Question

If the distance between the earth and sun were to be doubled from its present value, the number of days in a year would be :

• A. 64.5
• B. 1032
• C. 182.5
• D. 730

Answer 1

The correct option is B 1032

Given,

Radius of rotation become double, $a_2=2a_1$

By Kepler’s law, $T^2$$\alpha a^3$

$\frac{T_1^2}{a_1^3}$$=\frac{T_2^2}{a_2^3}$

$T_2^2$$={\left(\frac{a_2}{a_1}\right)}^3\times T_1^2$

$T_2^2$ $={\left(\frac{2}{1}\right)}^3\times T_1^2$

$T_2^2$ $=8\times T_1^2$

$T_2^2$ $=\sqrt{8}\times 365\text{days}$

$T_2=1032.37\text{days}$

Hence, $1032$ days in year.