do in magnetical experiments).   
      
   Conclusion:   
   Newton in 1687 had a minimal understanding of the role of masses   
   in gravity. Huygens published his centripetal law Fc = mpl*vm^2/sma   
   in 1659, 28 years before Newton's Principia. It produces the same   
   results for the 9 major planets as the gravitational law FG =   
   G*(M*mpl/sma^2) .  This law has been ascribed to Newton but cannot   
   be found anywhere in the Principia or any other writing of Newton.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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