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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| courses:ast301:1 [2024/02/18 02:03] – [7. Instability and pulsation] asad | courses:ast301:1 [2024/03/07 01:12] (current) – [4.2 Dynamical timescale] asad | ||
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| where we assume $N(N-1)\approx N^2$ because $N$ is large. The factor $N(N-1)/2$ comes from the **combination** of two items from a total of $N$ items: $_NC_2=N!/ | where we assume $N(N-1)\approx N^2$ because $N$ is large. The factor $N(N-1)/2$ comes from the **combination** of two items from a total of $N$ items: $_NC_2=N!/ | ||
| - | $$ M \langle v_i^2 \rangle_{av} - G\frac{M^2}{2} \langle r_{ij}^{-1} \rangle_{av} $$ | + | $$ M \langle v_i^2 \rangle_{av} - G\frac{M^2}{2} \langle r_{ij}^{-1} \rangle_{av} |
| and hence the **virial mass** of a cluster | and hence the **virial mass** of a cluster | ||
| Line 153: | Line 153: | ||
| The time needed to fall by a distance $R$ is found from the constant-force expression $s=at^2/2$, i. e. the dynamical timescale | The time needed to fall by a distance $R$ is found from the constant-force expression $s=at^2/2$, i. e. the dynamical timescale | ||
| - | $$ \tau_{in} = \sqrt{\frac{R}{a}} = \sqrt{R^3}{GM} $$ | + | $$ \tau_{in} = \sqrt{\frac{R}{a}} = \sqrt{\frac{R^3}{GM}} $$ |
| where density $\rho=M/ | where density $\rho=M/ | ||
courses/ast301/1.1708246988.txt.gz · Last modified: 2024/02/18 02:03 by asad