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|    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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