Question

the maximum and minimum distance of earth from sun are r1 and r2 respectivally. what will be the distance of earth from sun when it si perpendicular to the principle axis passing through sun in its orbital

Answer 1

Hey dear,

# Answer- l = 2 r1.r2/(r1+r2)

# Explaination-

For an elliptical orbit with eccentricity e, the position of a particle with perpendicular distance from focus l is represented as,

r=1/(l+ecosθ)

The maximum distance is given by

r1=1/(l−e)

1−e=l/r1 (1)

The minimum distance is given by

r2=1/(l+e)

1+e=l/r2 (2)

Adding (1)&(2),

2 = l/r1 + l/r2

2 = l [(r1+r2)/r1.r2]

l = 2 r1.r2/(r1+r2)

The distance when perpendicular to principal axis is given by 2 r1.r2/(r1+r2).

Thanks for asking.