Galaxy Formation and Evolution
EQUATIONS
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INFORMATION
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$$ \large M = \frac{Rv^2}{G} $$
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\(\\ \textbf{M} = mass \hspace{4 pt} interior \hspace{4 pt} to \hspace{4 pt} orbit \hspace{4 pt} (kg) \\ \textbf{R} = radius \hspace{4 pt} of \hspace{4 pt} (circular) \hspace{4 pt} orbit \hspace{4 pt} (m) \\ \textbf{v} = orbital \hspace{4 pt} speed \hspace{4 pt}(m \hspace{2 pt} s^{-1}) \\ \textbf {G} = gravitational \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{8 pt} (6.67384 x 10^{-11} \hspace{2 pt} m^3 \hspace{2 pt} kg^{-1} \hspace{2 pt} s^{-2})\) |
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$$ \large L \propto {v_{max}}^4 $$
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\( \textbf{L} = luminosity \hspace{4 pt} (W) \\ {v_{max}} = maximum \hspace{4 pt} rotation \hspace{4 pt} speed \\ \hspace{23 pt} of \hspace{4 pt} spiral \hspace{4 pt} galaxy \hspace{4 pt} (km \hspace{2 pt} s^{-1})\) |
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$$ \large M_B = -10.2 \hspace{2 pt} log \hspace{2 pt} (v_{max}) + 2.71 $$
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\( {M_B} = magnitude \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} B \hspace{4 pt} band \\ {v_{max}} = maximum \hspace{4 pt} rotation \hspace{4 pt} speed \\ \hspace{23 pt} of \hspace{4 pt} spiral \hspace{4 pt} galaxy \hspace{4 pt} (km \hspace{2 pt} s^{-1})\) |
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