Answer to Question #332008 in Astronomy | Astrophysics for erika miguel

Question

1.The period of Planet X to orbit on a certain star is 15.382 years. Given this data, compute the distance from Planet X to the star in miles. (NOTE: 1 km = 0.621 mile).

Answer 1

The Kepler's third law says

$$a^3=T^2$$

Hence, the distance from Planet X to the star

$$a=\sqrt[3]{T^2}=\sqrt[3]{15.382}=6.185 {\:\rm AU}\\ =9.2526*10^8\:\rm km=5.7459*10^8\: mi$$