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	[[Image:Solar Magnetic Field Lines.jpg\|thumb\|The magnetic field lines rotate together with the Sun as a solid object. Ionized material carried along the field lines will at some point <math> r_c </math> escape the magnetic field lines and thus take away the Sun's angular momentum]]
	'''Magnetic braking''' is a theory explaining the loss of solar [[angular momentum]] due to material getting captured by the [[solar magnetic field]] and thrown out at great distance from the surface of the Sun.

	~~==The problem==~~
	The currently accepted theory of the [[solar systems\|solar system's]] evolution states that the Solar System originates from a contracting gas cloud. As the cloud contracts, the [[angular momentum]] <math> L</math> must be [[angular momentum#Conservation of angular momentum\|conserved]]. Any small net rotation of the cloud will cause the spin to increase as the cloud collapses, forcing the material into a rotating disk. At the dense center of this disk a [[protostar]] forms, which gains heat from the [[gravitational energy]] of the collapse. As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to [[centrifugal force]] at the equator.

	~~Thus~~ the ~~rotation rate must~~ be ~~braked during the first 100,000 years of the star's life to avoid this scenario~~. ~~One possible explanation for the braking~~ is the ~~interaction~~ of ~~the protostar's magnetic field with the stellar wind~~. ~~In the case of our own Sun, when the planets' angular momenta~~ are ~~compared to the Sun's own, the Sun has less than 1% of its supposed angular momentum~~. ~~In other words~~, ~~the Sun has slowed down its spin while the planets have not.~~		Surely the second option would be more beneficial for any website. It is very easy to customize plugins according to the needs of a particular business. These templates are professionally designed and are also Adsense ready. Word - Press also provides protection against spamming, as security is a measure issue. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. <br><br>Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. Wordpress have every reason with it which promote wordpress development. If you liked this write-up and you would like to obtain extra details with regards to [http://9m.no/%EC%BD%A6%E5%A9%86 wordpress backup plugin] kindly take a look at our own web-page. This is the reason for the increased risk of Down Syndrome babies in women over age 35. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. Setting Up Your Business Online Using Free Wordpress Websites. You or your web designer can customize it as per your specific needs. Socrates: (link to ) Originally developed for affiliate marketers, I've used this theme again and again to develop full-fledged web sites that include static pages, squeeze pages, and a blog. <br><br>It is the convenient service through which professionals either improve the position or keep the ranking intact. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. When we talk about functional suitability, Word - Press proves itself as one of the strongest contestant among its other rivals. If you are looking for Hire Wordpress Developer then just get in touch with him. Where from they are coming, which types of posts are getting top traffic and many more. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. And, it is better that you leave it on for the duration you are writing plugin code. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts.

	~~==The idea behind magnetic braking==~~
	~~Ionized material captured by the magnetic field lines will rotate with the Sun~~ as ~~if it were~~ a ~~solid body~~. ~~As material escapes from the Sun due to the [[Solar wind]]~~, ~~the highly ionized material will be captured by the field lines~~ and ~~rotate with~~ the ~~same angular velocity as the Sun, even though~~ it is ~~carried far away from the Sun's surface~~, ~~until it eventually escapes. This effect of carrying mass far from the centre of the Sun~~ and ~~throwing it away robs the Sun of its spin~~.<~~ref~~>~~{{cite journal \|authors=Ferreira, J.; Pelletier, G.; Appl, S. \|title=Reconnection X~~-~~winds: spin-down~~ of ~~low-mass protostars \|journal=Monthly Notices of the Royal Astronomical Society \|year=2000 \|volume=312 \|issue=2 \|pages=387–397 \|bibcode=2000MNRAS~~.~~312~~.~~.387F \|doi=10.1046/j.1365~~-~~8711.2000.03215.x }}</ref><ref>{{cite news \|first=Terry \|last=Devitt \|title=What Puts The Brakes On Madly Spinning Stars? \|publisher=University of Wisconsin-Madison \|date=January 31, 2001 \|url=~~http://~~www~~.~~news.wisc.edu~~/~~5732 \|accessdate=2007~~-~~06-27 }}</ref> The same effect~~ is ~~used in slowing~~ the ~~spin~~ of ~~a [[Yo-yo de-spin\|rotating satellite]]; here two wires spool out weights~~ to a ~~distance slowing the satellites spin~~, ~~then the wires are cut, letting the weights escape into space and permanently robbing the spacecraft~~ of ~~its [[angular momentum]]~~.

