Question

A heavenly body viewed from two points diametrically opposite of the earth's equator,
shows a parallax of 30'' of arc. Find the distance of the heavenly body from the earth.
(radius of earth is 6400km) (8.8x10^10 m)

Answer 1

Answer:

Distance = 1.1 × 10⁷

Explanation:

Radius of the Earth = 6400 km .= 6.4 × 10⁶ km (Given)

Two points = Time = 2 minutes. 

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

θ = Basis/Distance

Therefore, 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 heavenly body is 1.1 × 10⁷ km.