Chapter 25, Problem 96A

To determine

To calculate:

The speed of the galaxy the direction in which the galaxy is moving.

Answer to Problem 96A

The speed of the galaxy is $4.73\times {10}^7$ m/s and because the light which is observed has a low frequency the galaxy should move away from the Earth.

Explanation of Solution

Given:

For a distant galaxy,

Frequency: $7.29\times {10}^{14}$ Hz

Observed Frequency: $6.14\times {10}^{14}$ Hz

Formula Used:

Formula used here is,

  $f_{obs}=f\left(1-\frac{v}{c}\right)$

Where,

  $f$ : Frequency

  $f_{obs}$ : observed Frequency

  $v$ : Velocity

  $c$ : Speed of light $\left(3.0\times {10}^8\right)$ m/s

Calculation:

The formula is written as,

  $f_{obs}=f\left(1-\frac{v}{c}\right)$

Rearrange the formula to find the velocity of the distant galaxy

  $v=c\left(1-\frac{f_{obs}}{f}\right)$

Substitute all the given values in the above formula,

  $=$ $\left(3.0\times {10}^8\right)$ m/s $\times \left(1-\frac{6.14\times {10}^{14}}{7.29\times {10}^{14}}\right)$ Hz

  $=$ $\left(3.0\times {10}^8\right)\times \left(\frac{7.29\times {10}^{14}-6.14\times {10}^{14}}{7.29\times {10}^{14}}\right)$

  $v$ $=$ $4.73\times {10}^7$ m/s

Conclusion:

Hence, the speed of the galaxy is $4.73\times {10}^7$ m/s and it must move away from the Earth.