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I have a doubt about the differentiation of the polar equation of an orbit:

[tex]r=\frac{p}{1+e\cos\nu}[/tex]

It represents the relative position of a planet with respect to the central body.

Here, p is the parameter, e is the eccentricity and r is the radius of the planet measured from the focus (where the central body is located).

If I differentiate it, I obtain the following result:

[tex]\dot{r}=\frac{\mathrm{d} }{\mathrm{d} t}\left ( \frac{p}{1+e\cos\nu} \right )[/tex]

[tex]p \left(\frac{e\dot{\nu}\sin \nu}{(1+e\cos\nu)^2}\right) = \frac{h^2}{\mu} \left(\frac{e\dot{\nu}\sin \nu}{(1+e\cos\nu)^2}\right)[/tex]

However, according to the text I'm reading, I should be getting this:

[tex]\dot{r}=\sqrt{\frac{\mu}{p}}e\sin\nu[/tex]

I'm not sure on how I could get this result.

Any ideas?

Thank you in advance.

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# Doubt about the polar equation of a Kepler orbit

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