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(C) The earth moves around the sun in an elliptical path. According to the properties of an ellipse:${r_1} = a(1 + e)$ (Aphelion distance)${r_2} = a(1

Vedclass · Accepted Answer

$\frac{{2{r_1}{r_2}}}{{{r_1} + {r_2}}}$

Vedclass · Answer

(C) The earth moves around the sun in an elliptical path. According to the properties of an ellipse:${r_1} = a(1 + e)$ (Aphelion distance)${r_2} = a(1 - e)$ (Perihelion distance)Adding these,we get ${r_1} + {r_2} = 2a$,so $a = \frac{{{r_1} + {r_2}}}{2}$.Multiplying these,we get ${r_1}{r_2} = a^2(1 - e^2)$.Since $b^2 = a^2(1 - e^2)$,we have ${r_1}{r_2} = b^2$.The distance from the sun when the earth is perpendicular to the major axis is the semi-latus rectum $(l)$ of the ellipse.The formula for the semi-latus rectum is $l = \frac{{{b^2}}}{a}$.Substituting the values,$l = \frac{{{r_1}{r_2}}}{({r_1} + {r_2})/2} = \frac{{2{r_1}{r_2}}}{{{r_1} + {r_2}}}$.

The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$ respectively. What is its distance from the sun when it is at a position perpendicular to the major axis of the orbit drawn from the sun?

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