An Elementary Treatise on the Lunar Theory: With a Brief Sketch of the History of the Problem Up to the Time of Newton |
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Page 1
... particle in the universe attracts every other particle , with a force varying directly as the mass of the attracting particle and inversely as the square of the distance between them . " The truth of this law cannot be established by ...
... particle in the universe attracts every other particle , with a force varying directly as the mass of the attracting particle and inversely as the square of the distance between them . " The truth of this law cannot be established by ...
Page 3
... particle be moving under the action of any number of forces some of which are very small , and let A be the position of the particle at any instant . Let two of these small forces m ,, m , be omitted , and suppose the path of the particle ...
... particle be moving under the action of any number of forces some of which are very small , and let A be the position of the particle at any instant . Let two of these small forces m ,, m , be omitted , and suppose the path of the particle ...
Page 4
... particle , ( x , y , z ) any function of x , y , z ; the disturbance produced in 4 ( x , y , z ) will be аф аф dy 84 ( x , y , z ) = xx Sx + where Sx = 8x + x + ... sum of disturbances along axis of x do Sy + Sz , omitting ( 8x ) 2 ...
... particle , ( x , y , z ) any function of x , y , z ; the disturbance produced in 4 ( x , y , z ) will be аф аф dy 84 ( x , y , z ) = xx Sx + where Sx = 8x + x + ... sum of disturbances along axis of x do Sy + Sz , omitting ( 8x ) 2 ...
Page 5
... particles . ( Princip . lib . I. prop . 75. ) Attractions of Spherical Bodies . 6. Let P be a particle situated at a distance OP = a from the centre of a uniform attract- ing sphere whose density is p and radius OA = c . a > c , the ...
... particles . ( Princip . lib . I. prop . 75. ) Attractions of Spherical Bodies . 6. Let P be a particle situated at a distance OP = a from the centre of a uniform attract- ing sphere whose density is p and radius OA = c . a > c , the ...
Page 6
... particle mass of element P will be PR2 along PR , and the resolved part mass of element of this long PO will be cose . x2 sec20 But the resultant attraction of the whole ring will clearly be the sum of the resolved parts along PO of the ...
... particle mass of element P will be PR2 along PR , and the resolved part mass of element of this long PO will be cose . x2 sec20 But the resultant attraction of the whole ring will clearly be the sum of the resolved parts along PO of the ...
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Common terms and phrases
3m²e accelerating forces Algebra angle angular velocity annual equation anomaly apogee apse line astronomers attraction bodies BROOKE FOSS WESTCOTT calculated Cambridge centre cloth coefficient considered correct cos2 Crown 8vo determined differential equations distance disturbing force E-Ma E+Ma earth eccentricity ecliptic ELEMENTARY TREATISE elliptic inequality epicycle equal evection expression Fcap fixed plane fourth order h²u³ higher order Hipparchus hu³ integration John's College Lunar Theory MACMILLAN AND CO'S Mathematical mean anomaly mean longitude mean motion mean value method moon moon's mean moon's motion moon's orbit nearly neglected Newton node numerous observations obtained order of approximation parallax particle perigee periodical terms position Ps-S Ptolemy quadrature quantity radius vector revolution Schools Second Edition second order shew sidereal month sin2 solution sphere student substituted syzygy third order true anomaly true longitude Tycho variation že²
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