Question

The period of revolution of planet A around the sun is 8 times that of B.The distance of A from the sun is how many times greater than that of B from the sun?

1)4

2)5

3)2

4)3

Answer 1

Step 1, Given

The period of revolution of planet A around the sun is 8 times that of B

Step 2,

From the Kepler's third law

We know,

$T^2\alpha r^3$ Where T is the time period and r is the distance from the sun

We can write

$\frac{{T_A}^2}{{T_B}^2}=\frac{{r_A}^3}{{r_B}^3}$

After putting all the values

${\left(\frac{8}{1}\right)}^2=\frac{{r_A}^3}{{r_B}^3}$

Or,

$\frac{r_A}{r_B}=4$

$Or,r_A=4r_B$

Hence radius of A is 4 times the radius of B