Question

The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?

Answer 1

Time taken by quasar light to reach Earth = 3 billion years

= 3 × 10⁹ years

= 3 × 10⁹ × 365 × 24 × 60 × 60 s

Speed of light = 3 × 10⁸ m/s

Distance between the Earth and quasar

= (3 × 10⁸) × (3 × 10⁹ × 365 × 24 × 60 × 60)

= 283824 × 10²⁰ m

= 2.8 × 10²² km

Answer 2

The time taken by light from the quasar to the observer

t = 3.0 billion years = 3.0 x 10⁹ years As 1 ly = 9.46 x 10¹⁵ m

∴ Distance of quasar from the observer d = 3.0 x 109 x 9.46 x 1015 m

= 28.38 x 10²⁴ m = 2.8 x 10²⁵ m or 2.8 x 10²² km.