Question

Figure 37-27 is a graph of intensity versus wavelength for light reaching Earth from galaxy NGC 7319, which is about $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}$light-years away. The most intense light is emitted by the oxygen in NGC 7319. In a laboratory that emission is at wavelength $\mathbf{\lambda }\mathbf{=}\mathbf{513}\mathbf{}\mathbf{nm}$, but in the light from NGC 7319 it has been shifted to 525 nm due to the Doppler effect (all the emissions from NGC 7319 have been shifted). (a) What is the radial speed of NGC 7319 relative to Earth? (b) Is the relative motion toward or away from our planet?

Short answer

(a) The radial speed NGC7319 relative to Earth is 0.023c.

(b) The relative motion is away from our planet.

Step-by-step solution

Identification of given data

The wavelength of light emission in laboratory is ${\mathrm{\lambda }}_{\mathrm{l}}=513\mathrm{nm}$

The shifted wavelength of light emission is ${\mathrm{\lambda }}_{\mathrm{s}}=525\mathrm{nm}$

The speed for the variation in the colour of light from red to green is found by using the formula for Doppler shift.

Determination of radial speed for NGC7319 relative to Earth

(a)

The radial speed NGC7319 relative to Earth is given as:

$\mathrm{v}=\left(\frac{{\mathrm{\lambda }}_{\mathrm{s}}-{\mathrm{\lambda }}_{\mathrm{l}}}{{\mathrm{\lambda }}_{\mathrm{s}}}\right)\mathrm{c}$

Here, c is the speed of light.

Substitute all the values in the above equation.

$$\begin{gathered} \mathrm{v}=\left(\frac{525\mathrm{nm}-513\mathrm{nm}}{525\mathrm{nm}}\right)\mathrm{c} \\ \mathrm{v}=0.023\mathrm{c} \end{gathered}$$

Therefore, the radial speed NGC7319 relative to Earth is 0.023c.

Identification of motion of galaxy

(b)

As the line in the graph is shifted toward the larger wavelength, so the relative motion of the NGC7319 is away from our planet.