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I am using in my studies this beautiful book by Kippenhahn & Weigert, "Stellar Structure and Evolution", but I have some problems about collapsing polytropes (chapter 19.11)...

After defining dimensionless lenght-scale z by:

[itex]r=a(t)z[/itex]

and a velocity potential [itex]\psi[/itex]:

[itex]\frac{\partial r}{\partial t}=v_r=\frac{\partial \psi}{\partial r}[/itex]

the authors rewrite the Poisson equation:

[itex]\frac{1}{z^2}\frac{\partial}{\partial z}(z^2\frac{\partial \psi}{\partial z})=4\pi G\rho a^2[/itex]

but I think there should be the gravitational potential [itex]\phi[/itex] instead of [itex]\psi[/itex], in fact performing a simple dimensional analysis shows that the left hand side is a square lenght over time, while the right hand side is a square lenght over square time, so I think the equation is wrong... Am I right? Did I miss something?

Help please!

Thanks!

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# Poisson and continuity equation for collapsing polytropes

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