128.12.252.5: Changed link for "envelope"

2014-12-02T06:46:50Z

Changed link for "envelope"

en>Sroc: parentheses are not bolded

2013-12-20T05:59:02Z

parentheses are not bolded

← Older revision		Revision as of 07:59, 20 December 2013
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	~~I like Stamp collecting. <br>I try to learn Swedish in my spare time. <br>xunjie 豪華なである花のアップリケのバラ、~~		{{For\|the computer programming term\|spaghetti code}}
	~~ジャガー·ルクルトブルーエナメルによって名誉を与えられたプロトタイプの時計チャリティーオークション（ロット番号3064を委託し、~~
	より多くの価格設定に対する消費者の需要を満たすために、 [http://avtospetstrans.by/Controls/catalog/new/shop/goros.html ��`�� ] その後徐々に寒さになるが、
	~~東山梅はあなたに報酬を与えるようになった、~~
	このスタイルはナイトガウン、 [http://athenavineyards.com/media/duvetica.php �ޥå��ީ`�� `��] 一緒に1000年モデルワンスタイルをもたらします。
	~~取引のセキュリティに、~~
	新しい古典的な風合いの解釈と白の潮での今シーズンを調整したとして、[http://athenavineyards.com/media/duvetica.php �ޥå��ީ`�� `��] レディBoerは人材を誘致するための企業のための国際業務とグローバル市場とのマルチブランドのファッション事業者であるプライムパワー貯蓄プランは、
	~~①ベンの原稿が他のメディアに転載されているこのような原稿が私たちの見解を示すものではありませより多くの情報の普及は、~~
	~~いくつかの女性が少ない魅力的な気質。~~
	AQSIQ「衣類の繊維製品の自社ブランドの構築を加速するガイ意見書」（消費者連合の省[2009]第481）省が提案し実装するには業界団体に頼って、 [http://www.almondpress.org/hot/fashion/chanel.html ��ͥ�<br><br>å� 2014]

	~~My blog post~~ ... [http://~~www~~.~~swisscrossbow~~.ch/~~html~~/jp/~~good~~/~~gaga~~.~~html ガガミラノ時計メンズ新作~~]		[[File:Field tidal.png\|thumb\|260px\|[[Tidal forces]] acting on a spherical body in a non-homogeneous gravitational field. The effect originates from a source to the right (''or'' to the left) of the diagram. Longer arrows indicate stronger forces.]]

			In [[astrophysics]], '''spaghettification''' (sometimes referred to as the '''noodle effect'''<ref>{{citation
			\|title=Cosmic catastrophes: exploding stars, black holes, and mapping the universe, 2nd edition
			\|first1=J. Craig
			\|last1=Wheeler
			\|publisher=Cambridge University Press
			\|year=2007
			\|isbn=978-0-521-85714-7
			\|page=182
			\|url=http://books.google.be/books?id=j1ej8d0F8jAC}}
			</ref>) is the vertical stretching and horizontal compression of objects into long thin shapes (rather like [[spaghetti]]) in a very strong non-homogeneous gravitational field, and is caused by extreme [[tidal forces]]. In the most extreme cases, near [[black hole]]s, the stretching is so powerful that no object can withstand it, no matter how strong its components. Within a small region the horizontal compression balances the vertical stretching so that small objects being spaghettified experience no net change in volume.

			In his book ''[[A Brief History of Time]]'' (1988), [[Stephen Hawking]] describes the flight of a fictional [[astronaut]] who, passing within a black hole's [[event horizon]], is "stretched like spaghetti" by the gravitational gradient (difference in strength) from head to toe. However, the term "spaghettification" was established well before this; [[Nigel Calder]], for example, uses it in his book ''[[The Key to the Universe\|The Key to the Universe: A Report on the New Physics]]'' (Viking Press, 1977), a companion to a one-off [[BBC]] TV documentary: ''The Key to the Universe''.

