# Talk:Circular orbit

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## WTF

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 ${\displaystyle v={\sqrt {2\mu \over {r}}}}$ and not ${\displaystyle v={\sqrt {\mu \over {r}}}}$. I mean, the kinetic energy is ${\displaystyle mv^{2} \over {2}}$ and the potential energy is :${\displaystyle -GMm \over {r}}$. On the orbit, total energy is minimized (E=0).

Therefore :${\displaystyle v={\sqrt {2\mu \over {r}}}}$ .

This error carries on to the period. ${\displaystyle T=\pi {\sqrt {2r^{3} \over {\mu }}}}$ not ${\displaystyle T=2\pi {\sqrt {r^{3} \over {\mu }}}}$

And also, if we're talking about circular orbits, might as well give the real orbital energy conservation equation ${\displaystyle {v^{2} \over {2}}-{\mu \over {r}}=0}$ . I have no clue why it was equal to something other than 0 before.

It's as if someone went through this and purposely screwed things up. Anyway I cleaned things up.

Headbomb 03:22, 17 May 2007 (UTC)

The energy is not zero. The formulas were correct.--Patrick 12:53, 22 June 2007 (UTC)

## Equation of Motion, delta V and Virial theorem

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)

I restored it.--Patrick 12:58, 22 June 2007 (UTC)

## Orbital velocity in general relativity

Is the orbital velocity of circular orbits in general relativity exactly the same as in the Newtonian case or are there any subtle differences? Agge1000 12:57, 11 November 2007 (UTC)

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. Xavath (talk) 23:34, 21 February 2012 (UTC)

## More details please

This is the first time I'm looking at these equations, can someone clarify what the two different R's are in the equation: ${\displaystyle \mathbf {a} =-{\frac {v^{2}}{r}}{\frac {\mathbf {r} }{r}}=-\omega ^{2}\mathbf {r} }$ — Preceding unsigned comment added by Nhilton (talkcontribs) 20:07, 27 September 2012 (UTC)

As far as I can tell, ${\displaystyle \mathbf {r} }$ in all cases is radius. I do not understand why it is presented as it is, and further, the article Circular_motion#Uniform_circular_motion presents the formula as ${\displaystyle a\,={\frac {v^{2}}{r}}\,={\omega ^{2}}{r}}$, and for the sake of clarity, I am going to replace the former with the later. T.Randall.Scales (talk) 19:43, 2 January 2015 (UTC)

## standard gravitational parameter does not agree with link.

The definition of the standard gravitational parameter from here:

http://en.wikipedia.org/wiki/Standard_gravitational_parameter


does not agree with the text from here:

http://en.wikipedia.org/wiki/Circular_orbit#Velocity  — Preceding unsigned comment added by 98.125.78.211 (talk) 09:05, 19 February 2015 (UTC)