Question

Two planets A and B of equal mass are having their period of revolutions _T A _and _T B _such that T A= 2 T B. These planets are revolving in the circular orbits of radii _r A _and _r B _respectively. Which out of the following would be the correct relationship of their orbits?

• A. $\text2r^{2}_A = r^{3}_B$
• B. $r^{3}_{A} = 2r^{3}_B$
• C. $r^{3}_A = 4r^{3}_B$
• D. $T^{2}_A - T^{2}_B = \frac{π²} {GM} ( r^{3}_B - 4r^{3}_A )$

Answer 1

Answer: (C)

$r^{3}_A = 4r^{3}_B$

Answer 2

The correct answer is (C) : $r^{3}_A = 4r^{3}_B$
$T_A = 2T_B$
Now
$T^{2}_A ∝ r^{3}_A$
$⇒( \frac{r_A}{r_B} )^3 = (\frac{T_A}{T_B} )^2$
$⇒ r^{3}_A = 4r^{3}_B$