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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?
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Solution 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
Solution 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.
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