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 10
... direction . Therefore , by the principle above stated , we must apply to both M and M ' accelerating forces equal and opposite to this latter force , and M ' will move about M fixed , the accelerating 1 = μu2 , if μ = M + M ' and r ...
... direction . Therefore , by the principle above stated , we must apply to both M and M ' accelerating forces equal and opposite to this latter force , and M ' will move about M fixed , the accelerating 1 = μu2 , if μ = M + M ' and r ...
Page 11
... direction of motion being repre- sented by the arrow . Let MD be the position of Mu when t = 0 , then D M YMD = ε and is called the epoch , DMμ = nt , ΥΜΑ = α = longitude of the apse ; * - therefore , mean anomaly = AMμnt + ε — α , true ...
... direction of motion being repre- sented by the arrow . Let MD be the position of Mu when t = 0 , then D M YMD = ε and is called the epoch , DMμ = nt , ΥΜΑ = α = longitude of the apse ; * - therefore , mean anomaly = AMμnt + ε — α , true ...
Page 13
... direction of the sun's motion at any instant is 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 ...
... direction of the sun's motion at any instant is 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 ...
Page 15
... direction GM , m'.E.SG + SE3 m'.M.SG SM3 GS . SE SG2 + GE + 2.SG . GE cosa , = SMSG + GM " -2.SG . GM cos w . Y3 SE ᏚᏳ SG4 1 1 3.GE Hence = COS @ omitting EM \ 2 1 = SG ? COS W 1 3.GM + SM3 ᏚᏳ SG Now E.GE = M.GM = ( M + E ) GM.GE ...
... direction GM , m'.E.SG + SE3 m'.M.SG SM3 GS . SE SG2 + GE + 2.SG . GE cosa , = SMSG + GM " -2.SG . GM cos w . Y3 SE ᏚᏳ SG4 1 1 3.GE Hence = COS @ omitting EM \ 2 1 = SG ? COS W 1 3.GM + SM3 ᏚᏳ SG Now E.GE = M.GM = ( M + E ) GM.GE ...
Page 17
... direction of the first point of Aries , —that is , a fixed line in our plane of reference from which the longitudes of the bodies are reckoned . TES ' ' the sun's longitude . The difference in the sun's longitude , as seen from E or ...
... direction of the first point of Aries , —that is , a fixed line in our plane of reference from which the longitudes of the bodies are reckoned . TES ' ' the sun's longitude . The difference in the sun's longitude , as seen from E or ...
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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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