Define astronomical unit,light year,and parsec.

(N/A) Astronomical Unit $(AU)$: The average distance between the Sun and the Earth is called an astronomical unit.
$1 AU = 1.496 \times 10^{11} \text{ m}$
Light Year: The distance travelled by light in a vacuum in $1$ year is called $1$ light year. The speed of light in a vacuum is $c = 2.99 \times 10^{8} \text{ m s}^{-1}$.
$\therefore$ Distance travelled in $1$ year $= c \times t$
$= 2.99 \times 10^{8} \times 365 \times 24 \times 3600$
$= 9.46 \times 10^{15} \text{ m}$
Light year is used to measure distances between celestial objects.
Parsec $(pc)$: The distance at which the average radius of the Earth's orbit subtends an angle of $1^{\prime\prime}$ (arc second) is called $1$ parsec $(pc)$.
From the figure,$\theta \text{ (rad)} = \frac{\text{arc}}{\text{radius}} = \frac{l}{r}$
$\therefore r = \frac{l}{\theta} = \frac{1 AU}{1^{\prime\prime}}$ where $1 AU = 1.496 \times 10^{11} \text{ m}$ and $1^{\prime\prime} = \frac{1}{60 \times 60} \times \frac{\pi}{180} \text{ radians}$.
$\therefore r = \frac{1.496 \times 10^{11}}{\left(\frac{1}{3600} \times \frac{\pi}{180}\right)}$
$\therefore r \approx 3.08 \times 10^{16} \text{ m}$