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?

Options

• `2"r"_"A"^2="r"_"B"^2`

• `"r"_"A"^3=2"r"_"B"^3`

• `"r"_"A"^3=4"r"_"B"^3`

• `"T"_"A"^2-"T"_"B"^2=pi^2/"GM"("r"_"B"^3-4"r"_"A"^3)`

Answer 1

`bb("r"_"A"^3=4"r"_"B"^3)`

Explanation:

By kepler's law T² ∝ r³

⇒ `("T"_"A"/"T"_"B")^2=("r"_"A"/"r"_"B")^3`

⇒ 2² = `("r"_"A"/"r"_"B")^3` 

⇒ `"r"_"A"^3=4"r"_"B"^3`