Problem #$7[10$ marks$]$ Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be $43\mathrm{.}3$ km$/$s and $58\mathrm{.}6$ km$/$s$.$ The slower planet$$s orbital period is $7\mathrm{.}60$ years. $($a$)$ What is the mass of the star? $($b$)$ What is the orbital period of the faster planet, in years?