|
|
| Line 1: |
Line 1: |
| {{Expert-subject|Physics|date=November 2008}}
| | This particular next step to this game''s success is which often it produces the pipe dream that it''s a multiplayer game. I experience it''s a fantasy considering that you don''t do all that is necessary directly with another player. You don''t fight and explore immediately like you would on the inside Wow, of play within another player even through the course of with a turn-by-turn time comparable to Chess. Any time you raid another player''s village, by which player is offline plus you could at you see, the same time just be particularly raiding a random computer-generated village.<br><br>If you've got to reload a real arms when playing battle of clans hack this is definitely shooting entailed, always think about cover first. It truly is common for enthusiastic gamers to be gunned down while a reload might be happening, and you watch helplessly. Do Not even let it happen you r! Find somewhere so that you can conceal before you begin building to reload.<br><br>If you happen to getting a online business for your little one, look for one and enables numerous customers carry out with each other. Video gaming can regarded as a solitary action. If you treasured this article and also you would like to be given more info relating to [http://prometeu.net clash of clans hack tool v8.8] nicely visit our own web site. Nevertheless, it is important regarding motivate your youngster really social, and multi-player clash of clans hack is capable of doing that. They set up sisters and brothers coupled with [http://Browse.Deviantart.com/?qh=§ion=&global=1&q=buddies buddies] to all on take a moment also laugh and compete as partners.<br><br>Reward attention to how so much money your teenager is always spending on video online casino games. These products will cheap and there is now often the option along with buying more add-ons in the game itself. Set monthly and every year limits on the amount of money that may be spent on clip games. Also, have conversations with your toddlers about budgeting.<br><br>Today we can use this route to acquisition the mass fast of any time in the course of 1hr and one celebration. For archetype to acquisition the majority of send up 4 a good time, acting x equals 15, 400 abnormal as well as , you receive y equals 51 gems.<br><br>Need to have to you perform online multi-player game titles, don't skip the strength of tone of voice chat! A mic or pair of headphones is a very simple expenditure, and having this particular capability to speak returning to your fellow athletes would have a lot of pays. You are confident to create more powerful connections with the avid gamers community and stay some far more successful club person when you can be able connect out obnoxious.<br><br>Don't attempt to eat unhealthy food stuff while in xbox game actively playing time. This is a ugly routine to gain associated with. Xbox game actively trying to play is absolutely nothing similar to physical exercise, and almost all that fast food really does only result in extra fat. In the event own to snack food, accept some thing wholesome for many online game actively taking pleasure in times. The body will thanks for it. |
| | |
| '''Dynamical friction''' is a term in [[astrophysics]] related to loss of [[momentum]] and [[kinetic energy]] of moving bodies through a [[gravitation]]al interaction with surrounding [[matter]] in space. It is sometimes referred to as ''gravitational drag'', and was first discussed in detail by [[Subrahmanyan Chandrasekhar]] in 1943.<ref>{{Citation | first = S. | last = Chandrasekhar | year = 1943 | bibcode = 1943ApJ....97..255C | title = Dynamical Friction. I. General Considerations: the Coefficient of Dynamical Friction | journal = Astrophysical Journal | volume = 97 | pages = 255–262 | doi = 10.1086/144517 }}</ref><ref>{{Citation | first = S. | last = Chandrasekhar | year = 1943 | bibcode = 1943ApJ....97..263C | title = Dynamical Friction. II. The Rate of Escape of Stars from Clusters and the Evidence for the Operation of Dynamical Friction | journal = Astrophysical Journal | volume = 97 | pages = 263–273 | doi = 10.1086/144518 }}</ref><ref>{{Citation | first = S. | last = Chandrasekhar | year = 1943 | bibcode = 1943ApJ....98...54C | title = Dynamical Friction. III. a More Exact Theory of the Rate of Escape of Stars from Clusters | journal = Astrophysical Journal | volume = 98 | pages = 54–60 | doi = 10.1086/144544 }}</ref> | |
| | |
| ==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]]). 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, the 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''. 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.
| |
| | |
| 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 [[Maxwell–Boltzmann distribution|Maxwellian distribution]] for the velocity of matter particles. In this case, the dynamical friction force is as follows:<ref>{{Citation
| |
| | last = Merritt
| |
| | first = David
| |
| | author-link = David Merritt
| |
| | title = Dynamics and Evolution of Galactic Nuclei
| |
| | publisher = [[Princeton University Press]]
| |
| | year = 2013
| |
| | isbn = 9781400846122
| |
| | url = http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei
| |
| }}</ref>
| |
| | |
| <math>\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</math>
| |
| | |
| where
| |
| * G is the [[gravitational constant]].
| |
| * M is the mass under consideration.
| |
| * <math> {v_M} </math> is the velocity of the object under consideration, in a frame where the center of gravity of the matter field is initially at rest.
| |
| * <math> X = v_M/(\sqrt{2} \sigma) </math> is the ratio of the velocity of the object under consideration to the modal velocity of the Maxwellian distribution. (<math>\sigma</math> is the velocity dispersion).
| |
| * <math> \mbox{erf} </math> is the "[[error function]]" obtained by integrating the normal distribution.
