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 ix
... INTEGRATION OF THE DIFFERENTIAL EQUATIONS . 25 General Process described 28 27 Terms of a higher order which must be retained 30 30 Solution to the first order 32 35 Introduction of c and g 35 Page . Art . 41 Connexion between 0 ' and.
... INTEGRATION OF THE DIFFERENTIAL EQUATIONS . 25 General Process described 28 27 Terms of a higher order which must be retained 30 30 Solution to the first order 32 35 Introduction of c and g 35 Page . Art . 41 Connexion between 0 ' and.
Page 22
... integration has never yet been effected , except for particular values of P , T , and S ; and the method which we are in consequence forced to adopt , is that of successive approximation , by which the values of u , 0 , and s are ...
... integration has never yet been effected , except for particular values of P , T , and S ; and the method which we are in consequence forced to adopt , is that of successive approximation , by which the values of u , 0 , and s are ...
Page 27
... sun μ * : : m2 : 1 , or the disturbing force of the sun is of the second order when compared with the direct action of the earth . CHAPTER IV . INTEGRATION OF THE DIFFERENTIAL EQUATIONS . SECTION ORDER OF DISTURBING FORCE . 27.
... sun μ * : : m2 : 1 , or the disturbing force of the sun is of the second order when compared with the direct action of the earth . CHAPTER IV . INTEGRATION OF THE DIFFERENTIAL EQUATIONS . SECTION ORDER OF DISTURBING FORCE . 27.
Page 28
... INTEGRATION OF THE DIFFERENTIAL EQUATIONS . SECTION I. General process described . 25. The differential equations which we have obtained are , as already stated , incapable of solution in their general forms ; and even when P , T , & c ...
... INTEGRATION OF THE DIFFERENTIAL EQUATIONS . SECTION I. General process described . 25. The differential equations which we have obtained are , as already stated , incapable of solution in their general forms ; and even when P , T , & c ...
Page 29
... integration of the equations ( a ) , ( B ) , ( y ) can be per- formed when the second members are circular functions of ; and as the first approximation will give us the values of u and s in that form , these values when admissible will ...
... integration of the equations ( a ) , ( B ) , ( y ) can be per- formed when the second members are circular functions of ; and as the first approximation will give us the values of u and s in that form , these values when admissible will ...
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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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