Define Astronomical unit, light year and parsec.

Explanation

Astronomical Unit (AU) = Average distance between the Sun and the Earth is called astronomical unit.
1 AU = `1.496 xx 10^(11)` m
Light Year : Distance travelled by light in vacuum in 1 year is called 1 light year.
Speed of light in vacuum `c = 2.99 xx 10^(8) ms^(-1)`
`:.` Distance travelled in 1 year =ct
`=2.99xx10^(8)xx365xx24xx3600`
`=9.46xx10^(15) m`
Light year is used to measure distance between celestial objects. Parsec (pc): Distance at which average radius of earth.s orbit subtend angle of 1" (arc second) is called 1 parsec (pc).

From figure `theta` (rad)= `(arc)/("radius")=(l)/(r)`
`:.r=(l)/(theta)=(1AU)/(1..)`
`(1AU=1.496xx10^(11)m)`
`:.I..(1)/(60xx60)xx(pi)/(180)` (radian)
`:.r=(1.496xx10^(11))/(((1)/(60xx60)xx(pi)/(180)))`
`:.r=3.08xx10^(16) m`