	~~==Theory behind magnetic braking==~~
	~~{{unreferenced section\|date=April 2013}}~~
	~~{{original research section\|date=April 2013}}~~
	As ~~ionized material follows the Sun~~'~~s magnetic field lines, due~~ to the ~~effect of the field lines being frozen in the [[plasma (physics)\|plasma]], the charged particles feel a force <math> \mathbf{F} </math> of the magnitude:~~
	~~:<math> \mathbf{F}=q \mathbf{v} \times \mathbf{B} </math>~~
	~~where <math>q</math> is the charge, <math>\mathbf{v}</math> is the velocity~~ and ~~<math>\mathbf{B}</math> is the magnetic field vector~~. ~~This bending action forces the particles to "[[corkscrew]]" around the magnetic field lines while held in place by a "magnetic pressure"~~<~~math~~> ~~P_B~~ <~~/math~~>~~, or "energy density", while rotating together with the Sun as a solid body:~~

	~~:<math>P_B=\frac{B^2}{2 \mu_0} </math>~~

	~~Since magnetic field strength decreases with the cube of the distance there will be a place where the kinetic gas pressure <math> P_g </math> of the ionized gas~~ is ~~great~~ enough to ~~break away from the field lines:~~

	~~:<math> P_g=n m v^2 </math>~~
	~~where n is~~ the ~~number~~ of ~~particles, m is the mass~~ of the ~~individual particle and v is~~ the ~~radial velocity away form~~ the ~~Sun~~, or ~~the speed of the solar wind.~~

	~~The magnetic field strength as a function of radius~~ can ~~be approximated~~ as:
	~~:<math> B~~(r)~~=\frac{D_\odot}{r^3} </math>~~

	~~The critical distance where the material will break away from the field lines can then be calculated as the distance where the kinetic pressure~~ and ~~the magnetic pressure are equal~~, i.e.
	~~:<math> P_B=P_g \Rightarrow</math>~~

	~~:<math> \frac{B(rc)^2}{2\mu_0}=n m v^2\Rightarrow</math>~~

	:<~~math~~> ~~\frac{D_{\odot}^2}{2\mu_0 r_c^6}=n m v^2~~<~~/math~~>

	~~If the solar mass loss~~ is ~~omni-directional then~~ the ~~mass loss <math>n m= \frac{dM/dt}{4\pi r^2 v}</math>; plugging this into~~ the ~~above equation and isolating~~ the ~~critical radius~~ it ~~follows that~~
	~~:<math>r_c=\left(\frac{2\pi D_\odot ^2}{\mu_0 v \dot{M}}\right)^{1 \over 4}</math>~~

	~~===Present day value===~~
	~~Currently~~ it ~~is estimated that:~~
	* The mass loss of the Sun is about <math>\dot{M}=dM/dt=2 \cdot 10^9 kg/s~~</math>~~
	* The solar wind speed is <math>v=5\cdot10^5m/s</math>
	* The dipole field is <math>D_{\odot}=8 \cdot 10^{22} T m^3</math>

	~~This leads~~ to ~~a critical radius <math>r_c =3.4 R_\odot</math>. This means that the ionized plasma will rotate together with the Sun as a solid body until~~ it ~~reaches~~ a ~~distance~~ of ~~nearly 3~~.~~4 the radius~~ of the ~~Sun;~~ from ~~there the material will break off~~ and ~~stop affecting the Sun~~.

	~~The amount of solar mass needed to be thrown out along the field lines to make the Sun completely stop rotating can then be calculated using the specific angular momentum:~~
	:<~~math~~>~~\frac{j_\odot}{j_c}=\left(\frac{R_\odot}{r_c}\right)^2 \approx 10%~~<~~/math~~>
	~~About 1/10~~ of the ~~solar mass~~ should ~~thus have be lost by now due~~ to ~~this effect, but if~~ the ~~present mass loss rate was stable throughout~~ the ~~Sun's "life" only about 0~~.~~01% of the Sun's original mass would~~ have ~~been lost~~. ~~This indicates~~ that ~~either the Sun's mass loss must have been higher in the past~~ or that the ~~Sun's magnetic field~~ has ~~been much stronger~~.

	~~==References==~~
	~~{{reflist}}~~

	~~==See also==~~
	* [[Stellar magnetic field]]
	* [[Stellar rotation]]

	~~[[Category:Conservation laws]]~~
	~~[[Category:Concepts in physics]]~~
	~~[[Category:Physical quantities]]~~
	~~[[Category:Rotation]]~~
	~~[[Category:Rotational symmetry]]~~

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[[Image:Solar Magnetic Field Lines.jpg|thumb|The magnetic field lines rotate together with the Sun as a solid object. Ionized material carried along the field lines will at some point <math> r_c </math> escape the magnetic field lines and thus take away the Sun's angular momentum]]
'''Magnetic braking''' is a theory explaining the loss of solar [[angular momentum]] due to material getting captured by the [[solar magnetic field]] and thrown out at great distance from the surface of the Sun.

==The problem==
The currently accepted theory of the [[solar systems|solar system's]] evolution states that the Solar System originates from a contracting gas cloud. As the cloud contracts, the [[angular momentum]] <math> L</math> must be [[angular momentum#Conservation of angular momentum|conserved]]. Any small net rotation of the cloud will cause the spin to increase as the cloud collapses, forcing the material into a rotating disk. At the dense center of this disk a [[protostar]] forms, which gains heat from the [[gravitational energy]] of the collapse. As the collapse continues, the rotation rate can increase to the point where the accreting protostar can break up due to [[centrifugal force]] at the equator.

