An astronomical unit (AU) is equal to the average distance from Earth to the Sun, about 92.9 * 10⁶ mi. A parsec (pc) is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of arc. A light-year (ly) is the distance that light, traveling through a vacuum with a speed of 186 000 mi/s, would cover in 1.0 year. Express the Earth - Sun distance in (a) parsecs and (b) light - years.

Light year is the distance, ray of light travels in one year at the speed of 186000 mi/s

Distance traveled by light in one year

= speed x time

186000 x 365 x 24 x 60 x 60 miles

= 5.8657 x 10¹² mi

the Earth - Sun distance in light - years.

= 92.9 * 10⁶ mi. / 5.8657 x 10¹² mi light years

= 15.84 x 10⁻⁶ light years

To calculate in terms of parsec

1 degree angle

= 60 x 60 second

π / 180 radian = 60 x 60 second

1 second = 3.14 / 180 x 3600

= 4.84 x 10⁻⁶ rad

one parsec = 1AU / one second

92.9 * 10⁶ mi / one second

= 92.9 * 10⁶ mi / 4.84 x 10⁻⁶ rad

= 19.19 x 10¹² mi

the Earth - Sun distance in parsec.

= 92.9 * 10⁶ mi. / 19.19 x 10¹² parsec.

= 4.84 x 10⁻⁶ parsec.