Question

The orbit of the earth is an ellipse with eccentricity $\frac{1}{60}$ with Sun at one focus, the major axis being approximately $186\times {10}^6$ miles in length. The shortest and longest distance of the earth from the sun is

• A. $9145\times {10}^4$ miles, $9455\times {10}^4$ miles
• B. $9147\times {10}^4$ miles, $9457\times {10}^4$ miles
• C. $9145\times {10}^6$ miles, $9455\times {10}^6$ miles
• D. None of these

Answer 1

The correct option is A $9145\times {10}^4$ miles, $9455\times {10}^4$ miles

Given $2a=186\times {10}^6$ and $e=\frac{1}{60}$

$\Rightarrow a=93\times {10}^6$ and $e=\frac{1}{60}$

The shortest length of earth from sun is $a-ae=a(1-e)=93\times {10}^6\times \left(\frac{59}{60}\right)=9145\times {10}^4$

The longest distance of earth from sun is $a+ae=a(1+e)=93\times {10}^6\times \left(\frac{61}{60}\right)=9455\times {10}^4$

Therefore correct option is $A$