Question

The full relativistic expression for the cosmological redshift is $z + 1 = \sqrt{\frac{c + v}{c - v}}$ where $v$ is the radial speed of the distant source. (a) Show that in the non-relativistic limit the above approaches the expression $z \approx v/c$ (b) A distant quasar is found at redshift $z = 6$. As a fraction of lightspeed $c$, calculate the speed at which this quasar appears to be receding from Earth. (c) Another quasar has much smaller redshift $z = 0.023$. Find how far away from Earth this quasar is. You may use that the Hubble constant is $H_0 = 69 \frac{km}{sec \ Mpc}$

          The full relativistic expression for the cosmological redshift is
$z + 1 = \sqrt{\frac{c + v}{c - v}}$
where $v$ is the radial speed of the distant source.
(a) Show that in the non-relativistic limit the above approaches the expression
$z \approx v/c$
(b) A distant quasar is found at redshift $z = 6$. As a fraction of lightspeed $c$, calculate
the speed at which this quasar appears to be receding from Earth.
(c) Another quasar has much smaller redshift $z = 0.023$. Find how far away from
Earth this quasar is.
You may use that the Hubble constant is $H_0 = 69 \frac{km}{sec \ Mpc}$

$The full relativistic expression for the cosmological redshift is z + 1 = √((c + v)/(c - v)) where v is the radial speed of the distant source. (a) Show that in the non-relativistic limit the above approaches the expression z ≈ v/c (b) A distant quasar is found at redshift z = 6. As a fraction of lightspeed c, calculate the speed at which this quasar appears to be receding from Earth. (c) Another quasar has much smaller redshift z = 0.023. Find how far away from Earth this quasar is. You may use that the Hubble constant is H0 = 69 (km)/(sec Mpc)$

Added by Heidi G.

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