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 10
... eccentricity being e , the semi - latus rectum h2 μ and the angle made by the apse line with the prime radius a . In the relative motion of the moon , or in that of the sun about the earth , the orbit would , as observation informs us ...
... eccentricity being e , the semi - latus rectum h2 μ and the angle made by the apse line with the prime radius a . In the relative motion of the moon , or in that of the sun about the earth , the orbit would , as observation informs us ...
Σελίδα 23
... 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 ) During one revolution , 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 ) During one revolution , the ...
Σελίδα 63
... eccentricity , and a ' the longitude of the apse . * Hence , the terms we are now considering indicate motion in an ellipse ; the mean motion being p the eccentricity e , and the longitude of the apse a + ( 1 - c ) pt ; that is , the ...
... eccentricity , and a ' the longitude of the apse . * Hence , the terms we are now considering indicate motion in an ellipse ; the mean motion being p the eccentricity e , and the longitude of the apse a + ( 1 - c ) pt ; that is , the ...
Σελίδα 66
... eccentricity of the moon's orbit produced by the evection . Taking the elliptic inequality and the evection together , we have - 0 = pt + 2e sin ( cpt - a ) + že sin 2 ( cpt — a ) - - + 15 me sin { ( 2 – 2m − c ) pt − 2ẞ + a } . Let a ...
... eccentricity of the moon's orbit produced by the evection . Taking the elliptic inequality and the evection together , we have - 0 = pt + 2e sin ( cpt - a ) + že sin 2 ( cpt — a ) - - + 15 me sin { ( 2 – 2m − c ) pt − 2ẞ + a } . Let a ...
Σελίδα 67
... eccentricity is E and longitude of the apse a ' - 8 ; therefore the evection , taken in conjunction with elliptic in- equality , has the effect of rendering the eccentricity of the moon's orbit variable , increasing it by me when the ...
... eccentricity is E and longitude of the apse a ' - 8 ; therefore the evection , taken in conjunction with elliptic in- equality , has the effect of rendering the eccentricity of the moon's orbit variable , increasing it by me when the ...
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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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