of the equation is the gravitational acceleration produced on the object under consideration by the stars or celestial bodies, as acceleration is the ratio of velocity and time. Maxwell's distribution 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 i.e., and with a Maxwellian distribution for the velocity of matter particles i.e., where is the total number of stars and is the dispersion. In this case, the dynamical friction formula is as follows: where is the ratio of the velocity of the object under consideration to the modal velocity of the Maxwellian distribution. is the error function. is the density of the matter field. In general, a simplified equation for the force from dynamical friction has the form where the dimensionless numerical factor depends on how compares to the velocity dispersion of the surrounding matter. But note that this simplified expression diverges when ; caution should therefore be exercised when using it. Density of the surrounding medium 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. One of these terms is from the gravitational force between the object and the wake. The second term is because the more massive the object, the more matter will be pulled into the wake. The force is also proportional to the inverse square of the velocity. 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. Applications Dynamical friction is particularly important in the formation of planetary systems and interactions between galaxies. Protoplanets During the formation of planetary systems, dynamical friction between the protoplanet and the protoplanetary disk causes energy to be transferred from the protoplanet to the disk. This results in the inward migration of the protoplanet. Galaxies When galaxies interact through collisions, dynamical friction between stars causes matter to sink toward the center of the galaxy and for the orbits of stars to be randomized. This process is called violent relaxation and can change two spiral galaxies into one