How Does Galaxy Rotation and Recession Affect Observed Light Frequencies?

[gamesandmore]

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the galactic center is receding from the Earth at a relative speed of uG = 1.5e6 m/s. Relative to the center, the tangential speed is vT = 0.3e6 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 than the emitted frequency of 6.400e14 Hz.

Vt = wr
fo = fs (1 +- vrel/c)

No idea where to start

 

[Kurdt]

I am assuming that you have to work out what the measured frequencies of A and B are given their emitted frequency? You have the equation for finding the observed frequency compared to the emitted frequency:

[tex] f_o=f_s \left(1+\frac{v}{c}\right)[/tex]

What is the relative velocity of points A and B from the Earth?

 

[ogb p]

I would first analyze the given information and try to understand the phenomenon described. Based on the provided data, it seems that we are dealing with the Doppler effect, which is the change in frequency of a wave (in this case, light) due to relative motion between the source and the observer.

The fact that the galaxy is both rotating and receding from the Earth suggests that the light coming from different regions of the galaxy will have different frequencies when measured on Earth. This is because the speed at which the light is moving towards or away from Earth is different for different regions of the galaxy.

The equation Vt = wr is the formula for tangential velocity, where w is the angular velocity and r is the distance from the center. This equation explains why the tangential speed at locations A and B is the same, as they are equidistant from the center.

The equation fo = fs (1 +- vrel/c) is the formula for the Doppler effect, where fo is the observed frequency, fs is the emitted frequency, vrel is the relative velocity between the source and the observer, and c is the speed of light. This equation explains why the frequencies of light from regions A and B are not the same and are different from the emitted frequency. The relative speed of the galactic center (1.5e6 m/s) is much larger than the tangential speed (0.3e6 m/s), so we can assume that the observed frequencies will be significantly different from the emitted frequency.

In conclusion, the phenomenon described in the content is a result of the relative motion between the distant galaxy and the Earth, causing different regions of the galaxy to have different observed frequencies of light. This is a common occurrence in astronomy and is important for understanding the properties and behavior of celestial objects. Further analysis and research on this phenomenon could provide valuable insights into the nature of distant galaxies.