Changes between Version 13 and Version 14 of SelfGravityDevel


Ignore:
Timestamp:
03/05/12 13:44:29 (13 years ago)
Author:
Baowei Liu
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • SelfGravityDevel

    v13 v14  
    88The electric field generated by a point charge [[latex($Q$)]] is
    99
    10 [[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$)]]
     10 [[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$)]]
    1111
    1212On the other hand, the gravitational acceleration by a point mass of [[latex($M$)]] is
    1313
    14 [[latex($g=-G\frac{M}{r^{2}}$)]]  [[BR]]
     14 [[latex($g=-G\frac{M}{r^{2}}$)]]  [[BR]]
    1515
    1616The Poisson equation for electrostatic potential [[latex($\phi_{e}$)]] is
    1717
    18 [[latex($\nabla^{2}\phi=-\frac{\rho}{\epsilon_{0}}$)]]
     18 [[latex($\nabla^{2}\phi=-\frac{\rho}{\epsilon_{0}}$)]]
    1919
    2020Analytically  we can get the Poisson equation for the gravity
    2121
    22 [[latex($\nabla^{2}\phi=4\pi G\rho$)]]
     22 [[latex($\nabla^{2}\phi=4\pi G\rho$)]]
    2323
    2424where [[latex($\rho$)]] is the mass density. This equation describes how the potential [[latex($\phi$)]] is determined by the mass density distribution.
     
    2626For example, consider the uniform density distribution
    2727
     28{{{
     29#!latex
     30\begin{equation}\label{eq:uniDensity}
     31\rho=\begin{cases} \rho_{0}, &r<R \\
     32                   0, & r\ge R
     33     \end{cases}
     34\end{equation}
     35}}}
    2836
    2937== Implementation ==