The two satellites orbit around the same planet, so we can use Kepler's third law, which states that the ratio between the cube of the radius of the orbit and the orbital period is constant for the two satellites:
[tex] \frac{r_1^3}{T_1^2}= \frac{r_2^3}{T_2^2} [/tex]
where
[tex]r_1[/tex] is the orbital radius of the first satellite
[tex]r_2[/tex] is the orbital radius of the second satellite
[tex]T_1[/tex] is the orbital period of the first satellite
[tex]T_2[/tex] is the orbital period of the second satellite
If we use the data of the problem and we re-arrange the equation, we can calculate the orbital period of the second satellite:
[tex]T_2 = \sqrt{T_1^2 ( \frac{r_2}{r_1} )^3} = \sqrt{(18.0 h)^2 ( \frac{3\cdot 10^7 m}{2 \cdot 10^7 m} )^3} = 33.1 h[/tex]
