Dynamical friction - Citizendia

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. Astrophysics is the branch of Astronomy that deals with the Physics of the Universe, including the physical properties ( Luminosity, In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The kinetic energy of an object is the extra Energy which it possesses due to its motion Gravitation is a natural Phenomenon by which objects with Mass attract one another Matter is commonly defined as being anything that has mass and that takes up space. It is sometimes referred to as gravitational drag, and was first discussed in detail by Subrahmanyan Chandrasekhar in 1943. Padma Vibhushan Subrahmanyan Chandrasekhar, FRS ( Tamil: சுப்பிரமணியன் சந்திரசேகர் English ˌtʃʌndrəˈʃeɪkɑr( Year 1943 ( MCMXLIII) was a Common year starting on Friday (the link will display full 1943 calendar of the Gregorian calendar. ^[1]^[2]^[3]

1 Intuitive account
2 Chandrasekhar dynamical friction formula
- 2.1 Density of the surrounding media
3 Applications
4 Notes and References

Intuitive account

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). In Orbital mechanics and Aerospace engineering, a gravitational slingshot, gravity assist or swing-by is the use of the relative movement and 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 the light bodies are attracted by gravity toward the larger body moving through the cloud, and therefore the density at that location increases and is referred to as a gravitational wake. In the meantime, object under consideration has moved forward. Therefore, the gravitational attraction of the wake pulls it backward and slows 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. In Orbital mechanics and Aerospace engineering, a gravitational slingshot, gravity assist or swing-by is the use of the relative movement and This technique is sometimes used by interplanetary probes to obtain a boost in velocity by passing close by a planet.

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. In Mathematics and Physics, a phase space, introduced by Willard Gibbs in 1901 is a Space in which all possible states of a System

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:^[4]

$\textbf{f}_{dyn} = M \frac{d\textbf{v}_M}{dt} = -\frac{4\pi \mbox{Ln}(\Lambda) G^2 M^2 \rho}{v_M^3}\left[\mbox{erf}(X)-\frac{2X}{\sqrt{\pi}}e^{-X^2}\right]\textbf{v}_M$

where

G is the gravitational constant.
M is the mass under consideration.
$v M$ is the velocity of the object under consideration, in a frame where the center of gravity of the matter field is initially at rest.
$X = v_M/(\sqrt{2} \sigma)$ is the ratio of the velocity of the object under consideration to the modal velocity of the Maxwellian distribution. ( $σ$ is the velocity dispersion).
$erf$ is the "error function" obtained by integrating the normal distribution. In Mathematics, the error function (also called the Gauss error function) is a Special function (non- elementary) which occurs in Probability
$ρ$ is the density of the matter field.
$Ln(Λ)$ is the "Coulomb logarithm". A Coulomb collision is a Collision between two particles when the force between them is given by Coulomb's Law.

In general, a simplified equation for the force from dynamical friction $\textbf{f}_{dyn}$ has the form

$\textbf{f}_{dyn} \approx C \frac{G^2 M^2 \rho}{v^2_M}$

where the dimensionless numerical factor $C$ depends on how $v M$ compares to the velocity dispersion of the surrounding matter. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units ^[5]

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.

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. Protoplanets are moon-sized planets or larger embryos within Protoplanetary discs They are believed to form out of kilometer-sized Planetesimals that attract each A protoplanetary disk (or proplyd) is a rotating Circumstellar disk of dense gas surrounding a young newly formed star a T Tauri star or Herbig star 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 larger elliptical galaxy. A spiral galaxy is a Galaxy belonging to one of the three main classes of galaxy originally described by Edwin Hubble in his 1936 work “The Realm of the An elliptical galaxy is a Galaxy belonging to one of the three main classes of galaxy originally described by Edwin Hubble (whose name was dedicated

Photons

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. Fritz Zwicky ( February 14 1898 &ndash February 8 1974) was an American-based Swiss Astronomer of Bulgarian origin Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance Tired light is a class of hypothetical Redshift mechanisms that were proposed as an alternative explanation for the redshift-distance relationship as alternatives ^[6] 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. Sir Arthur Stanley Eddington, OM (28 December 1882 – 22 November 1944 was an English Astrophysicist of the early 20th century Zwicky promptly acknowledged the correction,^[7] 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 metric expansion of space. The metric expansion of space is the averaged increase of metric (i

Notes and References

^ Chandrasekhar, S. (1943), “Dynamical Friction. I. General Considerations: the Coefficient of Dynamical Friction.”, Astrophysical Journal 97: 255–262, <http://adsabs.harvard.edu/abs/1943ApJ....97..255C>
^ Chandrasekhar, S. (1943), “Dynamical Friction. II. The Rate of Escape of Stars from Clusters and the Evidence for the Operation of Dynamical Friction.”, Astrophysical Journal 97: 263–273, <http://adsabs.harvard.edu/abs/1943ApJ....97..263C>
^ Chandrasekhar, S. (1943), “Dynamical Friction. III. a More Exact Theory of the Rate of Escape of Stars from Clusters.”, Astrophysical Journal 98: 54–60, <http://adsabs.harvard.edu/abs/1943ApJ....98...54C>
^ Binney, James; Scott Tremaine (1994). Galactic Dynamics. Princeton University Press. The Princeton University Press is an independent publisher with close connections to Princeton University. ISBN 0-691-08445-9.
^ Carroll, Bradley; Dale Ostlie (1996). An Introduction to Modern Astrophysics. Weber State University. Weber State University (ˈwiːbər is a public university located in the city of Ogden in Weber County Utah USA ISBN 0-201-54730-9.
^ Zwicky, F. (1929), “On the Red Shift of Spectral Lines through Interstellar Space”, Proceedings of the National Academy of Science 15: 773–779, <http://adsabs.harvard.edu/abs/1929PNAS...15..773Z> .
^ Zwicky, F. (1929). "On the Possibilities of a Gravitational Drag of Light". Physical Review 34 (12): 1623–1624.

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