In astrophysics, dynamical friction or Chandrasekhar friction, sometimes called gravitational drag, is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space.
[1][2][3] An intuition for the effect can be obtained by thinking of a massive object moving through a cloud of smaller lighter bodies.
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.
There then exists a concentration of smaller objects behind the larger body (a gravitational wake), as it has already moved past its previous position.
Of course, the mechanism works the same for all masses of interacting bodies and for any relative velocities between them.
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.
where In general, a simplified equation for the force from dynamical friction has the form
The greater the density of the surrounding medium, the stronger the force from dynamical friction.
Similarly, the force is proportional to the square of the mass of the object.
The second term is because the more massive the object, the more matter will be pulled into the wake.
This means the fractional rate of energy loss drops rapidly at high velocities.
Dynamical friction is, therefore, unimportant for objects that move relativistically, such as photons.
This can be rationalized by realizing that the faster the object moves through the media, the less time there is for a wake to build up behind it.
Dynamical friction is particularly important in the formation of planetary systems and interactions between galaxies.
When the galaxy loses kinetic energy, it moves towards the center of the cluster.
This concentration of more massive stars in the cluster's cores tend to favor collisions between stars, which may trigger the runaway collision mechanism to form intermediate mass black holes.
[citation needed] Globular clusters orbiting through the stellar field of a galaxy experience dynamic friction.
This drag force causes the cluster to lose energy and spiral in toward the galactic center.
[7] Fritz Zwicky proposed in 1929 that a gravitational drag effect on photons could be used to explain cosmological redshift as a form of tired light.
[8] However, his analysis had a mathematical error, and his approximation to the magnitude of the effect should actually have been zero, as pointed out in the same year by Arthur Stanley Eddington.
Zwicky promptly acknowledged the correction,[9] although he continued to hope that a full treatment would be able to show the effect.
It is now known that the effect of dynamical friction on photons or other particles moving at relativistic speeds is negligible, since the magnitude of the drag is inversely proportional to the square of velocity.
Cosmological redshift is conventionally understood to be a consequence of the expansion of the universe.