Answer
(a) $2.21\times 10^{30}Kg=1.1solar masses$
(b) $151\frac{Km}{s}$
Work Step by Step
(a) We know that
$T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm}}$
$\implies Gm=(\frac{2\pi r^{\frac{3}{2}}}{T})^2$
This can be rearranged as:
$m=\frac{(\frac{2\pi r^{\frac{3}{2}}}{T})^2}{G}$
We plug in the known values to obtain:
$m=\frac{(\frac{2\pi(6.43\times10^9 )^{\frac{3}{2}}}{2.67\times 10^5})^2}{6.67\times 10^{-11}}=2.21\times 10^{30}Kg=1.1solar masses$
(b) We know that
$v=\frac{2\pi r}{T}$
We plug in the known values to obtain:
$v=\frac{2\pi(6.43\times 10^9)}{2.67\times 10^5}$
$v=1.51\times 10^5\frac{m}{s}=151\frac{Km}{s}$
