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Chapter 21: Problem 36

Suppose a galaxy is observed with a redshift equal to \(2 .\) How much has the universe expanded since that light was emitted from these galaxies?

Short Answer

Expert verified
The universe has expanded by a factor of 3 since the light was emitted.

Step by step solution

01

- Understand Redshift

Redshift is a measure of how much the wavelength of light is stretched due to the expansion of the universe. It is denoted by the symbol \(z\). In this problem, a redshift of \(z = 2\) is given.
02

- Formula for Expansion

The universe's expansion since the light was emitted can be calculated using the formula: \[ 1 + z = \frac{a_{\text{current}}}{a_{\text{emitted}}} \] where \(a_{\text{current}}\) is the current scale factor of the universe, and \(a_{\text{emitted}}\) is the scale factor when the light was emitted.
03

- Calculate Expansion

Given \(z = 2\), substitute this value into the formula: \[ 1 + 2 = \frac{a_{\text{current}}}{a_{\text{emitted}}} \] This simplifies to: \[ 3 = \frac{a_{\text{current}}}{a_{\text{emitted}}} \]
04

- Interpret the Results

The result means that the current scale factor of the universe is 3 times the scale factor when the light was emitted. Hence, the universe has expanded by a factor of 3 since the light was emitted from the galaxy.

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Key Concepts

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

Redshift
When we observe galaxies far away, their light appears redder than expected. This phenomenon is called redshift. It happens because the universe is expanding, stretching the wavelength of light as it travels through space.
Redshift is measured by the symbol \(z\). A redshift of \(z = 2\) tells us that the wavelength of light has stretched by a factor of 3 since it left the galaxy (since \(1 + z = 3\)).
Calculating redshift is crucial because it helps astronomers understand how much the universe has stretched over time.
Here’s what you need to know about the redshift:
  • Galaxies are moving away from us
  • The speed at which they move away makes their light wavelengths longer
  • Redshift (z) measures how much that light has stretched
Cosmology
Cosmology studies the universe as a whole. It includes looking at its origin, evolution, structure, and eventual fate.
A major fascination in cosmology is understanding the universe's expansion. Observing redshift in distant galaxies provides evidence for this ongoing expansion.
Essential insights from cosmology include:
  • The Big Bang theory, which posits the universe started from an extremely dense and hot point
  • The observation of cosmic microwave background radiation, which is the afterglow of the Big Bang
  • The understanding that the universe's expansion is accelerating, thanks to a mysterious force called dark energy
Scale Factor
The scale factor (\(a\)) tells us how much the universe has expanded at any point in time. It’s a key concept in cosmology for quantifying the expansion.
Regarding the original exercise, \(a_{\text{current}}\) represents the scale factor now, and \(a_{\text{emitted}}\) is the scale factor when the light left the galaxy. The formula involving redshift and the scale factor is: \[1 + z = \frac{a_{\text{current}}}{a_{\text{emitted}}}\]
Given \(z = 2\), we get \[1 + 2 = \frac{a_{\text{current}}}{a_{\text{emitted}}} = 3\]
This implies the universe has expanded three times since the light was emitted from that distant galaxy.
To recap:
  • A higher scale factor means more expansion
  • The scale factor changes over time as the universe expands
  • Seeing the scale factor helps us understand the universe's history and future

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Most popular questions from this chapter

For more details on the history of the discovery of the expanding universe, go to the American Institute of Physics' "Cosmic Journey: A History of Scientific cosmology" website (wwwaip.org/history/cosmology/). Read through the sections titled "Island Universes," "The Expanding Universe," and "Big Bang or Steady State?" Why was Albert Einstein "irritated" by the idea of an expanding universe? What was the contribution of Belgian astrophysicist (and Catholic priest) Georges Lemaitre? What is the steady-state theory, and what was the main piece of evidence against it?

The Hubble time \(\left(1 / H_{0}\right)\) represents the age of a universe that has been expanding at a constant rate since the Big Bang. Calculate the age of the universe in years if \(H_{0}=80 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\) (Note: 1 year \(=3.16 \times 10^{7}\) seconds, and \(1 \mathrm{Mpc}=3.09 \times 10^{19} \mathrm{km} .\)

Science's greatest strength is the self-correcting nature of scientific inquiry: minds can be changed in the face of new data, as described in the Process of Science Figure. Consider a modern paradigm of science such as the Big Bang, climate change, or the power source of stars. In a short paragraph, describe your current viewpoint, and give a piece of evidence that would make you change your mind if it were true. For example, Einstein believed the universe was static. Measurements of the movement of galaxies caused him to change his mind.

You observe a distant quasar in which a spectral line of hydrogen with rest wavelength \(\lambda_{\text {rest }}=121.6 \mathrm{nm}\) is found at a wavelength of \(547.2 \mathrm{nm}\). What is its redshift? When the light from this quasar was emitted, how large was the universe compared to its current size?

Which of the following was not created as a result of Big Bang nucleosynthesis? a. helium b. lithium c. hydrogen d. deuterium e. carbon
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