- #1
AmenoParallax
- 11
- 0
Hello everybody!
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:
r=a(t)z
and a velocity potential \psi:
\frac{\partial r}{\partial t}=v_r=\frac{\partial \psi}{\partial r}
the authors rewrite the Poisson equation:
\frac{1}{z^2}\frac{\partial}{\partial z}(z^2\frac{\partial \psi}{\partial z})=4\pi G\rho a^2
but I think there should be the gravitational potential \phi instead of \psi, in fact performing a simple dimensional analysis shows that the left hand side is a square length over time, while the right hand side is a square length over square time, so I think the equation is wrong... Am I right? Did I miss something?
Help please!
Thanks!
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:
r=a(t)z
and a velocity potential \psi:
\frac{\partial r}{\partial t}=v_r=\frac{\partial \psi}{\partial r}
the authors rewrite the Poisson equation:
\frac{1}{z^2}\frac{\partial}{\partial z}(z^2\frac{\partial \psi}{\partial z})=4\pi G\rho a^2
but I think there should be the gravitational potential \phi instead of \psi, in fact performing a simple dimensional analysis shows that the left hand side is a square length over time, while the right hand side is a square length over square time, so I think the equation is wrong... Am I right? Did I miss something?
Help please!
Thanks!
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