The longest and the shortest distance of a planet from sun is R1 and R2 . Distance from sun when it is normal to major axis of orbit is

R1=(1+e)a;R2=(1−e)aa=R1+R22; R1R2=1−e2a2semi-latus rectum =b2a=a21−e2a=R1R2R1+R22=2R1R2R1+R2

The longest and the shortest distance of a planet from sun is R1 and R2 . Distance from sun when it is normal to major axis of orbit is

R1=(1+e)a;R2=(1−e)aa=R1+R22; R1R2=1−e2a2semi-latus rectum =b2a=a21−e2a=R1R2R1+R22=2R1R2R1+R2

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The longest and the shortest distance of a planet from sun is R₁ and R₂ . Distance from sun when it is normal to major axis of orbit is

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$\frac{R_{1} + R_{2}}{2}$

$\sqrt{\frac{R_{1}^{2} + R_{2}^{2}}{2}}$

$\frac{R_{1} R_{2}}{R_{1} + R_{2}}$

$\frac{2 R_{1} R_{2}}{R_{1} + R_{2}}$

answer is D.

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Detailed Solution

$\begin{array}{l} R_{1} = (1 + e) a; R_{2} = (1 - e) a \\ a = \frac{R_{1} + R_{2}}{2}; R_{1} R_{2} = (1 - e^{2}) a^{2} \end{array}$
semi-latus rectum $= \frac{b^{2}}{a}$
$= \frac{a^{2} (1 - e^{2})}{a} = \frac{R_{1} R_{2}}{\frac{R_{1} + R_{2}}{2}} = \frac{2 R_{1} R_{2}}{R_{1} + R_{2}}$