The largest and the shortest distance of the earth from the sun are r_1 and r_2respectively. Calculate the distance from the sun when it is at perpendicular distance to major axis of the orbit drawn from the sun

The largest and the shortest distance of the earth from the sun are r_

1.	The largest and the shortest distance of the earth from the sun are r_1 and r_2respectively. Calculate the distance from the sun when it is at perpendicular distance to major axis of the orbit drawn from the sun
Answer» Solution :Since `E = c/a RARR c =ea "" THEREFORE r_1 = a+c=a+ea=a(1+e)` ` r_2 = a -c =a -ea = a (1-e)` Required distance`L = (b^2)/(a)` (semi latus rectum ) we have `r_1+r_2 = 2a` and `r_-r_2 =a(1+e) -a(1-e) = 2ae rArr e= (r_1-r_2)/(r_1+r_2)` Also `b^2 = a^2 (1-e^2)` ` therefore L = (b^2)/(a) = (a^2 (1-e^2))/(a) = a (1-e^2)` ` = ((r_1+r_2)/(2)) [1-((r_1-r_2)/(r_1+r_2))^2]` on simplification , `L = (2r_1r_2)/(r_1+r_2) "or " 2/L = (1)/(r_1) + (1)/(r_2)`