			==A simple example==
			[[File:Spaghettification.gif\|center]]
			The four objects follow the lines of the gravitoelectric field,<ref>Thorne, Kip S. ♦ [http://einstein.stanford.edu/content/sci_papers/papers/nz-Thorne_101.pdf#page=3&view=FitV Gravitomagnetism, Jets in Quasars, and the Stanford Gyroscope Experiment] From the book "Near Zero: New Frontiers of Physics" (eds. J. D. Fairbank, B. S. Deaver, Jr., C. W. F. Everitt, P. F. Michelson), W. H. Freeman and Company, New York, 1988, pp. 3, 4 (575, 576) ♦ ''"From our electrodynamical experience we can infer immediately that any rotating spherical body (e.g., the sun or the earth) will be surrounded by a radial gravitoelectric (Newtonian) field '''''g''''' and a dipolar gravitomagnetic field '''''H'''''. The gravitoelectric monopole moment is the body's mass M; the gravitomagnetic dipole moment is its spin angular momentum S."''</ref> directed towards the celestial body's centre. In accordance with the [[inverse-square law]], the lowest of the four objects experiences the biggest gravitational acceleration, so that the whole formation becomes stretched into a filament. Now imagine that the green blobs in the diagram are parts of a larger object. A rigid object will resist distortion—internal elastic forces develop as the body distorts to balance the tidal forces, so attaining mechanical equilibrium. If the tidal forces are too large, the body may yield and flow plastically before the tidal forces can be balanced, or fracture.

			==Examples of weak and strong tidal forces==
			In the gravity field due to a point mass or spherical mass, for a uniform rope or rod oriented in the direction of gravity, the [[tensile force]] at the center is found by integration of the tidal force (see [[Tidal_force#Mathematical_treatment\|magnitude of tidal force]]) from the center to one of the ends. This gives <math> \frac{\mu l m}{4 r^3}</math>, where <math>\mu</math> is the [[standard gravitational parameter]] of the massive body, ''l'' is the length of the rope or rod, ''m'' is its mass, and ''r'' is the distance to the massive body. For non-uniform objects the tensile force is smaller if more mass is near the center, and up to twice as large if more mass is at the ends. In addition, there is a horizontal compressive force toward the center.

			For massive bodies with a surface, the tensile force is largest near the surface, and this maximum value is only dependent on the object and the average density of the massive body (as long as the object is small relative to the massive body). For example, for a rope with a mass of 1 kg and a length of 1 m, and a massive body with the average density of the Earth, this maximum tensile force due to the tidal force is only 0.4 μN.

			Due to the high density, the tidal force near the surface of a [[white dwarf]] is much stronger, causing in the example a maximum tensile force of up to 0.24 N. Near a [[neutron star]], the tidal forces are again much stronger: if the rope has a tensile strength of 10,000 N and falls vertically to a neutron star of 2.1 solar masses, setting aside that it would melt, it would break at a distance of 190 km from the center, well above the surface (the typical radius is about 12 km).<ref>An 8 m piece of the same type of rope, hence with a mass of 8 kg, would in each case break already at a distance that is 4 times as high.</ref>

			While in the previous case objects would actually be destroyed and people killed by the heat, not the tidal forces, near a [[black hole]] (assuming that there is no nearby matter), objects would actually be destroyed and people killed by the tidal forces, because there is no radiation. Moreover, a black hole has no surface to stop a fall. As an object falls into a black hole, the tidal forces increase to infinity, so nothing can resist them. Thus, the infalling object is stretched into a thin strip of matter. Close to the [[Gravitational singularity\|singularity]], the tidal forces even tear apart molecules.

