Dynamical friction

"In this paper it is shown that a star must experience dynamical friction, i.e., it must suffer from a systematic tendency to be decelerated in the direction of its motion. This dynamical friction which stars experience is one of the direct consequences of the fluctuating force acting on a star due to the varying complexion of the near neighbors. From considerations of a very general nature it is concluded that the coefficient of dynamical friction, \eta, must be of the order of the reciprocal of the time of relaxation of the system. Further, an independent discussion based on the two-body approximation for stellar encounters leads to the following explicit formula for the coefficient of dynamical friction: \eta = 4\pi m_1 (m_1 + m_2)G^2/v^3 log_e [D_0\overline {|u|^2}/G(m_1+m_2)] \int_{0}^{v} N(v_1) \,dv_1, where m_l and m_2 denote the masses of the field star and the star under consideration, respectively; G, the constant of gravitation; D_0 the average distance between the stars; \overline {|u|^2}, the mean square velocity of the stars; N(v_1) dv_1, the number of field stars with velocities between v_1 and v_1 + dv_1; and, finally, v, the velocity of the star under consideration. It is shown that the foregoing formula for η is in agreement with the conclusions reached on the basis of the general considerations. Finally, some remarks are made concerning the further development of these ideas on the basis of a proper statistical theory."

"We investigate dynamical friction on a test object (such as a bar or satellite) which rotates or revolves through a spherical stellar system. We find that frictional effects arise entirely from near-resonant stars and we derive an analog to Chandrasekhar's dynamical friction formula which applies to spherical systems. We show that a formula of this type is valid so long as the angular speed of the test object changes sufficiently rapidly. If the angular speed is slowly changing two new effects appear: a reversible dynamical feedback which can stabilize or destabilize the rotation speed, and permanent capture of near-resonant stars into librating orbits. We discuss orbital decay of satellites in the light of these results."

"A test particle traveling through a collisionless gravitating background suffers a dissipative drag force known as dynamical friction. As with other dissipative forces, this friction must be related to fluctuations in the underlying medium (fluctuation-dissipation theorem). However, this long recognized aspect of the force did not easily yield to analysis until now, and Chandrasekhar’s celebrated formula was obtained by considering momentum exchanges resulting from encounters between a test particle and field particles which were ideal- ized as occurring sequentially. In this paper we return to the underlying basic physics and develop a theory of the interaction of the test particle with the stochastic force of the background. This enables us to derive in a unified way the Chandrasekhar formula for the friction (for the full range of m/M) and the heating of the particle by background fluctuations."