en>Rjwilmsi: /* References */Added 3 dois to journal cites using AWB (10104)

2014-05-08T15:13:56Z

References: Added 3 dois to journal cites using AWB (10104)

en>The Disambiguator: /* Hirzebruch Signature Theorem */ signature of a quadratic form

2013-04-21T21:14:28Z

Hirzebruch Signature Theorem: signature of a quadratic form

← Older revision		Revision as of 23:14, 21 April 2013
Line 1:		Line 1:
			The '''Leonard–Merritt mass estimator''' is a formula for estimating the mass of a spherical [[stellar system]] using the apparent (angular) positions and [[proper motions]] of its component [[star]]s. The distance to the stellar system must also be known.

			Like the [[virial theorem]], the Leonard–Merritt estimator yields correct results regardless of the degree of velocity anisotropy. Its statistical properties are superior to those of the virial theorem. However, it requires that two components of the velocity be known for every star, rather than just one for the virial theorem.<ref>{{Cite journal
			\| doi = 10.1086/167287
			\| last1 = Leonard \| first1 = Peter
			\| last2 = Merritt \| first2 = David
			\| author2-link = David Merritt
			\| title = The Mass of the Open Star Cluster M35 as Derived from Proper Motions
			\| journal = The Astrophysical Journal
			\| volume = 339
			\| issue =
			\| pages = 195–208
			\| date = 10 April 1989
			\| bibcode = 1989ApJ...339..195L
			\| issn =}}
			</ref>

	~~Bonus: WP Twin and WP Twin Auto Backup:~~ (~~link to~~ ) ~~While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites~~. ~~Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in~~ the ~~business market. A pinch of tablet centric strategy can get your Word - Press site miles ahead~~ of ~~your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:~~. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. This particular wordpress plugin is ~~essential for not only having~~ the ~~capability where you improve your position, but to enhance your organic searches for your website.~~ <br><br>~~For those who have any inquiries concerning where by along with how you can employ [http:~~//~~jrurl.at~~/~~wordpressbackupplugin140236 wordpress dropbox backup], you~~ are ~~able~~ to ~~email us from our web site. Generally~~, ~~for my private income-making market websites~~, ~~I will thoroughly research~~ and ~~discover~~ the ~~leading 10 most worthwhile niches to venture into~~. ~~If you are a positive thinker businessman then today you have to put your business online. Our Daily Deal Software plugin brings the simplicity~~ of ~~setting up a Word - Press blog to~~ the ~~daily deal space. t need to use~~ the ~~back button or~~ the ~~URL to get to your home page~~. 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>Photography is an entire activity~~ in ~~itself~~, ~~and a thorough discovery of it~~ is ~~beyond~~ the ~~opportunity of this content~~. ~~Word - Press has ensured~~ the ~~users~~ of ~~this open source blogging platform do not have to troubleshoot on their own, or seek outside help~~. ~~I hope this short Plugin Dynamo Review will assist you~~ to ~~differentiate whether Plugin Dynamo is Scam or~~ a ~~Genuine~~. ~~You~~ or ~~your web designer can customize it as per your specific needs~~. ~~For any web design~~ and ~~development assignment~~, ~~this is definitely one of~~ the ~~key concerns, specifically for online retail outlets as well as e-commerce websites.~~ <br><br>~~It is~~ the ~~convenient service through which professionals either improve~~ the ~~position or keep the ranking intact. Quttera - Quttera describes itself as a 'Saa - S [Software as~~ a ~~Service] web-malware monitoring and alerting solution for websites~~ of ~~any size and complexity. re creating a Word - Press design yourself~~, ~~the good news is there are tons of Word - Press themes to choose from. If you choose a blog~~ then ~~people will be able to post articles on your site and people will be able to make comments on your posts~~ (~~unless you turn comments off~~). ~~It does take time~~ to ~~come up having a website that gives you~~ the ~~much needed results hence~~ the ~~web developer must be ready to help you along~~ the ~~route~~. <br><br>~~Internet is not only the source for information, it is also one of the source for passive income~~. ~~I'm a large fan of using Word~~ - ~~Press to create pretty much any sort~~ of ~~web page. Just download it from~~ the ~~website~~ and ~~start using the same~~. ~~It is a fact that Smartphone using online customers do not waste much of their time in struggling with drop down menus~~. ~~Customers within a few seconds after visiting a site form their opinion about the site~~.		The estimator has the general form

			<math>

			\langle M(r)\rangle = {16\over 3\pi G}
			\langle R\left(2V_R^2 + V_T^2\right)\rangle.

			</math>

			The angle brackets denote averages over the ensemble of observed stars. <math> M(r) </math> is the mass contained within a distance <math>r</math> from the center of the stellar system; <math>R</math> is the projected distance of a star from the apparent center; <math>V_R</math> and <math>V_T</math> are the components of a star's velocity parallel to, and perpendicular to, the apparent radius vector; and <math>G</math> is the [[gravitational constant]].