			==Inside or outside the event horizon==
			The point at which tidal forces destroy an object or kill a person will depend on the black hole's size. For a [[supermassive black hole]], such as those found at a galaxy's center, this point lies within the [[event horizon]], so an astronaut may cross the event horizon without noticing any squashing and pulling, although it remains only a matter of time, as once inside an event horizon, falling towards the center is inevitable. For small black holes whose [[Schwarzschild radius]] is much closer to the singularity, the tidal forces would kill even before the astronaut reaches the event horizon.<ref>{{cite book
			\|title=General relativity: an introduction for physicists
			\|first1=Michael Paul
			\|last1=Hobson
			\|first2=George
			\|last2=Efstathiou
			\|first3=Anthony N.
			\|last3=Lasenby
			\|publisher=Cambridge University Press
			\|year=2006
			\|isbn=0-521-82951-8
			\|page=265
			\|url=http://books.google.com/books?id=5dryXCWR7EIC&pg=PA265}}, [http://books.google.com/books?id=5dryXCWR7EIC&pg=PA265 Chapter 11, p. 265]
			</ref><ref>{{cite book
			\|title=Astronomy: a physical perspective
			\|edition=2
			\|first1=Marc Leslie
			\|last1=Kutner
			\|publisher=Cambridge University Press
			\|year=2003
			\|isbn=0-521-52927-1
			\|page=150
			\|url=http://books.google.com/books?id=2QVmiMW0O0MC}}, [http://books.google.com/books?id=2QVmiMW0O0MC&pg=PA150 Chapter 8, p. 150]
			</ref> For example, for a black hole of 10 Sun masses<ref>The smallest black hole that can be formed by natural processes at the current stage of the universe has over twice the mass of the Sun.</ref> and the above-mentioned rope at 1000 km distance, the tensile force halfway along the rope is 325 N. It will break at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a black hole of 10,000 Sun masses it will break at a distance of 3200 km, well inside the Schwarzschild radius of 30,000 km.

			==References==
			{{reflist}}
			* {{cite book \| author=Melia, Fulvio \| title= The Black Hole at the Center of Our Galaxy \| publisher=Princeton University Press \| year=2003 \| id=ISBN 0-691-09505-1}}
			* {{cite book \| author=Hawking, Stephen \| title= A Brief History of Time \| publisher=Bantam Books \| year=1988 \| id=ISBN 0-553-38016-8}}
			*[http://www.youtube.com/watch?v=h1iJXOUMJpg Neil DeGrasse Tyson: Death by Black Hole (clear explanation of the term)]

			{{Black holes}}

			[[Category:Black holes]]
			[[Category:Effects of gravitation]]
			[[Category:Fictional astronauts]]
			[[Category:Metaphors referring to food and drink]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-05T23:03:14Z

ISBNs (Build KC)

New page

I like Stamp collecting. <br>I try to learn Swedish in my spare time. <br>xunjie 豪華なである花のアップリケのバラ、
ジャガー·ルクルトブルーエナメルによって名誉を与えられたプロトタイプの時計チャリティーオークション（ロット番号3064を委託し、
より多くの価格設定に対する消費者の需要を満たすために、 [http://avtospetstrans.by/Controls/catalog/new/shop/goros.html ��`�� ] その後徐々に寒さになるが、
東山梅はあなたに報酬を与えるようになった、
このスタイルはナイトガウン、 [http://athenavineyards.com/media/duvetica.php �ޥå��ީ`�� `��] 一緒に1000年モデルワンスタイルをもたらします。
取引のセキュリティに、
新しい古典的な風合いの解釈と白の潮での今シーズンを調整したとして、[http://athenavineyards.com/media/duvetica.php �ޥå��ީ`�� `��] レディBoerは人材を誘致するための企業のための国際業務とグローバル市場とのマルチブランドのファッション事業者であるプライムパワー貯蓄プランは、
①ベンの原稿が他のメディアに転載されているこのような原稿が私たちの見解を示すものではありませより多くの情報の普及は、
いくつかの女性が少ない魅力的な気質。
AQSIQ「衣類の繊維製品の自社ブランドの構築を加速するガイ意見書」（消費者連合の省[2009]第481）省が提案し実装するには業界団体に頼って、 [http://www.almondpress.org/hot/fashion/chanel.html ��ͥ�<br><br>å� 2014]

My blog post ... [http://www.swisscrossbow.ch/html/jp/good/gaga.html ガガミラノ時計メンズ新作]

Slowly varying envelope approximation - Revision history

128.12.252.5: Changed link for "envelope"

en>Sroc: parentheses are not bolded

en>Helpful Pixie Bot: ISBNs (Build KC)