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Dynamical friction is a term in astrophysics related to loss of momentum and kinetic energy of moving bodies through a gravitational interaction with surrounding matter in space. It is mainly related to Fritz Zwickys Tired Light. It is sometimes referred to as gravitational drag, and was first discussed in detail by Subrahmanyan Chandrasekhar in 1943. Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ...
In classical mechanics, momentum (pl. ...
The kinetic energy of an object is the extra energy which it possesses due to its motion. ...
“Gravity†redirects here. ...
This article or section does not cite any references or sources. ...
Fritz Zwicky (February 14, 1898 – February 8, 1974) was an American-based Swiss astronomer. ...
Subrahmanyan Chandrasekhar (October 19, 1910 – August 21, 1995) was an Indian-American physicist, astrophysicist and mathematician. ...
1943 (MCMXLIII) was a common year starting on Friday (the link is to a full 1943 calendar). ...
Conservation laws
The mentioned effect must exist according to the principle of conservation of (potential and kinetic) energy and to the principle of conservation of momentum. In classical mechanics, momentum (pl. ...
Conservation of energy Conservation of potential and kinetic energy means: Any source or sink of potential energy results inversely in a sink or source of kinetic energy, macroscopically well known already by Newton law but valid until minimal relations of a few or one single basic Planck's Quantums (see Planck's constant). One of the most astonishing physical facts is called: A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...
Divergence theorem (Gauss) This rarely considered theorem has a very important result for any kind of distributed masses: The divergence theorem, (see subsection "gravity") says: "Applied to a gravitational field we get that the surface integral is -4πG times the mass inside, regardless of how the mass is distributed, and regardless of any masses outside". This means within a (thought, even infinitely!) inflated balloon: In vector calculus, the divergence theorem, also known as Gauss theorem, Ostrogradskys theorem, or Ostrogradsky–Gauss theorem is a result that links the divergence of a vector field to the value of surface integrals of the flow defined by the field. ...
- An equally distributed gas makes that the gravity at its shell increases while the mass of gas increases within the (thought, consistently) inflated balloon.
- All distinct masses within such an (thought increasing) balloon must be included, e.g. all kind of stars, black holes, etc.
Conservation of momentum The momentum is conserved as any gravitational interactions between two or more bodies correspond to elastic collisions between those bodies. An elastic collision is a collision in which the total kinetic energy of the colliding bodies after collision is equal to their total kinetic energy before collision. ...
E.g. when a heavy body B moves through a cloud of lighter bodies, the gravitational interaction between B and the light bodies causes the light bodies to accelerate and gain momentum and kinetic energy (see sling effect). Since energy and momentum are conserved, B has to lose a part of its momentum and energy equal to the sums of all momenta and energies gained by the light bodies. Because of the loss of momentum and kinetic energy of the body under consideration the effect is called dynamical friction. Sling effect is an effect of accelerating a body in space (as e. ...
Gravitational wake An equivalent way of thinking about this process is that the light bodies near B are attracted by its gravity toward its position and therefore the density at that location increases and is referred to as a gravitational wake. In the meantime, B has moved forward. Therefore, the gravitational attraction of the wake pulls B backward and slows it down.
"Loss" of momentum and energy Of course the mechanism works the same for all masses of interacting bodies and for any relative velocities between them. However, while in the above case the most probable outcome is the loss of momentum and energy by the body under consideration, in the general case it might be either loss or gain (when one body loses momentum and energy in an elastic collision the other one gains them). In a case when the body under consideration is gaining momentum and energy the same physical mechanism is called sling effect. Sling effect is an effect of accelerating a body in space (as e. ...
Chandrasekhar dynamical friction formula 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. By assuming a constant density though, a simplified equation for the force from dynamical friction, fd, may be found to be For other senses of this term, see phase space (disambiguation). ...
where G is the gravitational constant, M is the mass of the moving object, ρ is the density, and vM is the velocity of the object in the frame in which the surrounding matter was initially at rest. In this equation C is not a constant but depends on how vM compares to the velocity dispersion of the surrounding matter (Carroll and Ostlie 1996).
Density of the surrounding media The greater the density of the surrounding media, 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 though the media, the less time there is for a wake to build up behind it.
Results Dynamical friction is particularly important in the formation of planetary systems and interactions between galaxies.
Proplanets 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. In cosmogony, a protoplanet is a quasi-planetoid which is slightly larger than a planetesimal and orbits within a solar nebulas protoplanetary discs. ...
A protoplanetary disc (also protoplanetary disk, proplyd) is an accretion disc surrounding a T Tauri star. ...
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 larger elliptical galaxy. A spiral galaxy is a type of galaxy in the Hubble sequence which is characterized by the following physical properties: Spiral Galaxy M74 presents a face-on view of its spiral arms. ...
An elliptical galaxy is a type of galaxy in the Hubble sequence characterized by the following physical properties: The giant elliptical galaxy NGC 4881 (the spherical glow at upper left) lies at the edge of the Coma Cluster of Galaxies. ...
Zwicky's result for the universe Zwicky proposed in August 26, 1929 such an Integration of the whole Gravitational Potential in Physics: F.Zwicky p.775 ff., especially: "In regard to D (diametre of a sphere), it must be remarked that it should be as large as the dimension of the space over which masses are distributed, if those masses are regarded as independent from each other. But the masses are in reality coupled by gravitational forces and the effect of an external perturbation upon them must be computed by considering the system of the far distant masses as a whole.". In physics, gravitational potential is the measure of potential energy an object possesses due to its position in a gravitational field. ...
In geometry, a diameter (Greek words diairo = divide and metro = measure) of a circle is any straight line segment that passes through the center and whose endpoints are on the circular boundary, or, in more modern usage, the length of such a line segment. ...
A sphere is a perfectly symmetrical geometrical object. ...
He took the momentum-law instead of the related energy-law: While divergence theorem gives a summary of all energy - result on a shell (Surface integral) and the total sum of sources and sinks of its internal volume (Volume integral) are equal regardless of extern sources or sinks - Zwicky calculated single photons by the same basis, the local differential Poisson equation. He differentiated it by dt, got thereby the Momentum (product of one small mass with its velocity v), with a first result "2πlG2LD" = 4πG*lLD (see there) similar to -4πG*M above. Supposing that gravity waves have the velocity of light c, he used the theory of the retarded potentials. Taking velocity of the light v = c with Planck mass m = h  /c² he got his approximation for redshifts of photons and got: “Light travelling a distance L then would lose the momentum... = l.4πfpDL/c²". In mathematics, a surface integral is a definite integral taken over some surface that may be a curved set in space; it can be thought of as the double integral analog of the path integral. ...
In mathematics — in particular, in multivariable calculus — a volume integral refers to an integral over a 3-dimensional domain. ...
Poissons equation is the partial differential equation: Or alternately: or i. ...
In classical mechanics, momentum (pl. ...
These are the retarded potentials for an arbitrary source. ...
In reality Zwicky described here a "potential energy-loss" less a so named "dynamical friction" or "tired light" (see lit. to Zwicky).
References - Carroll, Bradley; Dale Ostlie (1996). An Introduction to Modern Astrophysics. Weber State University. ISBN 0-201-54730-9.
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