Two planets are rotating around a star in elliptical orbits. The orbit of planet $1$ has semi$-$major axis $a_1=0\mathrm{.}27$ astronomical units $($AU$).$ Its period is $T_1=2\mathrm{.}7$ years. The orbit of planet $2$ has semi$-$major axis $a_2=0\mathrm{.}78AU.$

Part $($a$)$

Express the period of planet $2,T_2,$ in terms of $T_1,a_1$ and $a_2.$