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.

Explanation:

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.