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

Question #332008

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).


1
Expert's answer
2022-04-21T13:00:57-0400

The Kepler's third law says

a3=T2a^3=T^2

Hence, the distance from Planet X to the star

a=T23=15.3823=6.185AU=9.2526108km=5.7459108mia=\sqrt[3]{T^2}=\sqrt[3]{15.382}=6.185 {\:\rm AU}\\ =9.2526*10^8\:\rm km=5.7459*10^8\: mi


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