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Download ebook Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac Volume 3

Download ebook Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac Volume 3

Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac Volume 3 by United States Naval Office
Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac Volume 3
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Author: United States Naval Office
Page Count: 40 pages
Published Date: 10 May 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
Format: Pdf
ISBN: 9781231158418
File size: 15 Mb
Download Link: Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac Volume 3
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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. 1891 Excerpt: ...include every pair of elements of the two masses. Again, if fi be so expressed as to involve the rectangular co-ordinates x, Y, and z of the center of gravity of the earth, and also those of the center of gravity of the moon, viz,, tf, and?, the differential equations of motion of these centers of gravity will be, for the earth, d2x dn Mfc- = dx' d2Y d.(l Pz dn M dY = dz' and for the moon, d?g _ dn m 'dY dg' dtij _ dn d?Z __ dn m w-Tq" Let x, y, and e denote the rectangular co-ordinates of the center of gravity of the moon relative to the center of gravity of the earth, so that we have B, --x = x, tf-Y = y, 1785 M M 2" 209 Tf 1 is now so expressed as to involve the variables x, y, and z, we shall have If we suppose the co-ordinates of dM, relative to the center of gravity of M, are denoted by x', Y' and z', and those of lm, relative to the center of gravity of m, by ', ?/, and ', we shall have / p dM. dm n = J J f(.r + SS-x')4 + (.'/ + '/-v.')1 + (z +Z-y.iyf But, as we do not propose to take into account the inequalities arising from the figure of the moon, we shall assume that the bounding surface of this body is spherical, and that its mass is either homogeneous or that the density of the element dm is a function of its distance from the center of the bounding sphere. In this case, the integration involved in the last expression, relative to dm, can be accomplished; and the known result is ' =./ (.v-xy +(y-Vy + (z-z'ff X-Xf + y-VT + (, -ZTp = J ---f + f + " + The second term of the radical of the right-hand member of this equation is a quantity of the order of the ratio of the dimensions of the terrestrial spheroid 1o the radius of the lunar orbit, and the third term is of the order of t...

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