Question

the parallax of heavenly body measured from two points diametrically opposite on equator of the earth is 2 min.calculate distance of heavenly body. radius of the earth is 6400km

Answer 1

Radius of the Earth (or Basis) = 6400 km .= 6.4 × 10⁶ km. 
Time = 2 minutes. 
This means that the angle sustained by the Earth on the Heavenly bodies is 2'
  
Thus, converting it into radians, 

∵ 1' = 2.91 × 10⁻⁴ radians. 
∴ 2' = 5.8 × 10⁻⁴ radians. 


Hence, Parallax angle (θ) = 5.8 × 10⁻⁴ rad


Now, Using the Formula, 

 θ = Basis/Distance
∴ Distance = (6.4 × 10⁶)/(5.8 × 10⁻⁴) rad
   = 1.10 × 10¹⁰ m. 
   = 1.1 × 10⁷ km. 


Hence, the distance between the Earth and the Planet is 1.1 × 10⁷ km. 


Hope it helps. 

Answer 2

Hey there !

Solution :

Given : Parallax angle = 2 minutes

We know that, 

1 minute = 1 / 60 * π / 180 rad

=> 2 min = 2 / 60 * π / 180 rad

=> 2 min  = π / 30 * 180 rad

=> 2 min = π / 5400 rad

=> 2 min = 5.82 × 10⁻⁴ rad

Therefore Parallax angle = 5.82 × 10⁻⁴ rad.

We know that,

Parallax angle = Distance between Two points / Distance of planet

5.82 × 10⁻⁴ = 6400 / Distance of planet from earth

6400 = 6.4 × 10³ km

=> Distance of planet from earth = 6.4 × 10³ / 5.82 × 10⁻⁴

=> Distance of planet from earth = 6.4 / 5.82 * 10³ ⁻ ⁽ ⁻ ⁴ ⁾ km

=> Distance of planet from earth = 1.09 × 10⁷ km ≈ 1.1 × 10⁷ km ( Approx )

Therefore Distance of planet from earth is 1.09 × 10⁷ km.

Hope my answer helped :-)