Good Case Study About Doppler Shift

The Doppler Effect occurs when a source emitting any type of wave (e.g. sound, light) and an observer move towards or away from an observer. For example, light waves emitted from a source moving towards the observer will have shorter wavelengths and are said to have “blueshifted.” Conversely, light waves emitted by a source that is relatively moving away from the observer will be perceived as having longer wavelengths or have “redshifted” (Prather 73; Young and Freedman pp. 533-538).

Question 1

It is said to have blueshifted because of the shifting to shorter wavelengths.
The source emitting the light waves is a star that is moving closer to, or towards, the observer.
Question 2
Conversely, in situation B, the light source is moving away from the observed.
Since the light is shifted to longer wavelengths, it is said to be redshifted.
The observer will perceive light that is shifted to longer wavelengths.
Question 3
Meanwhile, in situations A and D the observed light is neither shifted to a longer nor shorter wavelength. Both the source and the observer in situation A are not moving—hence, the distance does not change between them. On the other hand, while the light source in situation D is moving, its motion is actually perpendicular to the line of sight of the observer, which does not change the relative distance between them. In both situations the observed light does not have shifted wavelengths.

Question 4

If the solar system moves in the Milky Way towards three stars A, C, and B (arranged closest to farthest from us, the observer), light coming from all stars will be perceived as blueshifted.

All of their lights will be shifted to shorter wavelengths.

Question 5
The color of a star is not enough evidence to determine its movement relative to an observer. The Doppler Effect explains a shift in the emitted light’s wavelengths is caused by the movement of the source relative to the observer (Landsberg and Sherman pp. 1-7). Therefore I agree with Student 2 that in order to verify if the stars Betelgeuse and Rigel are moving towards or away from us, the stars’ absorption spectra must be observed for shifts in wavelengths of the lines.
The three given spectra are said to each correspond to three different situations: (1) the star is not moving relative to the observer; (2) the star is moving towards the observer; and (3) the star is moving away from the observer. Hence, it can be inferred that line spectrum A, which contains lines in between two shifts, is the baseline. Thus, spectrum A corresponds to a star that is not moving relative to the observer.

Question 6

Consequently, using spectrum A as a reference point, we can determine which spectrum corresponds to which moving star. Since spectrum C has lines shifted to shorter wavelengths (towards the blue end of the spectrum), it corresponds to the star that is moving towards the observer.

Question 7

Conversely, since spectrum B has lines shifted to longer wavelengths (i.e. towards the red end of the spectrum), it corresponds to the star that is moving away from the observer.
The absorption line spectrum may also be used to determine the relative speed of stars moving towards or away from the observer (Prather 74).

Question 8

Line spectrum E is observed to have the greatest Doppler Shift compared to other two and relative to spectrum F, which serves as the reference point. Since Doppler shift is directly proportional to the speed of moving sources, it can be concluded that the star corresponding to the line spectrum E (i.e. star E) has the fastest speed among the three moving stars. Furthermore, the lines of spectrum E shifted to the red end of the spectrum. Hence, star E is moving away from the observer.

Question 9

The star corresponding to the line spectrum G (i.e. star G) has the slowest speed, because its line spectrum shows the least Doppler Shift relative to line spectrum F. Also, the lines of star G’s spectrum is shifted to the blue end. Hence, star G is moving towards the observer.

Question 10

An important line in a star’s absorption spectrum can be used to determine its movement relative to the observer. This important line is measured at a wavelength of 656 nm for stars that are at rest or are stationary.
Stars H and L both have this line measured at wavelengths shorter than 656 nm, at 649 nm and 647 nm, respectively. Hence, stars H and L are determined to give off light that appears blueshifted.
Conversely, stars I and K have line wavelength measurements greater than 656 nm, that is at 660 nm and 658 nm, respectively. Thus, stars I and K emit light that is perceived as redshifted.

Since it has already been determined to give off light that appears blueshifted, star L is moving towards the observer.

Question 11
Since the space probe (the source) is moving away from planet A (the observer), the radio signals will be perceived as redshifted.
Conversely, the probe is moving towards planets B and E; hence, radio signals from the space probe will appear blueshifted when observed from these planets.
Not all planets will receive radio signals from the space probe that are Doppler shifted. Since the space probe is moving perpendicular to planets C and D, no change in the relative distance between the source and the observer occurs. Thus, planets C and D will receive radio signals that are neither redshifted nor blueshifted.
Since the space probe is moving away from planet A and towards planet B, the radio signals will appear to have longer wavelengths when received by planet A and will have shorter wavelengths when received by planet B. Despite the source’s movement in different directions both planets A and B will experience the same Doppler shift of the radio signals because the speed of the source is constant (i.e. it moves away from planet A at the same speed it moves towards planet B).
The space probe is moving towards planets B and E. The radio signals they will receive will both have shorter wavelengths. The Doppler shift they both observe will be the same, because the space probe is moving towards them at the same speed.

References:

Prather, Edward E. Lecture-Tutorials for Introductory Astronomy. 2nd edition. Boston : Pearson, 2007. 74-77. Print.
Landsberg, Randy and Sherman, Reid. “Doppler Shift Day Lab.” Yerkes Summer Institute, 2005. 1-7. Print.
Young, H. D., Freedman, R. A. and Ford, A. L. Sears and Zemansky’s University Physics with Modern Physics. 13th Edition. San Francisco, CA: Addison-Wesley by Pearson. 533-538. Print.