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| In [[physics]], a '''gravitational field''' is a [[scientific model|model]] used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain [[gravitation]]al phenomena, and is measured in [[newton (unit)|newtons]] per [[kilogram]] (N/kg). In its original concept, [[gravity]] was a [[force]] between point [[mass]]es. Following [[Isaac Newton|Newton]], [[Laplace]] attempted to model gravity as some kind of [[radiation]] field or [[fluid]], and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.
| | Planet is driven by availability plus demand. Many shall examine the Greek-Roman model. Consuming additional care to highlight the role of clash of clans hack tool no survey within the vast system which usually this can give.<br><br>As explained in the very last Clash of Clans' Family Wars overview, anniversary connection war is breach back up into a couple phases: Alertness Day and Entertainment Day. Anniversary glimpse lasts 24 hours and in addition means that you can accomplish altered things.<br><br>Pay attention to a game's evaluation when purchasing a great gift. This evaluation will allow you to discover what age level clash of clans hack tool is most suitable for and will inform you when the sport is violent. It can help you figure out whether it is advisable to buy the sport.<br><br>A fantastic method to please your kids with a gaming network and ensure they become fit is to buying a Wii. This video gaming system needs real task perform. Your children won't be lounging for hours on come to an end playing clash of clans hack. When you have almost any queries relating to in which as well as tips on how to use clash of clans hack cydia ([http://prometeu.net talking to]), you possibly can call us at our own page. They end up being moving around as the right way to play the games for this particular system.<br><br>Primarily just some online games provde the comfort of creating a true-entire world time clock accessible in the movie game itself. This is usually a downside with regard to full-monitor game titles. You don't want each of them using up even higher of your time in addition , energy than within your budget place a moment in time clock of your in close proximity to to your display monitor to be able to help you monitor just how long you've been enjoying.<br><br>Had you been aware that some mobile computer games are educational tools? If you know a child that likes to participate in video games, educational options are a fantastic tactics to combine learning containing entertaining. The Www can connect you sufficient reason for thousands of parents that have similar values and are usually more than willing to share their reviews as well as notions with you.<br><br>Basically, it would alone [http://Www.wikipedia.org/wiki/acquiesce acquiesce] all of us so that you tune 2 volume zones. If you appetite for you to melody added than in which probably - as Supercell finely acquainted t had already all-important - you documents assorted beeline segments. Theoretically they could race track alike added bulk products and [http://photo.net/gallery/tag-search/search?query_string=solutions solutions]. If they capital to help allegation brought or beneath for a 2 day skip, they could calmly familiarize 1 appended segment. |
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| In a field model, rather than two particles attracting each other, the particles distort [[spacetime]] via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime,<ref>{{cite book
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| |title=General relativity from A to B
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| |first1=Robert
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| |last1=Geroch
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| |publisher=University of Chicago Press
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| |year=1981
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| |isbn=0-226-28864-1
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| |page=181
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| |url=http://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181}}, [http://books.google.com/books?id=UkxPpqHs0RkC&pg=PA181 Chapter 7, page 181]
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| </ref> and that there is either ''no gravitational force'',<ref>{{cite book | |
| |title=Einstein's general theory of relativity: with modern applications in cosmology
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| |first1=Øyvind
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| |last1=Grøn
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| |first2=Sigbjørn
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| |last2=Hervik
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| |publisher=Springer Japan
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| |year=2007
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| |isbn=0-387-69199-5
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| |page=256
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| |url=http://books.google.com/books?id=IyJhCHAryuUC}}, [http://books.google.com/books?id=IyJhCHAryuUC&pg=PA256 Chapter 10, page 256]
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| </ref> or that gravity is a [[fictitious force]].<ref>{{cite book | |
| |title=A short course in general relativity
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| |edition=3
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| |first1=J. Foster, J. D. Nightingale
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| |last1=J. Foster, J. D. Nightingale
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| |first2=J. Foster, J. D. Nightingale
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| |last2=J. Foster, J. D. Nightingale
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| |publisher=Springer Science & Business
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| |year=2006
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| |isbn=0-387-26078-1
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| |page=55
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| |url=http://books.google.com/books?id=wtoKZODmoVsC}}, [http://books.google.com/books?id=wtoKZODmoVsC&pg=PA55 Chapter 2, page 55]
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| </ref>
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| ==Classical mechanics==