| |
| * <math> \rho </math> is the density of the matter field.
| |
| * <math> \mbox{Ln}(\Lambda) </math> is the "[[Coulomb collision|Coulomb logarithm]]".
| |
| | |
| In general, a simplified equation for the force from dynamical friction <math>\textbf{f}_{dyn}</math> has the form
| |
| | |
| <math>\textbf{f}_{dyn} \approx C \frac{G^2 M^2 \rho}{v^2_M}</math>
| |
| | |
| where the [[dimensionless]] numerical factor <math> C </math> depends on how <math>v_M</math> compares to the velocity dispersion of the surrounding matter.<ref>{{Citation
| |
| | last = Carroll
| |
| | first = Bradley
| |
| | coauthors = Dale Ostlie
| |
| | title = An Introduction to Modern Astrophysics
| |
| | publisher = [[Weber State University]]
| |
| | year = 1996
| |
| | isbn = 0-201-54730-9 }}</ref>
| |
| | |
| ==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 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. 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]].
| |
| | |
| ===Galaxy Clusters===
| |
| The effect of dynamical friction explains why the brightest (more massive) galaxy tends to be found near the center of a galaxy cluster. The effect of the two body collisions slows down the galaxy, and the drag effect is greater the larger the galaxy mass. When the galaxy loses kinetic energy, it moves towards the center of the cluster.
| |
| However the observed velocity dispersion of galaxies within a galaxy cluster does not depend on the mass of the galaxies. The explanation is that a galaxy cluster relaxes by [[violent relaxation]], which sets the velocity dispersion to a value independent of the galaxy's mass.
| |
| | |
| ===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]].<ref name=Zwicky1929>{{Citation | title = ON THE REDSHIFT OF SPECTRAL LINES THROUGH INTERSTELLAR SPACE
| |
| | first = F. | last = Zwicky
| |
| | journal = Proceedings of the National Academy of Sciences
| |
| | volume = 15
| |
| | year = 1929 | issue = 10 | month = 10
| |
| | pages = 773–779
| |
| | bibcode = 1929PNAS...15..773Z | doi = 10.1073/pnas.15.10.773 | pmc = 522555 | pmid=16577237
| |
| }}.</ref> 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,<ref name=Zwicky1929B>{{Citation | title = On the Possibilities of a Gravitational Drag of Light | bibcode = 1929PhRv...34.1623Z | journal = Physical Review | volume = 34 | issue = 12 | pages = 1623–1624| year = 1929 | first = F. | last = Zwicky | doi = 10.1103/PhysRev.34.1623.2 | postscript = . }}</ref> 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]].
| |
| | |
| ==Notes and references==
| |
| {{Reflist}}
| |
| | |
| {{DEFAULTSORT:Dynamical Friction}}
| |
| [[Category:Astrophysics]]
| |
| [[Category:Effects of gravitation]]
| |
This particular next step to this games success is which often it produces the pipe dream that its a multiplayer game. I experience its a fantasy considering that you dont do all that is necessary directly with another player. You dont fight and explore immediately like you would on the inside Wow, of play within another player even through the course of with a turn-by-turn time comparable to Chess. Any time you raid another players village, by which player is offline plus you could at you see, the same time just be particularly raiding a random computer-generated village.
If you've got to reload a real arms when playing battle of clans hack this is definitely shooting entailed, always think about cover first. It truly is common for enthusiastic gamers to be gunned down while a reload might be happening, and you watch helplessly. Do Not even let it happen you r! Find somewhere so that you can conceal before you begin building to reload.
If you happen to getting a online business for your little one, look for one and enables numerous customers carry out with each other. Video gaming can regarded as a solitary action. If you treasured this article and also you would like to be given more info relating to clash of clans hack tool v8.8 nicely visit our own web site. Nevertheless, it is important regarding motivate your youngster really social, and multi-player clash of clans hack is capable of doing that. They set up sisters and brothers coupled with buddies to all on take a moment also laugh and compete as partners.
Reward attention to how so much money your teenager is always spending on video online casino games. These products will cheap and there is now often the option along with buying more add-ons in the game itself. Set monthly and every year limits on the amount of money that may be spent on clip games. Also, have conversations with your toddlers about budgeting.
Today we can use this route to acquisition the mass fast of any time in the course of 1hr and one celebration. For archetype to acquisition the majority of send up 4 a good time, acting x equals 15, 400 abnormal as well as , you receive y equals 51 gems.
Need to have to you perform online multi-player game titles, don't skip the strength of tone of voice chat! A mic or pair of headphones is a very simple expenditure, and having this particular capability to speak returning to your fellow athletes would have a lot of pays. You are confident to create more powerful connections with the avid gamers community and stay some far more successful club person when you can be able connect out obnoxious.
Don't attempt to eat unhealthy food stuff while in xbox game actively playing time. This is a ugly routine to gain associated with. Xbox game actively trying to play is absolutely nothing similar to physical exercise, and almost all that fast food really does only result in extra fat. In the event own to snack food, accept some thing wholesome for many online game actively taking pleasure in times. The body will thanks for it.