Good morning,(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Doubt about the polar equation of a Kepler orbit

**Physics Forums | Science Articles, Homework Help, Discussion**