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?

• A. 4
• B. 5
• C. 2
• D. 3

Answer 1

Answer: (A)

Period of revolution of planet $A\left(T_{A}\right)=8 T_{B}$.
According to Kepler's III law of planetary motion $T^{2} \propto R^{3}$.
Therefore $\left(\frac{r_{A}}{r_{B}}\right)^{3}=\left(\frac{T_{A}}{T_{B}}\right)^{2}=\left(\frac{8 T_{B}}{T_{B}}\right)^{2}=64$
or $\frac{r_{A}}{r_{B}}=4$
or $r_{A}=4 r_{B}$.