Answer:
Krypton
Explanation:
Kepler's third law states that the cube of the semimajor axis of the orbit of a planet is proportional to the square of the orbital period. Mathematically, we can write:
[tex]\frac{r^3}{T^2}=const.[/tex]
or
[tex]r^3 \propto T^2[/tex] (1)
where
r is the semimajor axis of the orbit
T is the orbital period
In this problem, we are told that Planet xoron has an orbital period twice as long as planet kripton: given relationship (1), this means that Planet xoron will also have a longer orbital radius (so, planet krypton has a shorter orbital radius).
Mathematically, we can write the equation as
[tex]\frac{r_x^3}{T_x^2}=\frac{r_k^3}{T_k^2}[/tex]
where 'x' stands for Xoron and 'k' stands for Krypton. Since
[tex]T_x = 2 T_k[/tex]
The ratio between the radii will be
[tex]\frac{r_x^3}{r_k^3}=\frac{T_x^3}{T_k^2}=\frac{(2T_k)^2}{T_k^2}=4[/tex]
So, Krypton will have a shorter average orbital radius.
