Changes between Version 59 and Version 60 of SelfGravityDevel
- Timestamp:
- 02/05/13 13:20:33 (12 years ago)
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SelfGravityDevel
v59 v60 28 28 #!latex 29 29 \begin{equation}\label{eq:uniDensity}\tag{1} 30 \rho= \begin{cases} \rho_ 0 &r < R \\31 0 & r\ge R30 \rho= \begin{cases} \rho_{0}, &r < R \\ 31 0, & r\ge R 32 32 \end{cases} 33 33 \end{equation} 34 34 }}} 35 35 36 {{{37 #!latex38 \begin{equation}\label{eq:uniDensity2}\tag{11}39 \rho= \begin{cases} \rho_0 & r < R \\40 0 & r \ge R41 \end{cases}42 \end{equation}43 }}}44 45 46 {{{47 #!latex48 \begin{equation}\label{eq:uniDensity3}\tag{12}49 \rho=\begin{cases} \rho_0 & r < R \\50 0 & r \ge R51 \end{cases}52 \end{equation}53 }}}54 55 {{{56 #!latex57 \begin{equation}\label{eq:uniDensity4}\tag{13}58 \rho=\begin{cases} \rho_0 & r < R \\59 0 & r \ge R60 \end{cases}61 \end{equation}62 }}}63 36 64 37 Use spherical coordinates, the Poisson equation for the density distribution Equation (1) can be written as … … 84 57 #!latex 85 58 \begin{equation}\label{eq:solUniSphere}\tag{4} 86 \phi(r)=\begin{cases} -\frac{4 59 \phi(r)=\begin{cases} -\frac{4\pi}{3} G\rho \frac{R^{3}}{r} & r>R\\ 87 60 -\frac{2\pi G\rho}{3}\left[R^{2}-r^{2}\right]-\frac{4\pi}{3}G\rho R^{2} &r\ge R 88 61 \end{cases}