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

Answer 1

Let `R` be the distance of the Earth from the sun when the Earth is at the position, perpendicular to the major axis of its elliptical orbit as shows in Fig.

From the property of ellipse, we have
`(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))`