An Elementary Treatise on the Planetary Theory; With a Collection of Problems

An Elementary Treatise on the Planetary Theory; With a Collection of Problems

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ...two, Had we considered a system of several planets, we should have obtained a result precisely similar to that of Art. 73. 80. From the form of the expression for tan i, the stability of the inclinations may be inferred. For it may be shewn, as in Art. 74, that tan i can never exceed these quantities being taken with the same sign. Since then Ni, N," Na &c. are found to be very small, it follows that the inclinations must always remain exceedingly small. In the case of two mutually disturbing planets, we learn from the expression in Art. 79, that tan i fluctuates between the limits Nl + Nt and Nl AT2. The periods of these o changes are the same for the two planets, being--j-; and /&! as appears from the equation of Art. 66, the maximum of each inclination will take place at the time of the minimum of the other. In the case of Jupiter and Saturn, the period is 50673 years; the maximum and minimum inclinations of Jupiter's orbit to the ecliptic are 2 2' 30" and 1" 17' 10," those of Saturn's orbit 2 32' 40" and 047'. 81. We now proceed to examine the expression which has been obtained in Art. 79 for the longitude of the node. We have-Jr. Bin (A. + 8.) + JT. Bin 8. l"---jvi cos (hj +al)+jytcos v The maxima and minima values of fl, if such exist, will be found by equating-=-to zero. Thus etc cos If this (disregarding sign) be not greater than unity, the node will oscillate, the period of a complete oscillation being othe same as that of the inclinations, viz.--T-. But if it be--"i greater than unity, there cannot be any stationary positions, and the node will move continually in one direction. It may be shewn, as in Art. 76, that the motion of the node will be fastest or slowest whenever more

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  • Paperback
  • 189 x 246 x 1mm | 68g
  • United States
  • English
  • black & white illustrations
  • 1236878604
  • 9781236878601