Scientists discover two planets orbiting a distant star. The average distance from the star to Planet A is 4 AU, and it takes 432 Earth days for Planet A to orbit the star. If it takes 1,460 days for Planet B to complete an orbit, what is the average distance from Planet B to the star?

C. 9 AU

Explanation:

The period (T) of Planet A is 432365=1.2 Earth years. The period of Planet B is 1,458365=4.0 Earth years. Kepler's Third Law states that

a3=kT2

Substituting the known values of a and T for Planet A, we have

43=k⋅1.22

64=k⋅1.4

k=45.7

Using this value for k, we can solve for the distance from Planet B to the star

a3=45.7⋅4.02

a3=731.2

a=9.0AU

An alternative solution is to notice that a3T2=k for both orbits, which means that the ratio a3T2 is the same for both orbits. So, 434322=x314582. Solving this proportion gives x3=729, so x=9.0AU.

idk what the options are but

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