Carnegie Institution of Washington Publication Volume 9, V. 1

Carnegie Institution of Washington Publication Volume 9, V. 1

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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. 1905 edition. Excerpt: ... by the proper value of--i--1, 11' i--1, 3" which corresponds to it. Perturbations of the second order with respect to the disturbing forces. Calling the parts of the perturbations of r, )6, Ft, which are of two dimensions with respect to the planetary masses, 521', (VB, 522., so that we have, with errors of the third order, where 5r, dfl, 81 are the perturbations which have just been determined, we shall have where, as before, there is no need of any distinction between ro and r. The following are the expressions for 5Q, and 5Q, Bearing in mind that X, Y, Z are homogeneous functions of r and r, it will be easy to deduce the following equations: do ' dv dv respect to the independent variable v. In computing the values of these functions, %', 82. and 53 must be expressed as functions of '0. Hence, if they are at first expressed in terms of t, it must be eliminated by means of the equation We may have given only the perturbation of the orbit longitude and the latitude above the elliptic orbit of the disturbing planet; in this case, calling the latter 511, the values of 52. and 5,5 will be given by the equations We see that, in order to obtain the perturbations of the second order it will be necessary to have, expressed in periodic series in terms of '0, the following nine quantities: For six of these whose expressions are the same method must be used as that which has been given for X Y Z The remaining three, X, Y and Z being considered as functions of the two variables v and 3, can be obtained from the equations The values of 2. --3. and,8, necessary for the computation of the first six quantities, can be obtained from the equations The terms to be integrated more

Product details

  • Paperback
  • 189 x 246 x 4mm | 163g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236570162
  • 9781236570161