Answer:
The planet and the Earth has the same orbital period.
Explanation:
The period can be determined by means of Kepler's third law:
[tex]T^{2} = r^{3}[/tex] (1)
Where T is the period of revolution and r is the orbital radius.
[tex]\sqrt{T^{2}} = \sqrt{r^{3}}[/tex]
[tex]T = \sqrt{r^{3}}[/tex] (2)
An astronomical unit (AU) is the distance between the Earth and the Sun ([tex]1.50x10^{8} km[/tex]).
Then, replacing that value in equation 2 it is gotten:
[tex]T = \sqrt{(1)^{3}} [/tex]
[tex]T = 1 AU[/tex]
But 1 year is equivalent to 1 AU according to Kepler's third law since 1 year is the orbital period of the Earth.
[tex]T = 1 AU \cdot \frac{1year}{1AU}[/tex] ⇒ [tex]1 year[/tex]
Hence, the planet and the Earth has the same orbital period.
Summary:
The planet takes the same time as the Earth to go around its host star.
