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The largest and shortest distances of the earth from the are r1 and r2. Its distance from the sun when it is the perpendicular to the major axis of the orbit drawn from the sun

The largest and shortest distances of the earth from the are r1 and r2. Its distance from the sun when it is the perpendicular to the major axis of the orbit drawn from the sun 

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Grade:12th pass

2 Answers

Parth
58 Points
3 years ago
see in this case earth is moving in elliptical path so
let we’ve 2a = major axis, and 2b = minor axis
hence a = (r1 +r2)/2
let distance = d  from property of ellipse it’ll be in directrix and d = (b^2)/a
hence you ‘ve a*(1 – e) = r1; which gives e= (r2-r1)/(r1+r2) e = eccentricity
e = root(1 – ((b/a)^2))
on solving you ‘ll get b = a*root( 1 – e^2)
hence b^2/a = a* (1 – e^2)
on putting r1,r2 
you’ll get  d = 2*r1*r2/(r1+r2)
hence option C
pls approve if it helps
Vikas TU
14149 Points
3 years ago
 Earth orbits around Sun in an Elliptical Orbit. Sun is at one of the two Foci. 
The major axis AB = AS + SB
                     = perihelion + aphelion
                     = r2 + r1 (given)
For an ellipse:   PS1 + PS2 = constant
        ∵   AS1 + AS2 = AB,   PS1 + PS2 = AB = r1 + r2
So When Earth P is at C,  
            
       CS1 + CS2 = AB 
       CS1 = CS2 = AB/2 = (r1 + r2)/2    Answer.
ΔC S2 S2  is Isosceles

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