Answer
The light was emitted $~~6.9\times 10^8~~$ years ago.
Work Step by Step
In part (a), we found that $\Delta t = \frac{r}{c-r~\alpha}$
We can find how long ago the light was emitted:
$\Delta t = \frac{r}{c-r~\alpha}$
$\Delta t = \frac{r}{c-r~H}$
$\Delta t = \frac{6.55\times 10^8~ly}{(3.0\times 10^8~m/s)-(6.55\times 10^8~ly)(0.0218~m/s~ly)}$
$\Delta t = \frac{6.55\times 10^8~ly}{2.8571\times 10^8~m/s}$
$\Delta t = \frac{6.55\times 10^8~ly}{0.9524~c}$
$\Delta t = 6.9\times 10^8~years$
The light was emitted $~~6.9\times 10^8~~$ years ago.
