Question 151: Gravitation

Question

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

Accepted Answer

$${T_A} = 2{T_B}$$
Now $$T_A^2 \propto r_A^3$$
$$ \Rightarrow {\left( {{{{r_A}} \over {{r_B}}}} \right)^3} = {\left( {{{{T_A}} \over {{T_B}}}} \right)^2}$$
$$ \Rightarrow r_A^3 = 4r_B^3$$

Answer

$$2r_A^2 = r_B^3$$

Answer

$$r_A^3 = 2r_B^3$$

Answer

$$r_A^3 = 4r_B^3$$

Answer

$$T_A^2 - T_B^2 = {{{\pi ^2}} \over {GM}}\left( {r_B^3 - 4r_A^3} \right)$$

Gravitation

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?

Choose the correct answer: