$1'' = \dots \text{rad}$

The Sun's angular diameter is measured to be $1920^{\prime \prime}$. The distance $D$ of the Sun from the Earth is $1.496 \times 10^{11} \ m$. What is the diameter of the Sun?

$A$ celestial object is observed from two points $A$ and $B$ on the Earth,which are diametrically opposite. The angle between the two observation directions is $2.9 \times 10^{-4} \text{ rad}$. Taking the diameter of the Earth to be $1.28 \times 10^4 \text{ km}$,find the distance between the Earth and the object.

The moon is observed from two diametrically opposite points $A$ and $B$ on Earth. The angle $\theta$ subtended at the moon by the two directions of observation is $1^{\circ} 54^{\prime}$. Given the diameter of the Earth to be about $1.276 \times 10^{7} \; m$,compute the distance of the moon from the Earth.

$A$ man wishes to estimate the distance of a nearby tower from him. He stands at a point $A$ in front of the tower $C$ and spots a very distant object $O$ in line with $AC$. He then walks perpendicular to $AC$ up to $B$,a distance of $100 \; m$,and looks at $O$ and $C$ again. Since $O$ is very distant,the direction $BO$ is practically the same as $AO$; but he finds the line of sight of $C$ shifted from the original line of sight by an angle $\theta = 40^{\circ}$ ($\theta$ is known as 'parallax'). Estimate the distance (in $m$) of the tower $C$ from his original position $A$.

Calculate the angle of $(a)$ $1^{\circ}$ (degree),$(b)$ $1^{\prime}$ (minute of arc),and $(c)$ $1^{\prime \prime}$ (second of arc) in radians. Use $360^{\circ} = 2\pi \text{ rad}$,$1^{\circ} = 60^{\prime}$,and $1^{\prime} = 60^{\prime \prime}$.