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 vi
... true longitude was taken for independent variable . To determine the latitude , they , by analogy to Newton's method , employed the differential variations of the motion of the node and of the inclination of the orbit . Laplace ...
... true longitude was taken for independent variable . To determine the latitude , they , by analogy to Newton's method , employed the differential variations of the motion of the node and of the inclination of the orbit . Laplace ...
Page x
... 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 40 41 51 52 53 523 CHAPTER V. NUMERICAL VALUES OF THE COEFFICIENTS . 60 First Method . 61 Second Method . Theoretical ...
... 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 40 41 51 52 53 523 CHAPTER V. NUMERICAL VALUES OF THE COEFFICIENTS . 60 First Method . 61 Second Method . Theoretical ...
Page 11
... longitude of the apse ; * - therefore , mean anomaly = AMμnt + ε — α , true anomaly = AMM ' = TM MM ' - MA = 0 - a . 12. To express the mean anomaly in terms of the true in a series ascending according to the powers of e , as far as e2 ...
... longitude of the apse ; * - therefore , mean anomaly = AMμnt + ε — α , true anomaly = AMM ' = TM MM ' - MA = 0 - a . 12. To express the mean anomaly in terms of the true in a series ascending according to the powers of e , as far as e2 ...
Page 40
... true longitudes at time t , longitude of perigees when t = 0 ; 0 ' — = sun's true anomaly , - p't + B- = But , by Art . ( 13 ) , ...... mean anomaly . true anomaly mean anomaly + 2e ' sin ( mean anomaly ) + & c .; therefore because ...
... true longitudes at time t , longitude of perigees when t = 0 ; 0 ' — = sun's true anomaly , - p't + B- = But , by Art . ( 13 ) , ...... mean anomaly . true anomaly mean anomaly + 2e ' sin ( mean anomaly ) + & c .; therefore because ...
Page 51
... latitude and the time in terms of the true longitude ; but the principal object of the analytical investigations of the Lunar Theory being the formation of tables which give the coordinates of the moon at stated times , we must express ...
... latitude and the time in terms of the true longitude ; but the principal object of the analytical investigations of the Lunar Theory being the formation of tables which give the coordinates of the moon at stated times , we must express ...
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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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