Question

The principle of 'parallax' is used in the determination of distance of very distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is the baseline is above the diameter of the Earth's Orbit 3 × 10¹¹ m. However the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1" (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1" (second) of arc from opposite ends of a baseline equal to the distance of from the Earth to the Sun. How much is a perisic in terms of metres?

Answer 1

Hii dear,

# Given-
Radius of Earth’s orbit
r = d/2 = 1.5×10^11 m
Distance parallax angle
Θ = 1" = 4.847×10^–6 rad.
Distance of star from earth
D = ?

# Parsec-
It is defined as the distance at which the average radius of the Earth’s orbit subtends an angle of 1"

# Formula-
We know
Θ = r/D
D = r/Θ
D = (1.5×10^11)/(4.847×10^–6)
D = 3.09×10^16 m

Hence, 1 parsec ≈ 3.09×10^16 m.

Hope that was useful...