Question

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
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))/(2)`

Answer 1

Correct Answer - C
Let `r_(1)` and `r_(2)` be the shortest and longer distance of the earth w.r.t. sun which will be when earth is at `A` and `B` as shown in Fig. If `R` is the distance, them from the property of the ellipse
`(1)/(R ) + (1)/(R ) = (1)/(r_(1)) + (1)/(r_(2))` or `(2)/(R) = (r_(1) + r_(2))/(r_(1) r_(2))`
or `R = (2r_(1)r_(2))/(r_(1) + r_(2))`