Question

The longest and the shortest distance of our planet from sun is and $R_1$ and $R_2$. Distance from sun when it is normal to major axis of orbit is .

• A. $\frac{R_1+R_2}{2}$
• B. $\sqrt{\frac{R^2_1+R^2_2}{2}}$
• C. $\frac{R_1R_2}{R_1+R_2}$
• D. $\frac{2R_1R_2}{R_1+R_2}$

Answer 1

Answer: (D)

$\frac{2R_1R_2}{R_1+R_2}$

Answer 2

$r_1 = (1 +e) a ;r_2 = (1 - e) a$
$a = \frac{r_1+r_2}{2} ; r_1r_2 = (1 - e^2)a^2$
= $\frac{b^2}{a}$
$= \frac{a^2(1 - e^2)}{a} = \frac{r_1r_2}{\frac{r_1+r_2}{2}} = \frac{2r_1r_2}{r_1+r_2}$