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 × 10⁸ 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 star emits light of wavelength 525 nm that is shifted, in the received light, to 523 nm on one side of the star and to 527 nm on the other side, what is the rotational period of the star? A) 34 days B) 32 days C) 24 days D) 16 days

Question

Quizplus · Accepted Answer

The change in wavelength due to the Doppler effect can be used to calculate the velocity of the star's surface. The formula for the Doppler shift in light is $\Delta \lambda / \lambda = v / c$, where $\Delta \lambda$ is the change in wavelength, $\lambda$ is the original wavelength, $v$ is the velocity of the object, and $c$ is the speed of light. Given $\lambda = 525$ nm, $\Delta \lambda = 2$ nm (from 525 nm to 527 nm or from 525 nm to 523 nm), we can solve for $v$. The rotational velocity $v$ is related to the rotational period $T$ by the formula $v = 2\pi r / T$, where $r$ is the radius of the star. Given $r = 2.5 \times 10^8$ km, we can solve for $T$ using these relationships, leading to a rotational period of approximately 16 days.

It Is Possible to Detect Doppler Shifts in the Light