Two planets P$1$ and P$2$ orbit around a star S in circular orbits with speeds v$1=44\mathrm{.}8$ km$/$s$,$ and v$2=59\mathrm{.}6$ km$/$s respectively.$($a$)$ If the period of the first planet P$1$ is $7\mathrm{.}10$ years, what is the mass of the star it orbits around? kg$($b$)$ Determine the orbital period of P$2.$