Question

The distance of a planet from the sun is $5$ times the distance between the earth and the sun. The Time period of the planet is:

• A. $5^{\frac{3}{2}}years$
• B. $5^{\frac{2}{3}}years$
• C. $5^{\frac{1}{3}}years$
• D. $5^{\frac{1}{2}}years$

Answer 1

The correct option is A $5^{\frac{3}{2}}years$

According to Kepler’s third law, square of time period of a planet is proportional to the cube of the semi-major axis of its elliptical orbit.
$T^2\propto R^3$
$\frac{T_{planet}^2}{T_{earth}^2}=\frac{R_{planet}^3}{R_{earth}^3}$
$T_{planet}=\sqrt{T_{earth}^2{\left(\frac{R_{planet}}{R_{earth}}\right)}^3}$
$T_{planet}=T_{earth}{\left(\frac{R_{planet}}{R_{earth}}\right)}^{3/2}$
$T_{planet}=5^{3/2}{T}_{earth}$