$A$ huge circular arc of length $4.4 \; ly$ subtends an angle of $4''$ (arcseconds) at the centre of the circle. How long would it take for a body to complete $4$ revolutions if its speed is $8 \; AU/s$?
Given: $1 \; ly = 9.46 \times 10^{15} \; m$,$1 \; AU = 1.5 \times 10^{11} \; m$.

Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms.

Substance	Atomic Mass $(u)$	Density $(10^3\,kg\,m^{-3})$
Carbon (diamond)	$12.01$	$2.22$
Gold	$197.00$	$19.32$
Nitrogen (liquid)	$14.01$	$1.00$
Lithium	$6.94$	$0.53$
Fluorine (liquid)	$19.00$	$1.14$

What is meant by the angular diameter of the moon?

$(a)$ How many astronomical units $(AU)$ make $1$ parsec?
$(b)$ Consider a sun-like star at a distance of $2$ parsecs. When it is seen through a telescope with $100$ magnification,what should be the angular size of the star? The Sun appears to be $(\frac{1}{2})^{\circ}$ from the Earth. Due to atmospheric fluctuations,the eye cannot resolve objects smaller than $1$ arc minute.
$(c)$ Mars has approximately half of the Earth's diameter. When it is closest to the Earth,it is at about $\frac{1}{2} AU$ from the Earth. Calculate what size it will appear when seen through the same telescope.

What is the typical order of magnitude of the distance between two atoms in solids?

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?