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The largest and the shortest distance of the earth from the sun are r₁ and r₂. Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun is

1. (r₁ + r₂)/4
2. (r₁ + r₂)/2
3. 2r₁r₂/(r₁ + r₂)
4. (r₁ + r₂)/3

Correct answer: 2r₁r₂/(r₁ + r₂)

Solution

The distance of the Earth from the Sun when it is perpendicular to the major axis corresponds to the semi-minor axis of the elliptical orbit. Using the relationship between the semi-major axis and semi-minor axis in an ellipse, the distance is given by the harmonic mean: 2r₁r₂/(r₁ + r₂).

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