An Elementary Treatise on the Lunar Theory: With a Brief Sketch of the History of the Problem Up to the Time of NewtonMacmillan, 1859 - 119 σελίδες |
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Σελίδα 21
... four variables u , 0 , s , and t are involved ( the accelerating forces P , T , and S are functions of these ) , the values of three of them , as u , 0 , s , could be obtained in terms of the fourth t ; that is DIFFERENTIAL EQUATIONS . 21 .
... four variables u , 0 , s , and t are involved ( the accelerating forces P , T , and S are functions of these ) , the values of three of them , as u , 0 , s , could be obtained in terms of the fourth t ; that is DIFFERENTIAL EQUATIONS . 21 .
Σελίδα 22
... fourth t ; that is , the radius vector , longitude , and latitude would be known corresponding to a given time . 21. But the integration has never yet been effected , except for particular values of P , T , and S ; and the method which ...
... fourth t ; that is , the radius vector , longitude , and latitude would be known corresponding to a given time . 21. But the integration has never yet been effected , except for particular values of P , T , and S ; and the method which ...
Σελίδα 25
... fourth and higher orders . Now , SM SM " + MM " = = SG2 + GM " -2SG.GM ' cos SGM ' + MM " therefore = r 12 ( 1 . GM ' GM - -2 cos SGM ' + 2012 ; 3 GM ' = + 18 p ' cos ( 0-0 ) } ; 1 SM3 γ for 0-0 or SE'M ' differs from SGM by less than 7 ...
... fourth and higher orders . Now , SM SM " + MM " = = SG2 + GM " -2SG.GM ' cos SGM ' + MM " therefore = r 12 ( 1 . GM ' GM - -2 cos SGM ' + 2012 ; 3 GM ' = + 18 p ' cos ( 0-0 ) } ; 1 SM3 γ for 0-0 or SE'M ' differs from SGM by less than 7 ...
Σελίδα 44
... fourth order , is retained be- cause 2-2m - 2c is small . T du h'us de = ( previous expression ) { -aec sin ( cơ — a ) } T ds hu3 do = 3m2ae cos { ( 2 - 2m — c ) 0 −2B + a } , = - for , to the first order , c = 1 ; ( same expression ) ...
... fourth order , is retained be- cause 2-2m - 2c is small . T du h'us de = ( previous expression ) { -aec sin ( cơ — a ) } T ds hu3 do = 3m2ae cos { ( 2 - 2m — c ) 0 −2B + a } , = - for , to the first order , c = 1 ; ( same expression ) ...
Σελίδα 50
... fourth order , but in it arises from combining terms hu2 not exceeding the third order . If , therefore , we had rejected terms beyond the third order indiscriminately , the expression dt do 1 would have contained this term , introduced ...
... fourth order , but in it arises from combining terms hu2 not exceeding the third order . If , therefore , we had rejected terms beyond the third order indiscriminately , the expression dt do 1 would have contained this term , introduced ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
accelerating forces Algebra angle angular velocity annual equation apogee approximation apse line argument astronomers attraction Author has endeavoured body calculated CAMBRIDGE CLASS BOOKS centre chapter cloth coefficient Collection of Examples connexion considered correction cos2 Crown 8vo determine differential equations distance disturbing force E-Ma E+Ma earth eccentricity ecliptic elliptic inequality epicycle equal evection expression fixed plane h2u³ higher order Hipparchus inclination ISAAC TODHUNTER John's College late Fellow Latin latitude Lunar M.A. Fellow mean motion mean place mean value method moon moon's mean longitude moon's motion moon's orbit nearly node numerous Examples observations obtained octants order of approximation particle perigee periodical terms position Ps-S Ptolemy quadrature quantity radius vector revolution Schools Second Edition second order shew sidereal month solution sphere student syzygy Theory third order tions true anomaly true longitude Tycho Brahé V₁ variation že²
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