Chapter 44, Problem 51P

To determine

To:

(a) show that when a light wave of Figs. 44.16 a and b travels at speed c from galaxy A to Earth, then

$∆t= \frac{r}{c- \alpha r}$

(b) show that the change in the wavelength ∆λ is given by

$\frac{∆\lambda }{\lambda }= \frac{r\alpha }{c-r\alpha }$

(c) use binomial equation to expand the right side of equation given in (b). Then write the resulting equation for $\frac{∆\lambda }{\lambda }$.

(d) retain the first expression in the binomial expansion in (c), and then write the resulting equation for ∆λ/λ.

(e) use Hubble’s Law to compare Doppler Effect result with cosmological expansion result of (d) and find the value of α.Then analyze the results.

(f) find the distance between the galaxy A and Earth when the light was emitted by using the result in (b), and the galaxy has a red shift of 0.050. (Assuming that the expansion rate of the universe is constant, as given in the chapter.)

(g) using the result in (a) calculate how long ago was the light emitted from galaxy A.

(h) using the Doppler Effect, calculate how long ago the light was emitted from galaxy A.

(i)  find the distance between the galaxy A and the Earth.

(j)  find the distance between the galaxy B and Earth when the light was emitted by using the result in (b), and the galaxy has a red shift of 0.080.

(k) using the result in (a) calculate how long ago was the light emitted from galaxy B.

(l) calculate the distance between galaxy A and B, when the light from galaxy A was emitted.