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 vi
... second order of small quantities , and this , though far from giving accurate values , is amply sufficient for the elucidation of the method . The differences in the analytical solutions arise from the various ways in which the position ...
... second order of small quantities , and this , though far from giving accurate values , is amply sufficient for the elucidation of the method . The differences in the analytical solutions arise from the various ways in which the position ...
Σελίδα x
... second order 51 True Longitude in terms of the Mean obtained by Reversion of Series 52 u and s in terms of t 54 Parallax of the Moon Page . 40 41 51 52 53 CHAPTER V. NUMERICAL VALUES OF THE COEFFICIENTS . 60 First Method . 61 Second ...
... second order 51 True Longitude in terms of the Mean obtained by Reversion of Series 52 u and s in terms of t 54 Parallax of the Moon Page . 40 41 51 52 53 CHAPTER V. NUMERICAL VALUES OF THE COEFFICIENTS . 60 First Method . 61 Second ...
Σελίδα 12
... order of approximation . - 0 - a = nt + ε — a + 2e sin ( 0 — a ) — şe2 sin 2 ( 0 — a ) ......... . ( 1 ) ; - - .. 0 ... second approximation . Substitute the second approximation in that small term of ( 1 ) which is multiplied by e , and ...
... order of approximation . - 0 - a = nt + ε — a + 2e sin ( 0 — a ) — şe2 sin 2 ( 0 — a ) ......... . ( 1 ) ; - - .. 0 ... second approximation . Substitute the second approximation in that small term of ( 1 ) which is multiplied by e , and ...
Σελίδα 22
... order , of 2 % = 7t0 is 8000 is second ...... third and so on , other fractions being considered as of the 1st , 2nd ... order . * * This approximate value of m is easily obtained ; -the moon is found to perform the tour of the heavens ...
... order , of 2 % = 7t0 is 8000 is second ...... third and so on , other fractions being considered as of the 1st , 2nd ... order . * * This approximate value of m is easily obtained ; -the moon is found to perform the tour of the heavens ...
Σελίδα 23
... second order . * ( 3 ) The eccentricity e ' of the elliptic orbit which the sun approximately describes about the earth is about , and this , approaching nearer in value to than to bō , will be considered as of the 1st order . ( 4 ) ...
... second order . * ( 3 ) The eccentricity e ' of the elliptic orbit which the sun approximately describes about the earth is about , and this , approaching nearer in value to than to bō , will be considered as of the 1st order . ( 4 ) ...
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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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