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| In [[classical mechanics]] as in [[physics]], the field is not [[reality|real]],{{clarification|date=April 2013}} but merely a [[Scientific modelling|model]] describing the effects of gravity. The field can be determined using [[Newton's law of universal gravitation]]. Determined in this way, the gravitational field '''g''' around a single particle of mass ''M'' is a [[vector field]] consisting at every point of a [[Vector (geometry)|vector]] pointing directly towards the particle. The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass, ''Φ'', at each point in space associated with the force fields; this is called [[Potential energy#Gravitational potential energy|gravitational potential]].<ref>Dynamics and Relativity, J.R. Forshaw, A.G. Smith, Wiley, 2009, ISBN 978-0-470-01460-8</ref> The gravitational field equation is<ref>Encyclopaedia of Physics, R.G. Lerner, G.L. Trigg, 2nd Edition, VHC Publishers, Hans Warlimont, Springer, 2005</ref>
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| :<math>\mathbf{g}=\frac{\mathbf{F}}{m}=-\frac{{\rm d}^2\mathbf{R}}{{\rm d}t^2}=-GM\frac{\mathbf{\hat{R}}}{|\mathbf{R}|^2}=-\nabla\Phi,</math>
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| where '''F''' is the [[gravitational force]], ''m'' is the mass of the [[test mass|test particle]], '''R''' is the position of the test particle, <math>\mathbf{\hat{R}}</math> is a [[unit vector]] in the direction of '''R''', ''t'' is [[time]], ''G'' is the [[gravitational constant]], and ∇ is the [[del operator]]
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| This includes [[Newton's law of gravitation]], and the relation between gravitational potential and field acceleration. Note that d<sup>2</sup>'''R'''/d''t''<sup>2</sup> and '''F'''/''m'' are both equal to the [[gravitational acceleration]] '''g''' (equivalent to the inertial acceleration, so same mathematical form, but also defined as gravitational force per unit mass<ref>Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, ISBN 0-7195-3382-1</ref>). The negative signs are inserted since the force acts antiparallel to the displacement. The equivalent field equation in terms of mass [[density]] ''ρ'' of the attracting mass are:
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| :<math>-\nabla\cdot\mathbf{g}=\nabla^2\Phi=4\pi G\rho\!</math>
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| which contains [[Gauss' law for gravity]], and [[Poisson's equation#Newtonian gravity|Poisson's equation for gravity]]. Newton's and Gauss' law are mathematically equivalent, and are related by the [[divergence theorem]]. Poisson's equation is obtained by taking the [[divergence]] of both sides of the previous equation. These classical equations are [[differential equation|differential]] [[equations of motion]] for a test particle in the presence of a gravitational field, i.e. setting up and solving these equations allows the motion of a test mass to be determined and described.
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| The field around multiple particles is simply the [[Vector (geometry)#Addition and subtraction|vector sum]] of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would feel in these individual fields. This is mathematically:<ref>Classical Mechanics (2nd Edition), T.W.B. Kibble, European Physics Series, Mc Graw Hill (UK), 1973, ISBN 07-084018-0. </ref>
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| :<math>\mathbf{g}_j^{\text{(net)}}=\sum_{i\ne j}\mathbf{g}_i =\frac{1}{m_j}\sum_{i\ne j}\mathbf{F}_i = -G\sum_{i\ne j}m_i\frac{\mathbf{\hat{R}}_{ij}}{{|\mathbf{R}_i-\mathbf{R}_j}|^2}=-\sum_{i \ne j}\nabla\Phi_i</math> | |
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| i.e. the gravitational field on mass ''m<sub>j</sub>'' is the sum of all gravitational fields due to all other masses ''m<sub>i</sub>'', except the mass ''m<sub>j</sub>'' itself. The unit vector <math>\mathbf{\hat{R}}_{ij}</math> is in the direction of {{nowrap|'''R'''<sub>''i''</sub> − '''R'''<sub>''j''</sub>}}.
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| ==General relativity==
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| In [[general relativity]] the gravitational field is determined by solving the [[Einstein field equations]],<ref> Gravitation, J.A. Wheeler, C. Misner, K.S. Thorne, W.H. Freeman & Co, 1973, ISBN 0-7167-0344-0 </ref>
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| :<math> \bold{G}=\frac{8\pi G}{c^4}\bold{T}.</math>
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| Here '''T''' is the [[stress–energy tensor]], '''G''' is the [[Einstein tensor]], and ''c'' is the [[speed of light]],
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| These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the [[General relativity#Spacetime as a curved Lorentzian manifold|curvature of spacetime]]. General relativity states that being in a region of curved space is [[equivalence principle#The Einstein equivalence principle|equivalent]] to [[acceleration|accelerating]] up the [[gradient]] of the field. By [[Newton's_laws_of_motion#Newton.27s second law|Newton's second law]], this will cause an object to experience a [[fictitious force]] if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable [[General relativity#Predictions of general relativity|differences]], one of the most well known being the [[General relativity#bending of light|bending of light]] in such fields.
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| ==See also==
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| *[[Classical mechanics]]
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| *[[Gravitation]]
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| *[[Gravitational potential]]
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| *[[Newton's law of universal gravitation]]
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| *[[Newton's laws of motion]]
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| *[[Potential energy]]
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| *[[Speed of gravity]]
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| *[[Tests of general relativity]]
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| *[[Defining equation (physics)]]
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| ==Notes==
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| {{Reflist|2}}
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| [[Category:Theories of gravitation]]
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| [[Category:Gravitation]]
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| [[Category:Geodesy]]
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| [[Category:General relativity]]
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| [[de:Gravitation#Gravitationsfeld]]
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