Question

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

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

Step-by-step solution

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.

Calculate the change in wavelength

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

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, \(V = (3×10^8 m/s) * (0.27×10^-9 m) / (396.85×10^-9 m) = 2.04×10^5 m/s\). This result is in meters per second. To convert it into kilometers per hour, we multiply by 3.6, which gives us \(7.34×10^8 km/h\). 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.

Key concepts

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.