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?
a. 6 au
b. 8 au
c. 9 au
d. 13.5 au

Option C - 9 AU

Step-by-step explanation:

To find : What is the average distance from Planet B to the star?

Solution :

According to kepler's law,

The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.

i.e.

We have given,

The average distance from the star to Planet A is AU.

It takes 432 Earth days for Planet A to orbit the star i.e.

It takes 1,460 days for Planet B to complete an orbit i.e.  

Substitute the values in

Taking root cube both side,

The average distance from Planet B to the star is 9 AU.

Therefore, Option C is correct.

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step-by-step explanation:

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step-by-step explanation: