. Carnegie Institution of Washington publication. SPECIAL CASE. 89 V. SPECIAL CASE i=0 i,=0 a^=0 e=0 S =0* This means that two bodies undisturbed by any exterior force revolve in circles, that the radius, mass, and angular velocity of rotation of one of them are so small that its rotational momentum and energy may be neglected, and that the axis of rotation of the other is perpendicular to the plane of their orbit. In this case equations (9) and (10) become, writing D in place of D^, (23) M = PhJ^^ E 71 1 W, pi ' D' (24) We may choose the direction of revolution of the bodies as the positive d
. Carnegie Institution of Washington publication. SPECIAL CASE. 89 V. SPECIAL CASE i=0 i,=0 a^=0 e=0 S =0* This means that two bodies undisturbed by any exterior force revolve in circles, that the radius, mass, and angular velocity of rotation of one of them are so small that its rotational momentum and energy may be neglected, and that the axis of rotation of the other is perpendicular to the plane of their orbit. In this case equations (9) and (10) become, writing D in place of D^, (23) M = PhJ^^ E 71 1 W, pi ' D' (24) We may choose the direction of revolution of the bodies as the positive direction. Then only a positive P can have a meaning in the problem, since a revolution in one direction can not be reversed without a collision of the bodies. D is positive or negative according as the rotation is in the same direction as the revolution or the opposite. Under the hypotheses adopted M is rigorously constant. When D=+oo then P=M^; when D = -^then P = 0: when D = lim(0-\-£) then P=-oo; when D = lim(0—e) then P = + 00 ; when D = — cc then P = M\ Consequently the curve defined by (23) is as given in fig. 9. The part of the figure to the right of the P-axis belongs to the case where the rotation of m-i and revolution of mj are in the same direction, and the part to the left where they are in opposite directions. ,P. Fia. 0. The slope of the curve, or the ratio of the rate of change of the period of revolution to that of rotation, is found from (23) to be dP / dD Sm^Pi dt dt D' (25) ? For a similar treatment of this problem see No. 5 of Darwin's Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Carnegie Institution of Washington. Washington, Carnegie Institution of Washington
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