			Like all estimators based on moments of the [[Jeans equations]], the Leonard–Merritt estimator requires an assumption about the relative distribution of mass and light. As a result, it is most useful when applied to stellar systems that have one of two properties:
			# All or almost all of the mass resides in a central object, or,
			# the mass is distributed in the same way as the observed stars.
			Case (1) applies to the nucleus of a galaxy containing a [[supermassive black hole]]. Case (2) applies to a stellar system composed entirely of luminous stars (i.e. no [[dark matter]] or [[black holes]]).

			In a cluster with constant mass-to-light ratio and total mass <math>M_T</math>, the Leonard–Merritt estimator becomes:

			<math>M_T = {32\over 3\pi G}
			\langle R \left(2V_R^2 + V_T^2\right)\rangle.</math>

			On the other hand, if all the mass is located in a central point of mass <math>M_0</math>, then:

			<math>M_0 = {16\over 3\pi G}
			\langle R\left(2V_R^2 + V_T^2\right)\rangle.</math>

			In its second form, the Leonard–Merritt estimator has been successfully used to measure the mass of the [[supermassive black hole]] at the center of the [[Milky Way]] [[galaxy]]<ref>{{Cite journal
			\| last1 = Schödel \| first1 = R
			\| last2 = Ott \| first2 = T \| first3 = R
			\| last4 = Eckart \| first4 = A
			\| last5 = Mouawad \| first5 = N
			\| last3 = Alexander \| first6 = T
			\| title = Stellar Dynamics in the Central Arcsecond of Our Galaxy
			\| journal = The Astrophysical Journal
			\| volume = 596
			\| issue = 2
			\| pages = 1015–1034
			\| date = 1 October 2003
			\| bibcode = 2003ApJ...596.1015S
			\| issn =\|arxiv = astro-ph/0306214 \|doi = 10.1086/378122 }}
			</ref>
			.<ref>{{Cite journal
			\| doi = 10.1051/0004-6361/200810922
			\| last1 = Schödel \| first1 = Rainer
			\| last2 = Merritt \| first2 = David
			\| author2-link = David Merritt
			\| last3 = Eckart \| first3 = Andreas
			\| title = The nuclear star cluster of the Milky Way: proper motions and mass
			\| journal = Astronomy and Astrophysics
			\| volume = 502
			\| issue = 1
			\| pages = 91–111
			\| date = 1 July 2009
			\| bibcode = 2009A&A...502...91S
			\| issn =\|arxiv = 0902.3892 }}
			</ref>

			==See also==
			* [[Virial theorem]]
			* [[Proper motion]]
			* [[Globular cluster]]

			==References==
			{{Reflist}}

			{{Use dmy dates\|date=September 2010}}

			{{DEFAULTSORT:Leonard-Merritt Mass Estimator}}
			[[Category:Astrometry]]
			[[Category:Celestial mechanics]]
			[[Category:Stellar astronomy]]
			[[Category:Supermassive black holes]]

en>GorillaWarfare: Reverted edits by 66.74.232.137 (talk) to last revision by Mild Bill Hiccup (HG)

2011-09-16T02:42:53Z

Reverted edits by 66.74.232.137 (talk) to last revision by Mild Bill Hiccup (HG)

New page

Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. This particular wordpress plugin is essential for not only having the capability where you improve your position, but to enhance your organic searches for your website. For those who have any inquiries concerning where by along with how you can employ [http://jrurl.at/wordpressbackupplugin140236 wordpress dropbox backup], you are able to email us from our web site. Generally, for my private income-making market websites, I will thoroughly research and discover the leading 10 most worthwhile niches to venture into. If you are a positive thinker businessman then today you have to put your business online. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. t need to use the back button or the URL to get to your home page. 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. Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. You or your web designer can customize it as per your specific needs. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. It is the convenient service through which professionals either improve the position or keep the ranking intact. Quttera - Quttera describes itself as a 'Saa - S [Software as a Service] web-malware monitoring and alerting solution for websites of any size and complexity. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. If you choose a blog then people will be able to post articles on your site and people will be able to make comments on your posts (unless you turn comments off). It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. Internet is not only the source for information, it is also one of the source for passive income. I'm a large fan of using Word - Press to create pretty much any sort of web page. Just download it from the website and start using the same. It is a fact that Smartphone using online customers do not waste much of their time in struggling with drop down menus. Customers within a few seconds after visiting a site form their opinion about the site.

Signature operator - Revision history

en>Rjwilmsi: /* References */Added 3 dois to journal cites using AWB (10104)

en>The Disambiguator: /* Hirzebruch Signature Theorem */ signature of a quadratic form

en>GorillaWarfare: Reverted edits by 66.74.232.137 (talk) to last revision by Mild Bill Hiccup (HG)