Question

The eccentricity of earths orbit is $0.0167$. The ratio of its maximum speed in its orbit to its minimum speed is:

• A. 2.507
• B. 1.0339
• C. 8.324
• D. 1.000

Answer 1

Answer: (B)

Eccentricity, $e=\frac{r_{\max }-r_{\min }}{r_{\max }+r_{\min }}=0.0167$
Therefore, $\frac{r_{\max }}{r_{\min }}=\frac{1+e}{1-e}$
$=\frac{1-0.0167}{1+0.0167}$
As angular momentum remains constant, hence
$r_{\max }\times v_{\min }=r_{\min }\times v_{\max }$
$\therefore \frac{v_{\max }}{v_{\min }}=\frac{r_{\max }}{r_{\min }}=\frac{1+0.0167}{1-0.0167}$
$=1.0339$