Question

If earth comes closer to sun by 3/4 th of the present distance, then the year of earth consists of how many days?

• A. $45.625days$
• B. $25.625days$
• C. $50.625days$
• D. $60.625days$

Answer 1

The correct option is A $45.625days$

According to Kepler's third law the square of orbital period $T$ of a planet is proportional to cube of it mean distance $R$ from the sun.

$T^2$ $\alpha$ $R^3$

$T$ $\alpha$ $\sqrt{R^3}$

$\frac{T_1}{T_2}=\frac{\sqrt{R_1^3}}{\sqrt{R_2^3}}$

$=\frac{\sqrt{R_1^3}}{\sqrt{{\left(\frac{R_1}{4}\right)}^3}}=\sqrt{4^3}=8$

$T_2=\frac{T_1}{8}$