Chapter 44, Problem 44.34E

(a)

To determine

To show: The equation ${\lambda }_0={\lambda }_{\text{S}}\sqrt{\frac{c+v}{c-v}}$ may be written as $1+z={\left(\frac{1+\beta }{1-\beta }\right)}^{1/2}$, where $\beta =\frac{v}{c}$.

(b)

To determine

The speed of the galaxy relative to earth if red shift is due to Doppler shift.

(c)

To determine

The distance of the galaxy from earth.