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 the perpendicular to the major axis of the orbit drawn from the sun

Options

A. `(r_(1) + r_(2))/4`
B. `(r_(1) + r_(2))/(r_(1) - r_(2))`
C. `(2r_(1)r_(2))/(r_(1) + r_(2))`
D. `(r_(1) + r_(2))/3`

Answer

C

Explanation

The earth moves in an elliptical orbit around the sun. When it is at A it is at the largest distance (`r_(1)`) from the sun. When it us at B it is at the shortest distance (`r_2`) from the sun. It is given that the earth is at B.
From the properties of the ellipse `1/r_(1) + 1/r_(2) = 2/R`
`therefore (r_(1) + r_(2))/(r_(1)r_(2)) = 2/R, therefore R = (2(r_(1) r_(2)))/(r_(1) + r_(2))`