Distance from Sun at Perpendicular to Major Axis – Rankers Physics
Topic: Gravitation
Subtopic: Keplers Law

Distance from Sun at Perpendicular to Major Axis

The largest and the shortest distance of the earth from the sun are $r_1$ and $r_2$. Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun is:

(1988)

$\frac{r_1+r_2}{4}$
$\frac{r_1+r_2}{r_1-r_2}$
$\frac{2r_1r_2}{r_1+r_2}$
$\frac{r_1+r_2}{3}$

Solution:

The distance from the sun when the planet is perpendicular to the major axis drawn from the sun is the semi-latus rectum of the elliptical orbit. It is calculated as the harmonic mean of the apoapsis and periapsis distances, giving $\frac{2r_1r_2}{r_1+r_2}$.

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