# Chapter 22 - Problems - Page 865: 55

The star is moving at a speed of $682~km/s$ with respect to the Earth. Since the observed wavelength is longer than the emitted wavelength, the star must be moving away from the Earth.

#### Work Step by Step

Let $\lambda_0 = 659.6~nm$ and let $\lambda' = 661.1~nm$ We can find the speed of the star $v$ with respect to the Earth: $\frac{v}{c} = \frac{\lambda'-\lambda_0}{\lambda_0}$ $v = \frac{\lambda'-\lambda_0}{\lambda_0}~c$ $v = \frac{661.1~nm-659.6~nm}{659.6~nm}~(3.0\times 10^8~m/s)$ $v = 6.82\times 10^5~m/s$ $v = 682~km/s$ The star is moving at a speed of $682~km/s$ with respect to the Earth. Since the observed wavelength is longer than the emitted wavelength, the star must be moving away from the Earth.

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