Question

Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/4th of the present distance, then the length of present day will be reduced by:

• A. 1/4
• B. 1/2
• C. 1/8
• D. 1/6

Answer 1

Answer: (C)

From Kepler's third law of planetary motion, the square of period of revolution of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit.
$T^2\propto a^3$
Given, $a^{\prime }=\frac{a}{4}$
$\therefore$ $\frac{T^2}{T{{}^{\prime }}^2}=\frac{a^3}{{\left(\frac{a}{4}\right)}^3}={(4)}^3$
$\Rightarrow$ $T^{\prime }=\frac{T}{{(4)}^{3/2}}=\frac{T}{8}$