Thus the rotation rate must be braked during the first 100,000 years of the star's life to avoid this scenario. One possible explanation for the braking is the interaction of the protostar's magnetic field with the stellar wind. In the case of our own Sun, when the planets' angular momenta are compared to the Sun's own, the Sun has less than 1% of its supposed angular momentum. In other words, the Sun has slowed down its spin while the planets have not.

==The idea behind magnetic braking==
Ionized material captured by the magnetic field lines will rotate with the Sun as if it were a solid body. As material escapes from the Sun due to the [[Solar wind]], the highly ionized material will be captured by the field lines and rotate with the same angular velocity as the Sun, even though it is carried far away from the Sun's surface, until it eventually escapes. This effect of carrying mass far from the centre of the Sun and throwing it away robs the Sun of its spin.<ref>{{cite journal |authors=Ferreira, J.; Pelletier, G.; Appl, S. |title=Reconnection X-winds: spin-down of low-mass protostars |journal=Monthly Notices of the Royal Astronomical Society |year=2000 |volume=312 |issue=2 |pages=387–397 |bibcode=2000MNRAS.312..387F |doi=10.1046/j.1365-8711.2000.03215.x }}</ref><ref>{{cite news |first=Terry |last=Devitt |title=What Puts The Brakes On Madly Spinning Stars? |publisher=University of Wisconsin-Madison |date=January 31, 2001 |url=http://www.news.wisc.edu/5732 |accessdate=2007-06-27 }}</ref> The same effect is used in slowing the spin of a [[Yo-yo de-spin|rotating satellite]]; here two wires spool out weights to a distance slowing the satellites spin, then the wires are cut, letting the weights escape into space and permanently robbing the spacecraft of its [[angular momentum]].

==Theory behind magnetic braking==
{{unreferenced section|date=April 2013}}
{{original research section|date=April 2013}}
As ionized material follows the Sun's magnetic field lines, due to the effect of the field lines being frozen in the [[plasma (physics)|plasma]], the charged particles feel a force <math> \mathbf{F} </math> of the magnitude:
:<math> \mathbf{F}=q \mathbf{v} \times \mathbf{B} </math>
where <math>q</math> is the charge, <math>\mathbf{v}</math> is the velocity and <math>\mathbf{B}</math> is the magnetic field vector. This bending action forces the particles to "[[corkscrew]]" around the magnetic field lines while held in place by a "magnetic pressure"<math> P_B </math>, or "energy density", while rotating together with the Sun as a solid body:

:<math>P_B=\frac{B^2}{2 \mu_0} </math>

Since magnetic field strength decreases with the cube of the distance there will be a place where the kinetic gas pressure <math> P_g </math> of the ionized gas is great enough to break away from the field lines:

:<math> P_g=n m v^2 </math>
where n is the number of particles, m is the mass of the individual particle and v is the radial velocity away form the Sun, or the speed of the solar wind.

The magnetic field strength as a function of radius can be approximated as:
:<math> B(r)=\frac{D_\odot}{r^3} </math>

The critical distance where the material will break away from the field lines can then be calculated as the distance where the kinetic pressure and the magnetic pressure are equal, i.e.
:<math> P_B=P_g \Rightarrow</math>

:<math> \frac{B(rc)^2}{2\mu_0}=n m v^2\Rightarrow</math>

:<math> \frac{D_{\odot}^2}{2\mu_0 r_c^6}=n m v^2</math>

If the solar mass loss is omni-directional then the mass loss <math>n m= \frac{dM/dt}{4\pi r^2 v}</math>; plugging this into the above equation and isolating the critical radius it follows that
:<math>r_c=\left(\frac{2\pi D_\odot ^2}{\mu_0 v \dot{M}}\right)^{1 \over 4}</math>

===Present day value===
Currently it is estimated that:
* The mass loss of the Sun is about <math>\dot{M}=dM/dt=2 \cdot 10^9 kg/s</math>
* The solar wind speed is <math>v=5\cdot10^5m/s</math>
* The dipole field is <math>D_{\odot}=8 \cdot 10^{22} T m^3</math>

This leads to a critical radius <math>r_c =3.4 R_\odot</math>. This means that the ionized plasma will rotate together with the Sun as a solid body until it reaches a distance of nearly 3.4 the radius of the Sun; from there the material will break off and stop affecting the Sun.

The amount of solar mass needed to be thrown out along the field lines to make the Sun completely stop rotating can then be calculated using the specific angular momentum:
:<math>\frac{j_\odot}{j_c}=\left(\frac{R_\odot}{r_c}\right)^2 \approx 10%</math>
About 1/10 of the solar mass should thus have be lost by now due to this effect, but if the present mass loss rate was stable throughout the Sun's "life" only about 0.01% of the Sun's original mass would have been lost. This indicates that either the Sun's mass loss must have been higher in the past or that the Sun's magnetic field has been much stronger.

==References==
{{reflist}}

==See also==
* [[Stellar magnetic field]]
* [[Stellar rotation]]

[[Category:Conservation laws]]
[[Category:Concepts in physics]]
[[Category:Physical quantities]]
[[Category:Rotation]]
[[Category:Rotational symmetry]]