$3.$ Spiral Galaxies

$($a$)(20$ points$)$ Calculate the total Mass of each spiral galaxy.

$($b$)$ Calculate the distance to each Spiral Galaxy using:

i$.(10$ points$)$ Leavitt Law $($Cepheid Distance$)$

ii$.(10$ points$)$ Tully$-$Fisher Relation

$($c$)(10$ points$)$ Which galaxies, if any, could belong to the same galaxy cluster $(\backslash (\backslash$sigma$\_\{$V$\_\{$r$\}\}\backslash$sim $150\backslash )\backslash (\backslash$mathrm$\{$km$\}/\backslash$mathrm$\{$s$\}\backslash ))?$

$($d$)(10$ points$)$ Why does modern Tully$-$Fisher work use $\backslash ($ I $\backslash )$ of $\backslash ($ H $\backslash )-$band photometry, instead of the original $\backslash ($ B $\backslash )-$band in which the relation was first discovered?