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Chapter 19: Problem 8

The simplest way to estimate the age of the universe is from a. using the slope of the Hubble law. b. the age of Moon rocks. c. models of stellar evolution. d. measurements of the abundances of elements.

Short Answer

Expert verified
a. using the slope of the Hubble law.

Step by step solution

01

- Identify Key Concept

The exercise asks for the simplest way to estimate the age of the universe. It provides four options which include different astronomical and scientific techniques.
02

- Analyze Each Option

a. Using the slope of the Hubble law: This involves calculating the Hubble constant, which gives the rate of expansion of the universe. By inverting the Hubble constant, one can estimate the age of the universe. b. The age of Moon rocks: This method dates the formation of lunar material but does not directly estimate the age of the universe. c. Models of stellar evolution: These models help estimate the age of stars but require complex calculations. d. Measurements of the abundances of elements: This involves studying the chemical composition of the universe, which infers the time passed since certain processes but is indirect.
03

- Select the Simplest Method

Among the given methods, using the slope of the Hubble law is the simplest. It directly relates the rate of expansion of the universe to its age using a straightforward mathematical relationship.

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Key Concepts

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

Hubble law
The Hubble law is a critical concept for understanding our universe's expansion. It states that the speed at which galaxies move away from us is proportional to their distance. This law is formulated as: \[v = H_0 \times d\] where:
  • \(v\) is the velocity of a galaxy moving away
  • \(d\) is the distance of the galaxy from us
  • \(H_0\), the Hubble constant, is the proportionality factor
This observation implies that the universe is expanding uniformly. By measuring the redshifts of galaxies (their speed), we can determine their distances and use Hubble's law to understand this expansion.
Hubble constant
The Hubble constant (\(H_0\)) is pivotal in cosmology. It quantifies the rate of the universe's expansion. To estimate the age of the universe, we use the inverse of the Hubble constant: \[ t = \frac{1}{H_0} \]. This simplifies to the notion that the universe's age is inversely related to its rate of expansion. Measuring \(H_0\) involves meticulous observation of distant galaxies and their velocities. Precise values of \(H_0\) come from several sources, including the Cosmic Microwave Background radiation and Type Ia supernovae. A more precise \(H_0\) helps us understand not only the universe's age but its entire expansion history.
Universe expansion
When we talk about the universe expanding, it means space itself is stretching, and galaxies are moving away from each other. This concept emerged from the observation of redshifts, where the light from galaxies shifts to longer (redder) wavelengths. The further away the galaxy, the faster it seems to move from us. This consistent pattern formed the basis of Hubble's discovery. Universe expansion underpins the ideas of the Big Bang and cosmic inflation. It also helps explain the observable distribution of galaxies and other large-scale structures. This ongoing expansion impacts everything from the life cycle of stars to the eventual fate of the universe itself.

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Most popular questions from this chapter

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. Assuming an \(H_{0}\) value of \(70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\) and a constant rate of expansion, calculate the age of the universe in years. How is the age different if \(H_{0}=75 \mathrm{km} / \mathrm{s} / \mathrm{Mpc} ?\left(\text { Note: } 1 \text { year }=3.16 \times 10^{7}\right.\) seconds and \(1 \mathrm{Mpc}=3.09 \times 10^{19} \mathrm{km} .\)

Assume that the most distant galaxies have a redshift \(z=10\) The average density of normal matter in the universe today is \(4 \times 10^{-28} \mathrm{kg} / \mathrm{m}^{3} .\) What was its density when light was leaving those distant galaxies? (Hint: Keep in mind that volume is proportional to the cube of the scale factor.)

Suppose you observe two galaxies: one at a distance of \(10.7 \mathrm{Mpc}\) with a recessional velocity of \(580 \mathrm{km} / \mathrm{s}\), and another at a distance of 337 Mpc with a radial velocity of 25,400 \(\mathrm{km} / \mathrm{s}\). a. Calculate the Hubble constant ( \(H_{0}\) ) for each of these two observations. b. Which of the two calculations would you consider to be more trustworthy? Why? c. Estimate the peculiar velocity of the closer galaxy. d. If the more distant galaxy had this same peculiar velocity, how would your calculated value of the Hubble constant change?

A distant galaxy has a redshift \(z=5.82\) and a recessional velocity \(v_{r}=287,000 \mathrm{km} / \mathrm{s}\) (about 96 percent of the speed of light). a. If \(H_{\mathrm{o}}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\) and if Hubble's law remains valid out to such a large distance, then how far away is this galaxy? b. Assuming a Hubble time of 13.7 billion years, how old was the universe at the look-back time of this galaxy? c. What was the scale factor of the universe at that time?

When they look into the universe, astronomers observe that nearly all galaxies are moving away from the Milky Way. This observation suggests that a. the Milky Way is at the center of the universe. b. the Milky Way must be at the center of the expansion. c. the Big Bang occurred at the location of the Milky Way. d. an observer in a distant galaxy would make the same observation.
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