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 2
... to the earth or the disturbing force will not be the same as the absolute force on either body . This will be fully investigated in Arts . ( 9 ) and ( 23 ) . cases : and there is a principle , called the 2 LUNAR THEORY .
... to the earth or the disturbing force will not be the same as the absolute force on either body . This will be fully investigated in Arts . ( 9 ) and ( 23 ) . cases : and there is a principle , called the 2 LUNAR THEORY .
Page 3
... called the " principle of the superposition of small motions , " which shows that in such a case the disturbing forces may be considered separately , and the algebraic sum of the disturbances so obtained will be the same as the ...
... called the " principle of the superposition of small motions , " which shows that in such a case the disturbing forces may be considered separately , and the algebraic sum of the disturbances so obtained will be the same as the ...
Page 10
... and the apse line is called the true anomaly . If n is the angular velocity of a radius vector which moving uniformly would accomplish its revolution in the same time as the true one , both passing through the 10 LUNAR THEORY .
... and the apse line is called the true anomaly . If n is the angular velocity of a radius vector which moving uniformly would accomplish its revolution in the same time as the true one , both passing through the 10 LUNAR THEORY .
Page 11
... called the mean anomaly , ɛ being a constant depending on the instant when the body is at the apse , its value being also equal to the angle be- tween the prime radius and the uniformly revolving one when t = 0 . Thus , if MY be the ...
... called the mean anomaly , ɛ being a constant depending on the instant when the body is at the apse , its value being also equal to the angle be- tween the prime radius and the uniformly revolving one when t = 0 . Thus , if MY be the ...
Page 13
... called the true ecliptic ; and , as a first rough result of calculation , ob- tained on supposition of the sun and earth being the only bodies in the universe , this plane , in which , according to the last section , an elliptic orbit ...
... called the true ecliptic ; and , as a first rough result of calculation , ob- tained on supposition of the sun and earth being the only bodies in the universe , this plane , in which , according to the last section , an elliptic 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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