Question

two planets move around the sun. the periodic times and mean radii of the orbits are T1,T2and R1,R2 respectively the ratio of T1/T2 is equal to

Answer 1

two planets move around the sun. the periodic times and mean radii of the orbits are T1,T2and R1,R2 respectively the ratio of T1/T2 is equal to

(r1/r2) 3/2


Hope it helpful

Answer 2

Answer: The correct answer is $(\frac{R_1}{R_2})^{\frac{3}{2}}$.

Explanation:

The mathematical expression of Kepler's third law is as follows;

$T^{2} ∝R^{3}$

Here, T is the time period and R is the radius.

In the given problem, two planets move around the sun. the periodic times and mean radii of the orbits are $T_{1}$,  $T_{2}$,  $R_{1}$ and  $R_{2}$.

Calculate the ratio of$\frac{T_1}{T_2}$ by using above expression.

$\frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}}$

$\frac{T_1}{T_2}=(\frac{R_1}{R_2})^{\frac{3}{2}}$

Therefore, the ratio of T1/T2 is equal to $(\frac{R_1}{R_2})^{\frac{3}{2}}$.