It is possible to detect Doppler shifts in the light emitted from each side of a rapidly spinning star. Suppose the light from a nearby star of radius $2.5 \times 10^{8} \mathrm{~km}$ is blue-shifted on one side of the star and red-shifted on the other side. Assume the center of mass of the star is stationary relative to Earth. If the rotational period of the star is $72 \mathrm{~h}$ and the star emits (unshifted) light of wavelength $525 \mathrm{~nm}$, what is the wavelength of the light received on Earth from the side of the star rotating toward us?
A) $504 \mathrm{~nm}$
B) $520 \mathrm{~nm}$
C) $546 \mathrm{~nm}$
D) $530 \mathrm{~nm}$
E) $514 \mathrm{~nm}$
F) $536 \mathrm{~nm}$

Question

Quizplus · Accepted Answer

The Doppler shift formula for light is $\Delta \lambda / \lambda = v / c$, where $v$ is the velocity of the star's surface, and $c$ is the speed of light. The velocity $v$ can be calculated using $v = 2\pi R / T$, where $R$ is the radius and $T$ is the period. Substituting the given values, we find the shifted wavelength to be approximately $514 \mathrm{~nm}$.

It Is Possible to Detect Doppler Shifts in the Light 2.5×108 km2.5 \times 10^{8} \mathrm{~km}2.5×108 km

It Is Possible to Detect Doppler Shifts in the Light $2.5 \times 10^{8} \mathrm{~km}$