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 3
... suppose the path of the particle under the action of the remaining forces to be AP in any given time . Let AP , be the path which would have been described in the same time if m , also had acted ; AP , differing very slightly from AP ...
... suppose the path of the particle under the action of the remaining forces to be AP in any given time . Let AP , be the path which would have been described in the same time if m , also had acted ; AP , differing very slightly from AP ...
Σελίδα 7
... Suppose P in the preceding article to be an elementary particle of a sphere M ' , whose centre O ' suppose at a distance a from O. Then , since action and reaction are equal and opposite , P will attract the whole sphere M just as it ...
... Suppose P in the preceding article to be an elementary particle of a sphere M ' , whose centre O ' suppose at a distance a from O. Then , since action and reaction are equal and opposite , P will attract the whole sphere M just as it ...
Σελίδα 20
... suppose , whence H H2 dH Trs . de de H = = Hu " , if u = 1 , Again , Therefore dt = dt 1 Hu = dr de • do hu 1 √ ( 1 + 2 / ( 1 + 2 fm de ) hu dr du = H dt de dt do ' d2r d du d dt d therefore ᏧᎾ dt = Substitute in ( ii ) , Hu2 2 ( H ...
... suppose , whence H H2 dH Trs . de de H = = Hu " , if u = 1 , Again , Therefore dt = dt 1 Hu = dr de • do hu 1 √ ( 1 + 2 / ( 1 + 2 fm de ) hu dr du = H dt de dt do ' d2r d du d dt d therefore ᏧᎾ dt = Substitute in ( ii ) , Hu2 2 ( H ...
Σελίδα 29
... within the proposed order . Such terms must therefore not be rejected , and we shall proceed to examine by what means they may be recognised . 27. Suppose then that after an approximation to a certain GENERAL PROCESS OF INTEGRATION . 29.
... within the proposed order . Such terms must therefore not be rejected , and we shall proceed to examine by what means they may be recognised . 27. Suppose then that after an approximation to a certain GENERAL PROCESS OF INTEGRATION . 29.
Σελίδα 30
... Suppose then that after an approximation to a certain order , the substitutions for the next step have brought the equation in u to the form d'u de + u = + G cos ( p0 + H ) + ...... ....... where the coefficient G is one order beyond ...
... Suppose then that after an approximation to a certain order , the substitutions for the next step have brought the equation in u to the form d'u de + u = + G cos ( p0 + H ) + ...... ....... where the coefficient G is one order beyond ...
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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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