A Commentary on Newton's Principia; With Supplementary Volume Designed for the Use of Students at the Universtities Volume 2

A Commentary on Newton's Principia; With Supplementary Volume Designed for the Use of Students at the Universtities Volume 2

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1833 edition. Excerpt: ...532, that if the mean motions n t and n' t of the two bodies f and /-', are very nearly in the ratio of i' to i so that V n'--in may be a very small quantity; there may insult in the mean motions of these bodies very sensible inequalities. This relation of the mean motions may also produce sensible variations in the excentricities of the orbits, and in the positions of their perihelions. To determine them, we shall resume the equation found in 534, M'Psin. (i'n't--int+ iV--ii)+ /' P'cos. (i' n't--in t+ i' t'--it), is equal to-g/f (i?cos.(i'n't-int+i'.'-if)-()sin.(i'n't-int+i'.'-io; m(i'n'-in)e I d e / v 'V d e / v we shall therefore, thus, after a very simple manner, find the variations of the excentricity and of the perihelion, depending upon the angle i' n' t--i n t + i' ef--i e. They arc connected with the variation of the corresponding mean motion, in such a way that the variation of the excentricity is _J_ (Ally 3 in Vde.dt/' iind the variation of the longitude of the perihelion is i' n'-i n /dj 3 i n e d e/ The corresponding variation of the excentricity of the orbit of p, due to the action of y., will be L_ (ALZL Si'n'. e' Vde'.dt/' and the variation of the longitude of its perihelion, will be i' n'--in /d g 3 i' n' e' Vde7/' and since by No. 532, '----&, ., the variations will be p V a & j (i' n'--i n) A V a & Si'.n'./'Va'VdeVdV' Si'n'.eV'Va' 'dV When the quantity i' n'--i n is very small, the inequality depending upon the angle i' n' t--i n t, produces a sensible one in the expression of the mean motion, amongst the terms depending on the squares of the perturbing masses; we have given the analysis of this in No. 582. This same inequality produces in the expression of d...show more

Product details

  • Paperback | 82 pages
  • 189 x 246 x 4mm | 163g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236532422
  • 9781236532428