Changes between Version 14 and Version 15 of u/BonnorEbert
- Timestamp:
- 10/03/12 15:18:44 (12 years ago)
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u/BonnorEbert
v14 v15 47 47 48 48 {{{#!latex 49 $ \frac {1}{r^2} \frac {d}{dr}~(r^2 \frac{d\phi_g}{dr}) ~= ~ 4\pi G \rho_c e^{{(-\phi_g/C_s^2)}}~ $\qquad--spherical coordinates49 \frac {1}{r^2} \frac {d}{dr}~(r^2 \frac{d\phi_g}{dr}) ~= ~ 4\pi G \rho_c e^{{(-\phi_g/C_s^2)}}~ \qquad--spherical coordinates 50 50 51 51 }}} … … 53 53 By making the following variable substitutions, 54 54 {{{#!latex d 55 $\psi ~= ~ \frac{\phi_g}{C_s^2}$ 55 \psi ~= ~ \frac{\phi_g}{C_s^2} 56 }}} 56 57 57 $\xi ~=~ (\frac{4 \pi G \rho_c}{C_s^2})^\frac{1}{2}~r$ 58 59 {{{#!latex 60 \xi ~=~ (\frac{4 \pi G \rho_c}{C_s^2})^\frac{1}{2}~r 58 61 }}} 59 62 … … 61 64 62 65 {{{#!latex 63 $ \frac{1}{\xi^2}\frac{d}{d\xi}(\xi^2\frac{d\psi}{d\xi}) = e^{-\psi} $\qquad(Lane-Emden Equation)(5)66 \frac{1}{\xi^2}\frac{d}{d\xi}(\xi^2\frac{d\psi}{d\xi}) = e^{-\psi} \qquad(Lane-Emden Equation)(5) 64 67 65 68 }}} … … 91 94 92 95 {{{#!latex 93 $P_i = P_o \Rightarrow $ 96 P_i = P_o \Rightarrow 97 }}} 94 98 95 $P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o $ 99 100 {{{#!latex 101 P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o 96 102 }}} 97 103
