Dynamical friction

In astrophysics, dynamical friction, sometimes called gravitational drag, is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space. It was first discussed in detail by Subrahmanyan Chandrasekhar in 1943.

An intuition for the effect can be obtained by thinking of a massive object moving through a cloud of smaller lighter bodies. The effect of gravity causes the light bodies to accelerate and gain momentum and kinetic energy (see slingshot effect). By conservation of energy and momentum, we may conclude that the heavier body will be slowed by an amount to compensate. Since there is a loss of momentum and kinetic energy for the body under consideration, the effect is called dynamical friction.

Another equivalent way of thinking about this process is that as a large object moves through a cloud of smaller objects, the gravitational effect of the larger object pulls the smaller objects towards it. There then exists a concentration of smaller objects behind the larger body (a gravitational wake), as it has already moved past its previous position. This concentration of small objects behind the larger body exerts a collective gravitational force on the large object, slowing it down.

Of course, the mechanism works the same for all masses of interacting bodies and for any relative velocities between them. However, while the most probable outcome for an object moving through a cloud is a loss of momentum and energy, as described intuitively above, in the general case it might be either loss or gain. When the body under consideration is gaining momentum and energy the same physical mechanism is called slingshot effect, or gravity assist. This technique is sometimes used by interplanetary probes to obtain a boost in velocity by passing close by a planet.

The full Chandrasekhar dynamical friction formula for the change in velocity of the object involves integrating over the phase space density of the field of matter and is far from transparent.

A commonly used special case is where there is a uniform density in the field of matter, with matter particles significantly lighter than the major particle under consideration and with a Maxwellian distribution for the velocity of matter particles. In this case, the dynamical friction force is as follows:

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