Changes between Version 13 and Version 14 of SelfGravityDevel
- Timestamp:
- 03/05/12 13:44:29 (13 years ago)
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SelfGravityDevel
v13 v14 8 8 The electric field generated by a point charge [[latex($Q$)]] is 9 9 10 [[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$)]]10 [[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$)]] 11 11 12 12 On the other hand, the gravitational acceleration by a point mass of [[latex($M$)]] is 13 13 14 [[latex($g=-G\frac{M}{r^{2}}$)]] [[BR]]14 [[latex($g=-G\frac{M}{r^{2}}$)]] [[BR]] 15 15 16 16 The Poisson equation for electrostatic potential [[latex($\phi_{e}$)]] is 17 17 18 [[latex($\nabla^{2}\phi=-\frac{\rho}{\epsilon_{0}}$)]]18 [[latex($\nabla^{2}\phi=-\frac{\rho}{\epsilon_{0}}$)]] 19 19 20 20 Analytically we can get the Poisson equation for the gravity 21 21 22 [[latex($\nabla^{2}\phi=4\pi G\rho$)]]22 [[latex($\nabla^{2}\phi=4\pi G\rho$)]] 23 23 24 24 where [[latex($\rho$)]] is the mass density. This equation describes how the potential [[latex($\phi$)]] is determined by the mass density distribution. … … 26 26 For example, consider the uniform density distribution 27 27 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 }}} 28 36 29 37 == Implementation ==