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 3
... fore PQ is parallel and equal to PP . 1 Hence the projection of the whole disturbance PQ on any straight line , being equal to the algebraical sum of the pro- jections of PP , and P , Q , will B 2 SUPERPOSITION OF SMALL MOTIONS . 3.
... fore PQ is parallel and equal to PP . 1 Hence the projection of the whole disturbance PQ on any straight line , being equal to the algebraical sum of the pro- jections of PP , and P , Q , will B 2 SUPERPOSITION OF SMALL MOTIONS . 3.
Page 5
... hence the famous problem of the Three Bodies . The planets being small and distant , their effect on the motion of the moon will not be of sufficient intensity to affect the order of approximation to which it is intended to carry the ...
... hence the famous problem of the Three Bodies . The planets being small and distant , their effect on the motion of the moon will not be of sufficient intensity to affect the order of approximation to which it is intended to carry the ...
Page 6
... Sz ; 2 23 -- ( a2 - c2 ) : 2a2 2 .. attraction of whole sphere = 2πρ 2a 6a2 ( from zac to z = a + c ) where M = mass of sphere - = = Απρο 3a2 M a 27 Απρο 3 Hence , the attraction of the whole sphere is precisely 6 LUNAR THEORY .
... Sz ; 2 23 -- ( a2 - c2 ) : 2a2 2 .. attraction of whole sphere = 2πρ 2a 6a2 ( from zac to z = a + c ) where M = mass of sphere - = = Απρο 3a2 M a 27 Απρο 3 Hence , the attraction of the whole sphere is precisely 6 LUNAR THEORY .
Page 7
... Hence , the attraction of the whole sphere is precisely the same as if the whole mass were condensed into its centre . COR . 1. The attraction of a shell radius = c and thickness Sc will be obtained from the preceding expression by ...
... Hence , the attraction of the whole sphere is precisely the same as if the whole mass were condensed into its centre . COR . 1. The attraction of a shell radius = c and thickness Sc will be obtained from the preceding expression by ...
Page 10
... Hence , P μ + u = = d02 h2u2 h2 9 do where h = r2 2 dt • и = twice the area described in a unit of time , μ u = { 1 + e cos ( 0 − a ) } , - e and a being constants to be determined by the circumstances of the motion at any given time ...
... Hence , P μ + u = = d02 h2u2 h2 9 do where h = r2 2 dt • и = twice the area described in a unit of time , μ u = { 1 + e cos ( 0 − a ) } , - e and a being constants to be determined by the circumstances of the motion at any given time ...
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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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