Question

If distance between the earth and the sun were half its present value, the number of days in a year would have been approximately

• A. 64.5
• B. 129
• C. 182.5
• D. 730

Answer 1

The correct option is B 129

According to Kepler's law

$\frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}$

Here $T_1=365$ days ; $T_2=?$

$R_1=R;R_2=\frac{R}{2}$

$\Rightarrow T_2=T_1{\left(\frac{R_2}{R_1}\right)}^{\frac{3}{2}}$

$=365{\left[\frac{\frac{R}{2}}{R}\right]}^{\frac{3}{2}}=129$ days