The maximum and minimum distance of earth from sun are $r_{1}$ and $r_{2}$ respectively. What will be the distance of earth from sun when it is perpendicular to the principal axis passing through sun in its orbit?

\frac{r_{1} + r_{2}}{4}

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(\frac{r_{1} + r_{2}}{r_{1} - r_{2}})

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\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}

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\frac{r_{1} + r_{2}}{3}

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Solution

The correct option is C $\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$
The position of the particle moving in elliptical orbit can be represented as $r = \frac{1}{1 + e cos θ}$
where $1$ is the perpendicular distance of the particle from focus
$e$ is the eccentricity of the ellipse.

$r_{1} = \frac{1}{1 - e}$

$r_{2} = \frac{1}{1 + e}$

Adding the two equations

$2 = \frac{1}{r_{1}} + \frac{1}{r_{2}}$

$1 = \frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$
Answer C:

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The maximum and minimum distance of earth from sun are r1 and r2 respectively. What will be the distance of earth from sun when it is perpendicular to the principal axis passing through sun in its orbit?

The correct option is C 2r1r2r1+r2 The position of the particle moving in elliptical orbit can be represented as r=11+ecosθwhere 1 is the perpendicular distance of the particle from focuse is the eccentricity of the ellipse.r1=11−er2=11+eAdding the two equations2=1r1+1r21=2r1r2r1+r2Answer C:

The maximum and minimum distance of earth from sun are $r_{1}$ and $r_{2}$ respectively. What will be the distance of earth from sun when it is perpendicular to the principal axis passing through sun in its orbit?