Question

the Sun's angular diameter is measured to be 1920 the distance D of the sun from the earth is 1.496 into 10 to the power 11 what is the diameter of the Sun​

Answer 1

Given :

▪ Angular diameter of sun = 1920"

▪ Distance b/w earth and sun = 1.496×10¹¹m

To Find :

▪ Diameter of the sun.

Formula :

☞ Size of an astronomical object :

$\bigstar\bf\:Linear\:Diameter= Distance\times Angular\:Diameter\\ \\ \bigstar\bf\:\red{D=d\times \theta}$

Calculation :

Here,

Distance of the sun from the earth, d = 1.496×10¹¹m

Sun's angular diameter, α = 1920"

We know that,

▪ 1" = 4.85×10$^{-6}$rad

Therefore,

▪ α = 1920×4.85×10$^{-6}$rad

▪ α = 9.31×10$^{-3}$rad

Sun's Diameter (D) = α×d

▪ D = (9.31×10$^{-3}$)(1.496×10¹¹)m

▪ $\bf\:D=1.39\times 10^9\:m$

Answer 2

$\blue{\bold{\underline{\underline{Question}}}}$

The Sun's angular diameter is measured to be 1920". The distance D of the sun from the earth is 1.496 ×10 11 m. So find the diameter of the Sun.

$\blue{\bold{\underline{\underline{Answer}}}}$

1.39×10^9m

$\blue{\bold{\underline{\underline{Explanation}}}}$

$we \: know \: that$

$1 = ( \frac{1}{3600} ) \times \frac{\pi}{180} \: rad$

$angular \: diameter \: theta = 1920$

$= 1920 \times \frac{\pi}{3600 \times 180} rad = 0.0093rad$

$diameter = theta \: r$

$= 0.0093 \times 1.496 \times {10}^{11} m$

$= 1.39 \times {10}^{9} m$