The largest and the shorest distance of earth from the sun `1.1 AU` and `0.92 AU`. What is its distance from the sun when it is perpendicular to the major axis of the orbit drawn from the sun ?

Explanation

Let `r_(1), r_(2)` be the largest and shortest distance of earth from the sun while orbiting around sun. If `R` is the disatance of earth from the sun in perpendicular position, to the major axis of the orbit drawn from the sun , then from the property of 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)) = (2xx (1.1) xx 0.92)/((1.1 + 0.92)) = 1.002 AU`