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Why the gamma factor has been introduced? And how? I mean, as far I know the gamma factor is a construct of and for special relativity. I don't understand why the scalar product of two different velocity vectors in any metric is equal to the gamma factor. In other words, why the orbital velocity has
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I don't know what textbook was employed here, but this formula for the orbital speed doesn't make a whole lot of sense to me. When you compute the angular momentum for the circular orbit and minimize this angular momentum, you should get the ISCO radius of 3r_s, no? The formula v=(GM/(r-r_s))^(1/2)
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Late to the party, but the bold r is the position relative to the center of the massive body as a vector. The regular r is the magnitude of this vector, which is also the distance from the center, or the radius.
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I think you mean v = r d\phi/dt? The problem here is that dt doesn't actually measure time relative to the local observer. It's just an arbitrary coordinate. The actual time difference is
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been defined through the gamma factor and, for example in spherical coordinates, not simply as v(r) = r d\phi/dr? In that case I obtain a different result. What is the difference?
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The equation of motion became redundant, and I really don't see what mentionning the Virial theorem or the delta V brought to the topic. Headbomb 03:33, 17 May 2007 (UTC)
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doesn't appear to give the correct ISCO radius when you follow this method. You do get the correct ISCO radius if you use the standard formula v=(GM/r)^(1/2), however.
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I'm aware this is an old question, but it looks bad unanswered. Yes, there are differences and I attempted to describe how to calculate the speed in GR.
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Is the orbital velocity of circular orbits in general relativity exactly the same as in the
Newtonian case or are there any subtle differences?
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I don't know if I'm just retarded and I'm missing something complete obvious, but it seems to me that the speed is given by
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This is the first time I'm looking at these equations, can someone clarify what the two different R's are in the equation:
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And also, if we're talking about circular orbits, might as well give the real orbital energy conservation equation
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on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
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on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
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in all cases is radius. I do not understand why it is presented as it is, and further, the article
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1024:{\displaystyle \mathbf {a} =-{\frac {v^{2}}{r}}{\frac {\mathbf {r} }{r}}=-\omega ^{2}\mathbf {r} }
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It's as if someone went through this and purposely screwed things up. Anyway I cleaned things up.
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How do you calculate the angular momentum? The conserved quantity is
631:. I have no clue why it was equal to something other than 0 before.
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The definition of the standard gravitational parameter from here:
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929:(because of the issue with time mentioned above in my answer to
822:{\displaystyle {\frac {1}{\sqrt {g_{tt}}}}r{\frac {d\phi }{dt}}}
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standard gravitational parameter does not agree with link.
1141:{\displaystyle a\,={\frac {v^{2}}{r}}\,={\omega ^{2}}{r}}
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http://en.wikipedia.org/Standard_gravitational_parameter
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The energy is not zero. The formulas were correct.--
624:{\displaystyle {v^{2} \over {2}}-{\mu \over {r}}=0}
206:, a collaborative effort to improve the coverage of
101:, a collaborative effort to improve the coverage of
565:{\displaystyle T=2\pi {\sqrt {r^{3} \over {\mu }}}}
515:{\displaystyle T=\pi {\sqrt {2r^{3} \over {\mu }}}}
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460:{\displaystyle v={\sqrt {2\mu \over {r}}}}
305:{\displaystyle v={\sqrt {2\mu \over {r}}}}
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671:Orbital velocity in general relativity
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899:{\displaystyle r^{2}{\dot {\phi }}}
220:Knowledge (XXG):WikiProject Physics
38:It is of interest to the following
760:{\displaystyle {\sqrt {g_{tt}}}dt}
637:Headbomb 03:22, 17 May 2007 (UTC)
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379:{\displaystyle mv^{2} \over {2}}
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415:{\displaystyle -GMm \over {r}}
1:
1212:09:05, 19 February 2015 (UTC)
1173:13:54, 13 November 2020 (UTC)
943:12:41, 13 November 2020 (UTC)
861:19:15, 17 December 2019 (UTC)
839:12:41, 13 November 2020 (UTC)
829:is actually the same result.
721:18:54, 16 February 2019 (UTC)
695:23:34, 21 February 2012 (UTC)
680:12:57, 11 November 2007 (UTC)
386:and the potential energy is :
214:and see a list of open tasks.
109:and see a list of open tasks.
1242:Start-Class physics articles
1073:{\displaystyle \mathbf {r} }
906:, which isn't equivalent to
223:Template:WikiProject Physics
1158:19:43, 2 January 2015 (UTC)
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312:and not
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36:scale.
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42::
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