How fast and in what direction is a star moving if its spectrum contains a line that shifts from 486.2 nm to 486.3 nm?
A)61.7 km/s away from you
B)61.7 km/s toward you
C)562 m/s away from you
D)562 m/s toward you

Question

Quizplus · Accepted Answer

The star is moving away from you because the spectral line has redshifted (shifted to a longer wavelength), indicating that the source of the light is moving away from the observer. The speed can be calculated using the Doppler effect formula for light: $v = c \frac{\Delta \lambda}{\lambda}$, where $v$ is the velocity of the star relative to the observer, $c$ is the speed of light ($3 \times 10^8$ m/s), $\Delta \lambda$ is the change in wavelength (0.1 nm or $0.1 \times 10^{-9}$ m), and $\lambda$ is the original wavelength (486.2 nm or $486.2 \times 10^{-9}$ m). Plugging in the numbers gives $v \approx 61.7$ km/s.

How Fast and in What Direction Is a Star Moving