Question

If the distance between the earth and the sun were reduced to half its present value, then the number of days in one year would have been

• A. $65$
• B. $129$
• C. $183$
• D. $730$

Answer 1

Answer: (B)

$129$

According to Kepler's law, $\frac{T_1^2}{T_2^2}=\frac{r_1^3}{r_2^3}$, where $T$ is the time period of revolution and $r$ is the radius of the orbit.

$\frac{T_1^2}{T_2^2}=\frac{r_1^3}{r_2^3}{r}_2=0.5r_1\Rightarrow T_2^2=\frac{T_1^2}{8}\Rightarrow T_2=\frac{T_1}{\sqrt{8}}=\frac{365}{\sqrt{8}}\approx 129$

Thus new time period is 129 days = number of days in a year. (since time period of revolution is 1 year).