earth at a relative speed of ug = 1.30 x 106 m/s. Relative to the center, the tangential speed is vT = 0.350 x 106 m/s for locations A and B, which are equidistant from the center. When the frequencies of the light coming from regions A and B are measured on earth, they are not the same and each is different from the emitted frequency of 7.691 x 1014 Hz. Find the measured frequency for the light from (a) region A and (b) region B. (Give your answer to 4 significant digits. Use 2.998 x 10° m/s as the speed of light.) Galaxy Earth

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**Explanation of Galaxy Motion and Frequency Measurement**

A distant galaxy is simultaneously rotating and receding from the Earth. In the illustration, the galactic center is moving away from Earth at a relative speed of \( u_G = 1.30 \times 10^6 \, \text{m/s} \). The tangential speed, relative to the center, is \( v_T = 0.350 \times 10^6 \, \text{m/s} \) for both locations A and B, which are equidistant from the galactic center.

The measured light frequencies from regions A and B differ from each other and from the emitted frequency of \( 7.691 \times 10^{14} \, \text{Hz} \). The task is to determine the measured frequency of light from:

(a) Region A  
(b) Region B  

**Calculation Requirement:**

Provide answers accurate to four significant digits, using \( 2.998 \times 10^8 \, \text{m/s} \) as the speed of light.

**Diagram Description:**

- The diagram illustrates a galaxy with a spiral structure.
- The galaxy's center is marked, and two opposite points, A and B, are labeled on the spiral arms, denoting regions of interest.
- An arrow, \( u_G \), points vertically upward from the galaxy, indicating the galaxy's recession speed relative to Earth.
- Two smaller arrows labeled \( v_T \) point tangentially from points A and B, illustrating the rotational speed at these regions.
- A vertical line extends from the Earth to the center of the galaxy, representing the line of sight.
Transcribed Image Text:**Explanation of Galaxy Motion and Frequency Measurement** A distant galaxy is simultaneously rotating and receding from the Earth. In the illustration, the galactic center is moving away from Earth at a relative speed of \( u_G = 1.30 \times 10^6 \, \text{m/s} \). The tangential speed, relative to the center, is \( v_T = 0.350 \times 10^6 \, \text{m/s} \) for both locations A and B, which are equidistant from the galactic center. The measured light frequencies from regions A and B differ from each other and from the emitted frequency of \( 7.691 \times 10^{14} \, \text{Hz} \). The task is to determine the measured frequency of light from: (a) Region A (b) Region B **Calculation Requirement:** Provide answers accurate to four significant digits, using \( 2.998 \times 10^8 \, \text{m/s} \) as the speed of light. **Diagram Description:** - The diagram illustrates a galaxy with a spiral structure. - The galaxy's center is marked, and two opposite points, A and B, are labeled on the spiral arms, denoting regions of interest. - An arrow, \( u_G \), points vertically upward from the galaxy, indicating the galaxy's recession speed relative to Earth. - Two smaller arrows labeled \( v_T \) point tangentially from points A and B, illustrating the rotational speed at these regions. - A vertical line extends from the Earth to the center of the galaxy, representing the line of sight.
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