next up previous contents
Next: Free-fall Time Up: The Poisson Equation of Previous: The Poisson Equation of   Contents


Consider a spherically symmetric density distribution. Using the Poisson equation, obtain the potential ($\phi$) and the gravitational acceleration ($g$) for a density distribution shown below.

=\rho_0 &{\rm for} r<R \\
=0 & {\rm for} r\ge R
\end{array} \right.

Hint: The Poisson equation (2.11) for the spherically symmetric system is

\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial \phi}{\partial r}\right)=4\pi G \rho.

Kohji Tomisaka 2007-07-08