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| [[File:World line.svg|thumb|Example of a light cone.]]
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| | <!-- PLEASE ADD CATEGORIES AND INTERWIKIS AT THE BOTTOM OF THIS PAGE --> |
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| In [[special relativity]], the '''Minkowski spacetime''' is a four-dimensional [[manifold]], created by [[Hermann Minkowski]]. It has four dimensions: three dimensions of space (x, y, z) and one dimension of time. Minkowski spacetime has a metric signature of (-+++) and is always flat. The convention in this article is to call Minkowski spacetime simply [[spacetime]].
| | === Usage === |
| | This template calculates surface gravity ''g'' of a spherical body of the mass M and radius R: |
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| However, Minkowski spacetime only applies in special relativity. [[General relativity]] used the notion of curved [[spacetime]] to describe the effects of gravity and accelerated motion.
| | <math>g=\frac{G*M}{R^2}</math>. |
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| ==Definition(s)==
| | G is the [[gravitational constant]]. The template should be used in the following way: |
| ===Mathematical===
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| Spacetime can be thought of as a four-dimensional coordinate system in which the axes are given by
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| <math>(x, y, z, ct)</math> | | <nowiki>{{Gr|M|R|PRE}}</nowiki>, |
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| They can also be denoted by
| | where M is body's mass in 10<sup>21</sup> kg, R is radius in km and PRE is the number of digits after decimal dot in the result (default is 3). The result is expressed in m/s<sup>2</sup>. |
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| <math>(x_1, x_2, x_3, x_4)</math>
| | Example (escape velocity of [[Titania (moon)|Titania]]): M=3.526{{Esp|21}} kg, R=788.9 km. |
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| Where <math>x_4</math> represents <math>ct</math>. The reason for measuring time in units of the speed of light times the time coordinate is so that the units for time are the same as the units for space. Spacetime has the differential for arc length given by
| | g={{Gr|3.526|788.9}} m/s<sup>2</sup>. |
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| <math>ds^2=-c^2dt^2+dx^2+dy^2+dz^2</math>
| | ===Related pages=== |
| | * {{tl|V2}} — computes escape velocity. |
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| This implies that spacetime has a metric tensor given by
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| | | <!-- CATEGORIES AND INTERWIKIS BELOW THIS LINE PLEASE --> |
| <math>g_{uv}=\begin{bmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{bmatrix}</math> | | [[Category:Astronomy templates]] |
| | | [[ar:قالب:GR]] |
| As before stated, spacetime is flat everywhere; to some extent, it can be thought of as a plane.
| | [[uk:Шаблон:Gr]] |
| | | </includeonly> |
| ===Simple===
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| Spacetime can be thought of as the "arena" in which all of the events in the universe take place. All that one needs to specify a point in spacetime is a certain time and a typical spatial orientation. It is hard (virtually impossible) to visualize four dimensions, but some analogy can be made, using the method below.
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| ==Spacetime diagrams==
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| [[File:Minkowski diagram - asymmetric.svg|thumb|In the theory of relativity both observers assign the event at A to different times.]]
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| Hermann Minkowski introduced a certain method for graphing coordinate systems in Minkowski spacetime. As seen to the right, different coordinate systems will disagree on an object's spatial orientation and/or position in time. As you can see from the diagram, there is only one spatial axis (the x-axis) and one time axis (the ct-axis). If need be, one can introduce an extra spatial dimension, (the y-axis); unfortunately, this is the limit to the number of dimensions: graphing in four dimensions is impossible. The rule for graphing in Minkowski spacetime goes as follows:
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| 1) The angle between the x-axis and the x'-axis is given by <math>tan \theta=\frac{v}{c}</math> where v is the velocity of the object
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| 2) The speed of light through spacetime ''always'' makes an angle of 45 degrees with either axis.
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| ==Spacetime in general relativity==
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| {{Main|Spacetime}}
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| In the general theory of relativity, [[Einstein]] used the equation
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| <math>R_{uv}-\frac{1}{2}g_{uv}R=8 \pi T_{uv}</math>
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| To allow for spacetime to actually curve; the resulting effects are those of gravity.
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| ==Related pages==
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| *[[Spacetime]]
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| *[[Special relativity]]
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| *[[General relativity]]
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| [[Category:Relativity]]
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Template:Mbox
Usage
This template calculates surface gravity g of a spherical body of the mass M and radius R:
[math]\displaystyle{ g=\frac{G*M}{R^2} }[/math].
G is the gravitational constant. The template should be used in the following way:
{{Gr|M|R|PRE}},
where M is body's mass in 1021 kg, R is radius in km and PRE is the number of digits after decimal dot in the result (default is 3). The result is expressed in m/s2.
Example (escape velocity of Titania): M=3.526Template:Esp kg, R=788.9 km.
g=Template:Gr m/s2.
Related pages
- {{V2}} — computes escape velocity.