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29 March, 10:16

If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?

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  1. 29 March, 12:18
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    The quasar is moving with 0.68 the speed of light.

    Explanation:

    let v be the speed quasar is moving with away from us, z be the redshift and c be the speed of light.

    Using the relativistic doppler shift formula, the fraction of the speed of light that the quasar is moving away from us is given by:

    v/c = [ (z - 1) ^2 - 1]/[ (z - 1) ^2 + 1]

    = [ (3.3 - 1) ^2 - 1]/[ (3.3 - 1) ^2 + 1]

    = 0.68

    Therefore, the quasar is moving with 0.68 the speed of light.
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