# Galaxy rotation curve: Applicability of formula

1. Feb 2, 2007

### v0id

1. The problem statement, all variables and given/known data
Derive and plot the rotation curve of a galaxy with logarithmic potential:
$$\Phi(R, z) = \frac{v_0^2}{2}\ln{(R_c^2 + R^2 + q_{\phi}^{-2} z^2)}$$
where $$R_c =$$ 2 kpc, $$q_{\phi} =$$ const. and $$v_o = 200 kms^{-1}$$. Note that $$v_c$$ is defined for z = 0 only.

2. Relevant equations
$$v_c^2 = -2 \Phi(R, z)$$

3. The attempt at a solution
I'm just wondering if the above equation for circular velocity is applicable in this case. All signs point to yes, but I'm just worried about additional criteria that I may be overlooking.