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

A Commentary on Newton's Principia; With a Supplementary Volume. Designed for the Use of Students at the Universities 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: ... tan. p" sin.--0) + (l,2) + &c. + (l, 0).. cos. (Y-6) +1-8)-Sycos-e-')+&c. &c. Astronomers refer the celestial motions to the moveable orbit of the earth; it is in fact from the plane of this orbit that we observe them; it is therefore important to know the variations of the nodes and the inclinations of the orbits, relatively to the orbit of one of the bodies ft, ft', ft," &c. for example to the orbit of ft. It is clear that q sin. (n t + 0--P cos. (n't + -') would be the latitude of p! above the fixed plane if it were in motion upon the orbit of ft. The latitude of this moveable plane above the same plane is q' sin.(n't + i) p' cos. (n't + i); but the difference of these two latitudes is very nearly the latitude of /' above the orbit of ft; calling therefore p/ the inclination, and #/ the longitude of the node of ft' upon the orbit of p, we shall have, by what precedes, tan. f/-V (p--p) + (q'--q)s; tan. -/ = jjjIf we take for the fixed plane, that of ft's orbit at a given epoch; we shall have at that epoch p = 0, q = 0; but the differentials d p and d q will not be zero; thus we shall have. d p; = (dp'--dp) sin. 0 + (d q'--d q) cos. &; J _ dp--dp) cos. S--(d q--d q) sin. 9 tan. p Substituting for d p, d q, d p', d q, &c. their values given by the equations (C) of the preceding No., we shall have = 1(1, 2)-(0, 2)I tan. p" sin. (?--") + f(l, 3)--(0,3) tan. f" sin. (ff--9") + &c. =-(1,0) + (1,2) + (1,3) + &c.J--(0, 1) + (l,2)-(0,2)?.-cos. V-f) + 1(1, 3)-(0, 3). cos. g--') + &c It is easy to obtain from these expressions the variations of the nodes, and inclinations of the orbits of the other bodies p," p"', &c. upon the moveable orbit of...show more

Product details

  • Paperback | 110 pages
  • 189 x 246 x 6mm | 213g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236580001
  • 9781236580009