Question

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

Answer 1

Answer:

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. $P^2\propto S^3$

We have given,

The average distance from the star to Planet A is $S_1=4$ AU.

It takes 432 Earth days for Planet A to orbit the star i.e. $P_1=432$

It takes 1,460 days for Planet B to complete an orbit i.e.  $P_2=1460$

Substitute the values in $(\frac{P_1}{P_2})^2=(\frac{S_1}{S_2})^3$

$(\frac{432}{1460})^2=(\frac{4}{S_2})^3$

$0.0875=(\frac{4}{S_2})^3$

Taking root cube both side,

$\sqrt[3]{0.0875}=\frac{4}{S_2}$

$0.444=\frac{4}{S_2}$

$S_2=\frac{4}{0.444}$

$S_2=9.00$

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

Therefore, Option C is correct.