Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and 5 AU (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is

Question

Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and 5 AU (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is (A) 1 year (B) 5 year (C) 11 year (D) 25 year

Tardigrade Admin · Accepted Answer

Given, semi-major axis of planets, RA=1 AU and RB=5 AU, and period of revolution of planet A, TA= 1 yr. As, ((TA/TB))2=((RA/RB))3 ⇒ ((1/TB))2=((1/5))3 ⇒ TB=√125=11.18 yr

Q. Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and $5 A U$ (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is

1 year

5 year

11 year

25 year

125 year

Given, semi-major axis of planets, $R_{A} = 1 A U$ and $R_{B} = 5 A U$ , and period of revolution of planet $A$ ,
$T_{A} = 1 yr .$
As, $(\frac{T _{A}}{T _{B}})^{2} = (\frac{R _{A}}{R _{B}})^{3}$
$\Rightarrow (\frac{1}{T _{B}})^{2} = (\frac{1}{5})^{3}$
$\Rightarrow T_{B} = 125 = 11.18 yr$

Q. Suppose to planets A and B revolved around a Sun in the galaxy. The semi major axis of A and B are 1 and 5AU (astronomical unit) respectively. If the period of revolution of A is 1 year, the period of revolution of B is