Changes between Version 11 and Version 12 of SelfGravityDevel

Timestamp:

03/05/12 10:53:36 (13 years ago)

Author:

Baowei Liu

Comment:

—

SelfGravityDevel

@@ -4 +4 @@
 
 == Physics ==
+=== Poisson Equation of Self Gravity ===
 
+The electric field generated by a point charge [[latex($Q$)]] is
 
+[[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$)]]
+
+On the other hand, the gravitational acceleration by a point mass of [[latex($M$)]] is
+
+[[latex($g=-G\frac{M}{r^{2}}$)]]  [[BR]]
+
+The Poisson equation for electrostatic potential [[latex($\phi_{e}$)]] is 
+
+[[latex($\nabla^{2}\phi=-\frac{\rho}{\epsilon_{0}}$)]]
+
+Analytically  we can get the Poisson equation for the gravity
+
+[[latex($\nabla^{2}\phi=4\pi G\rho$)]]
+
+where [[latex($\rho$)]] is the mass density. This equation describes how the potential [[latex($\phi$)]] is determined by the mass density distribution.
+
+For example, consider the uniform density distribution
+
+%%(latexrender) 
+[tex]
+\rho=\begin{cases} \rho_{0}, &r<R \\
+                   0, & r\ge R 
+     \end{cases}$)]]
+[\tex]
 
 == Implementation ==