Two planets

P$1$

and

P$2$

orbit around a star S in circular orbits with speeds

v$1=45\mathrm{.}6$ km$/$s$,$

and

v$2=59\mathrm{.}8$ km$/$s

respectively.

$($a$)$ If the period of the first planet

P$1$

is $7\mathrm{.}80$ years, what is the mass of the star it orbits around?

$($b$)$ Determine the orbital period of

P$2.$