Question

If a new planet is discovered rotating around the sun with its orbital radius double that of earth, then what will be its time period?
(In earth days)

• A. $1032\text{days}$
• B. $730\text{days}$
• C. $1295\text{days}$
• D. $1567\text{days}$

Answer 1

The correct option is A $1032\text{days}$

Time period of revolution of a planet revolving around the sun of mass $M$, is given by,

$T=2\pi \sqrt{\frac{r^3}{GM}}$

$\therefore T^2\propto r^3$

$\frac{T_1^2}{T_2^2}=\frac{r_1^3}{r_2^3}$

$\Rightarrow T_2^2={\left(\frac{r_2}{r_1}\right)}^3{T}_1^2$

Initial time period,

$T_1=1\text{year}=365\text{days}.$

As per equation, new orbital radius $r_2=2r_1$

$\therefore T_2^2={\left(\frac{2r_1}{r_1}\right)}^3\times 365$

$T_2=\sqrt{8}\times 365$

$T_2=1032\text{days}$

Hence, option $\left(A\right)$ is the correct answer.