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)

4

Answer 2

Period of revolution of planet $A (T_A) = 8T_B$
According to Kepler's III law of planetary motion
$T^2 \propto R^3$.
Therefore $\bigg( \frac{ r_A}{r_B } \bigg)^3 = \bigg( \frac{ T_A}{T_B } \bigg)^2= \bigg( \frac{ 8 T_B}{T_B } \bigg)^2 = 64$
or $\frac{ r_A}{r_B} = 4 \, \, \,$ or $\, \, \, \, r_A = 4 r_B$.