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A convenient formalism for averaging the losses produced by gravitationalradiation backreaction over one orbital period was developed in an earlierpaper. In the present paper we generalize this formalism to include the case ofa closed system composed from two bodies of comparable masses, one of themhaving the spin S.  We employ the equations of motion given by Barker and O'Connell, where termsup to linear order in the spin (the spin-orbit interaction terms) are kept. Toobtain the radiative losses up to terms linear in the spin, the equations ofmotion are taken to the same order. Then the magnitude L of the angularmomentum L, the angle kappa subtended by S and L and the energy E areconserved. The analysis of the radial motion leads to a new parametrization ofthe orbit.  From the instantaneous gravitational radiation losses computed by Kidder theleading terms and the spin-orbit terms are taken. Following Apostolatos,Cutler, Sussman and Thorne, the evolution of the vectors S and L in themomentary plane spanned by these vectors is separated from the evolution of theplane in space. The radiation-induced change in the spin is smaller than theleading-order spin terms in the momentary angular momentum loss. This enablesus to compute the averaged losses in the constants of motion E, L and L_S=L coskappa. In the latter, the radiative spin loss terms average to zero. Analternative description using the orbital elements a,e and kappa is given.  The finite mass effects contribute terms, comparable in magnitude, to thebasic, test-particle spin terms in the averaged losses.Comment: 12 pages, 1 figure, Phys.Rev.D15, March, 199

Spin effects in gravitational radiation back reaction. II. Finite mass effects