On Friday, 19 January 2018 21:23:21 UTC+11, qri...@gmail.com  wrote:   
   > 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.   
      
   As written in proposition 7, Newton does mention the mass of solar   
   objects. To quote from proposition 7 given by you below:   
      
   open quote:   
   > Proposition VII   
   > That there is a power of gravity tending to all bodies, proportional   
   > to the several quantities of matter which they contain.   
   end quote   
      
   Mathematically that amounts to: force of gravity upon a body =   
   proportional to (for all bodies in the universe(the sum of the masses of   
   one individual body with one of the rest))   
      
   The other propositions relating to distance make up the gravitational   
   equation that is well known, that is   
      
   Force of gravity upon a body is proportional to (for all bodies in the   
   universe( the sum of the masses of one individual body with one of the   
   rest divided by the square of the distance between their centres))   
      
   > 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."   
      
   Here Newton is saying that the same laws of physics apply to all bodies.   
   It is not as if the Earth's moon follow one law and the planets follow   
   another law.   
      
   > 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.   
      
   Here Newton is saying that the force of gravity between any two bodies   
   varies as the square of the distance between them.   
      
   > 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.   
      
   Here Newton is saying that the force of gravity by one mass with respect   
   to other masses is proportional to the quantity of matter contained in   
   the other masses - here the distance factor is held common.   
      
   > 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.   
      
   Propositions 6 and 7 show that he had the necessary understanding about   
   the role of masses in gravity.   
      
   Cheers,   
   Arindam Banerjee   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)