Question 24

Suppose the distance between earth and sun becomes half of its present distance. What is likely to happen to life?

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Solution

We know that $(t i m e p e r i o d)^{2} \propto (r a d i u s o f o r b i t)^{3} (T_{1})^{2} = K (r_{1})^{3} . . . (i) (T_{2})^{2} = K (r_{2})^{3} \Rightarrow T_{2}^{2} = K {(\frac{r_{1}}{2})}^{3} . . . (i i) [∵ r_{2} = \frac{r_{1}}{2}] ∴ \frac{T_{1}^{2}}{T_{2}^{2}} = \frac{r_{1}^{3}}{r_{1}^{3}} \times 8 \Rightarrow T_{2}^{2} = \frac{T_{1}^{2}}{8} \Rightarrow T_{2} = \frac{T_{1}}{2 \sqrt{2}}$
It means that time period reduces by $(\frac{1}{2 \sqrt{2}})$ factor.
So, the days in a year will be approx. 129 instead of 365 days.
Life may no longer exist.

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