Changes between Version 16 and Version 17 of SelfGravityDevel

Timestamp:

03/05/12 15:21:02 (13 years ago)

Author:

Baowei Liu

Comment:

—

SelfGravityDevel

@@ -34 +34 @@
 \end{equation}
 }}}
-Use spherical coordinates, the Poisson equation for the density distribution [[latex(\ref{eq:uniDensity})]] can be written as
+Use spherical coordinates, the Poisson equation for the density distribution Equation (1) can be written as
 
 {{{
@@ -46 +46 @@
 {{{
 #!latex
-\begin{equation}\label{eq:poissonSphCoord1}
+\begin{equation}\label{eq:poissonSphCoord1}\tag{3}
 \frac{\partial ^{2}\phi }{\partial r^{2}}+\frac{2}{r}\frac{\partial\phi}{\partial r}=4\pi G\rho
 \end{equation}
 
 }}}
+
+Solving Equation (3) with the density Equation (2), we obtain the solution for the potential for the uniform density sphere:
+{{{
+#!latex
+\begin{equation}\label{eq:solUniSphere}\tag{4}
+\phi(r)=\begin{cases} -\frac{4\pi}{3} G\rho \frac{R^{3}}{r} & r>R\\
+         -\frac{2\pi G\rho}{3}\left[R^{2}-r^{2}\right]-\frac{4\pi}{3}G\rho R^{2} &r\ge R
+        \end{cases} 
+\end{equation}
+}}}
+
 == Implementation ==