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Chapter 2: Problem 54

The light from galaxy NGC 22 I consists of a recognizable spectrum of wavelengths. However, all are shifted tow ard the shorter-wavelength end of the spectrum. In particular, the calcium "line" ordinarily observed at \(396.85 \mathrm{nm}\) is observed at \(396.58 \mathrm{nm}\). Is this galaxy moving toward or away from Earth? At what speed?

Short Answer

Expert verified
The galaxy NGC 22 I is moving towards the Earth with a speed of approximately \(7.34脳10^8 km/h\).

Step by step solution

01

Determine the direction of motion

When light from distant objects is shifted towards the shorter-wavelength end (blue end) of the spectrum, it indicates the object is moving closer to the observer. This is known as blueshift. Therefore, the galaxy NGC 22 I is moving towards Earth.
02

Calculate the change in wavelength

Subtract the observed wavelength from the ordinary wavelength to calculate the change in wavelength, which gives \(\Delta \lambda = 396.85 nm - 396.58 nm = 0.27 nm\)
03

Determine the speed

Use the formula for the Doppler Effect to calculate the speed of the galaxy. This formula is given by \(V = c \cdot \Delta \lambda / \lambda\) where \(c\) is the speed of light, \(\Delta \lambda\) is the change in wavelength and \(\lambda\) is the ordinary wavelength. Hence, \(V = (3脳10^8 m/s) * (0.27脳10^-9 m) / (396.85脳10^-9 m) = 2.04脳10^5 m/s\). This result is in meters per second. To convert it into kilometers per hour, we multiply by 3.6, which gives us \(7.34脳10^8 km/h\). Note that this speed is an approximation, and it's important to remember that the speed of light and the observed wavelength can change depending on various factors.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Blueshift
When observing the universe, astronomers frequently encounter a phenomenon called 'blueshift'. This occurs when the light from an astronomical object, such as a galaxy or star, appears to have been shifted towards the shorter-wavelength, or blue, end of the light spectrum. Understand that light is a wave, and as with any wave, its properties can change as the source of the light moves relative to an observer.

Blueshift is a key indicator that an object is moving closer to us. This shift is outlined by the Doppler Effect, which also applies to sound waves; you might have noticed the change in pitch of a passing siren as it moves towards and then away from you. For light, a move towards the blue end means the wavelengths are getting compressed as the source approaches, allowing us to infer not only the direction but also the velocity of the moving object when studied in conjunction with spectral lines.
Spectral lines
Spectral lines are like the fingerprints of elements in space, each element emitting or absorbing light at specific wavelengths that act as incredibly precise indicators for their presence in distant stars and galaxies. When astronomers analyze light from an astronomical object, they observe these lines at certain expected positions in the spectrum. However, when the object is in motion relative to us, these lines will appear shifted from their usual positions.

Understanding Spectral Shifts

For example, if a star is moving away from Earth, the lines shift towards the red end (redshift), and conversely, if it's approaching us, towards the blue end (blueshift). The analysis of these shifts allows astronomers to calculate not just the speed and direction of a star or galaxy, but also to deduce valuable information about the expansion of the universe and the behavior of distant celestial objects.
Galaxy motion
A galaxy's motion through space can reveal much about the underlying dynamics of the cosmos. By understanding the speed and direction of a galaxy's movement, astronomers can make inferences about cosmic phenomena such as the expansion of the Universe, gravitational interactions between galaxies, and even the distribution of dark matter. This movement also affects the light that reaches us from these galaxies, observed through the aforementioned Doppler shifts in their spectral lines.

To establish the motion, astronomers measure the redshift or blueshift and use this data to calculate the velocity of a galaxy either towards or away from us, contributing vastly to our understanding of cosmic evolution. Analyses of galaxy motion have even led to groundbreaking discoveries like the existence of cosmic dark flow and the accelerating expansion of the universe.
Light wavelength
The wavelength of light determines its color in the visible spectrum, with longer wavelengths corresponding to red and shorter wavelengths to blue. In astronomy, understanding the wavelength of light is crucial for several reasons. For one, it helps astronomers determine the chemical composition of celestial bodies since different elements emit and absorb light at different wavelengths.

Measuring Astronomical Distances

Light wavelength also plays a role in measuring astronomical distances. For instance, the standard candles method, which is used to determine how far away a galaxy is from Earth, relies on observed light wavelengths. Moreover, shifts in wavelengths of astronomical objects due to the Doppler Effect help determine their speed and motion. By understanding the complex relationship between light wavelength and astronomical phenomena, we gain a deeper insight into the workings of the universe.

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Most popular questions from this chapter

Write a C++ function prototype for a function that belongs to each of the following sets. a) string \(^{\text {string }}\) b) boot \(^{\text {float } \times \text { float }}\) c) float \(^{\text {int } t^{\text {int }}}\)

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Explain to your friend, who is willing to accept that light moves at the same speed in any frame, why clocks on a passing train are not synchronized. If it helps, assume that Anna is at the middle of the train.

If an object actually occupies less space physically when moving, it cannot depend on the direction we define as positive. As we know, an object aligned with the direction of relative motion is contracted whether it is fixed in frame \(S\) and viewed from \(S^{\prime}\), or the other way around. Use this idea to argue that distances along the \(y\) - and \(y^{\prime}\) -axes cannot differ at all. Consider a post of length \(L_{0}\) fixed in frame \(S\), jutting up from the origin along the \(+y\) -axis, with a saw at the top poised to slice off anything extending any higher in the passing frame \(S\). Also consider an identical post fixed in frame \(S\). What happens when the origins cross?

In a television picture tube, a beam of electrons is sent from the back to the front (screen) by an electron gun. When an electron strikes the screen, it causes a phosphor to glow briefly. To produce an image across the entire screen. the beam is electrically deflected up and down and left and right. The beam may sweep from left to right at a speed greater than \(c\). Why is this not a violation of the claim that no information may travel faster than the speed of light?
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