$1.$Two identical planets, P$1$ and P$2,$ orbit a star in concentric circular orbits in the star's equatorial plane.

P$1$ has an orbit of radius a$1=20$ AU; and P$2$ has an orbit of radius a$2=30$ AU and period T$2=30$ yr$.$ What is

the period T$1?$

A$)10\mathrm{.}45$ yrs

B$)15\mathrm{.}16$ yrs

C$)12\mathrm{.}92$ yrs

D$)5\mathrm{.}57$ yrs

E$)16\mathrm{.}33$yrs