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
... approximation is common to all . In the present work , the approximation is carried to the second order of small quantities , and this , though far from giving accurate values , is amply sufficient for the elucidation of the method ...
... approximation is common to all . In the present work , the approximation is carried to the second order of small quantities , and this , though far from giving accurate values , is amply sufficient for the elucidation of the method ...
Page vii
... approximation to a high order , this method offers the advantage of not requiring any reversion of series . Poisson proposed the method used in the planetary theory , that is , to determine the variation in the elements . of the moon's ...
... approximation to a high order , this method offers the advantage of not requiring any reversion of series . Poisson proposed the method used in the planetary theory , that is , to determine the variation in the elements . of the moon's ...
Page 5
... order of approximation to which it is intended to carry the solution in the following pages , and our problem is re- duced to the consideration of the three bodies , the sun , earth , and moon , acting on one another according to the ...
... order of approximation to which it is intended to carry the solution in the following pages , and our problem is re- duced to the consideration of the three bodies , the sun , earth , and moon , acting on one another according to the ...
Page 8
... order higher than that to which we intend to carry the present investi- gation : the error however , though very small , is appre- ciable , and if a nearer approximation were required , it would be necessary to have regard to this ...
... order higher than that to which we intend to carry the present investi- gation : the error however , though very small , is appre- ciable , and if a nearer approximation were required , it would be necessary to have regard to this ...
Page 12
... order of approximation . 0 — a = nt + e − a + 2e sin ( 0 — a ) — že2 sin 2 ( 0 — a ) ......... .. ( 1 ) ; - - - .. 0 ― a = nt + ε- a first approximation . - Substituting this in the first small terms of ( 1 ) , we get 0 - a = nt + ε ...
... order of approximation . 0 — a = nt + e − a + 2e sin ( 0 — a ) — že2 sin 2 ( 0 — a ) ......... .. ( 1 ) ; - - - .. 0 ― a = nt + ε- a first approximation . - Substituting this in the first small terms of ( 1 ) , we get 0 - a = nt + ε ...
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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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