Question 135: Gravitation

Question

Two planets A and B of equal mass are having their period of revolutions T
A
and T
B
such that T
A
= 2T
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?

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 T A and T B such that T A = 2T 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?

Choose the correct answer: