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 54
... perigee , which we have hitherto neglected . This will be done by writing c'e ' - 5 for 0 ' — 5 , c ' being a quantity which differs very little from unity . * - These values of u ' , ' , together with those of u and s in terms of e ...
... perigee , which we have hitherto neglected . This will be done by writing c'e ' - 5 for 0 ' — 5 , c ' being a quantity which differs very little from unity . * - These values of u ' , ' , together with those of u and s in terms of e ...
Page 64
... perigee to apogee , and therefore the true place before the mean ; and the contrary from apogee to perigee : at the apses the places will coincide . 68. The angular velocity of the apse is ( 1 - c ) p , or , if for c we put the value ...
... perigee to apogee , and therefore the true place before the mean ; and the contrary from apogee to perigee : at the apses the places will coincide . 68. The angular velocity of the apse is ( 1 - c ) p , or , if for c we put the value ...
Page 66
... perigee or between perigee and apogee . In quadratures 0 = pt + me sin ( ) — a ' ) , and the circumstances will be exactly reversed . In both cases , the correction will vanish when the apse happens to be in syzygy or quadrature at the ...
... perigee or between perigee and apogee . In quadratures 0 = pt + me sin ( ) — a ' ) , and the circumstances will be exactly reversed . In both cases , the correction will vanish when the apse happens to be in syzygy or quadrature at the ...
Page 70
... perigee ) , = pt - 3me ' sin ( sun's anomaly ) . Hence , while the sun moves from perigee to apogee , the true place of the moon will be behind the mean ; and from apogee to perigee , before it . The period being an anomalistic year ...
... perigee ) , = pt - 3me ' sin ( sun's anomaly ) . Hence , while the sun moves from perigee to apogee , the true place of the moon will be behind the mean ; and from apogee to perigee , before it . The period being an anomalistic year ...
Page 71
... perigee , that is at present about the 1st of January , and greatest when the sun is in apogee , or about the 1st of July . The annual equation is , to this order , independent of the eccentricity and inclination of the moon's orbit ...
... perigee , that is at present about the 1st of January , and greatest when the sun is in apogee , or about the 1st of July . The annual equation is , to this order , independent of the eccentricity and inclination of the moon's orbit ...
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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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