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Chapter 20: Problem 42

Assume that there are 1 trillion \(\left(10^{12}\right)\) galaxies in the universe, that the average galaxy has a mass equivalent to 100 billion \(\left(10^{11}\right)\) average stars, and that an average star has a mass of \(2 \times 10^{30} \mathrm{kg}\) a. Ignoring dark matter, how much mass (in kilograms) does the universe contain? b. If the mass of an average particle of normal matter is \(10^{-27} \mathrm{kg}\), how many particles are there in the entire universe?

Short Answer

Expert verified
The universe contains \(2 \times 10^{53}\) kg of mass and \(2 \times 10^{80}\) particles.

Step by step solution

01

- Understand the given values

Identify the given values in the problem:- Number of galaxies: \(10^{12}\)- Average mass of a galaxy: \(10^{11}\) average stars- Mass of an average star: \(2 \times 10^{30}\) kg- Mass of an average particle of normal matter: \(10^{-27}\) kg
02

- Calculate the mass of one galaxy

The mass of one galaxy is the product of the number of average stars per galaxy and the mass of an average star:\(10^{11} \text{ stars} \times 2 \times 10^{30} \text{ kg/star} = 2 \times 10^{41} \text{ kg}\)
03

- Calculate the mass of the universe

The mass of the universe is the product of the number of galaxies and the mass of one galaxy:\(10^{12} \text{ galaxies} \times 2 \times 10^{41} \text{ kg/galaxy} = 2 \times 10^{53} \text{ kg}\)
04

- Calculate the number of particles in the universe

Calculate the number of particles by dividing the mass of the universe by the mass of an average particle of normal matter:\(\frac{2 \times 10^{53} \text{ kg}}{10^{-27} \text{ kg/particle}} = 2 \times 10^{80} \text{ particles}\)

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Key Concepts

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

Galaxy Mass
Galaxies are vast collections of stars, gas, dust, and dark matter, all bound together by gravity. To understand the universe's mass, it's crucial to grasp the concept of galaxy mass. An average galaxy contains about 100 billion stars. This immense number gives us a starting point for calculating the mass of the universe. Each galaxy's mass is a product of the number of stars it hosts and the mass of an individual star. This mass is a staggering figure and plays a significant role in larger universe calculations.
Average Star Mass
The average mass of a star is key to understanding galaxy mass. In the context of our exercise, the average star's mass is given as \(2 \times 10^{30} \mathrm{kg}\). This value is based on typical star sizes found within our own galaxy, the Milky Way. By multiplying this mass with the number of stars in a galaxy, we can estimate the galaxy's total mass. Understanding the mass of stars helps in scaling up to larger astronomical entities.
Universe Particles
The universe is composed of countless particles, ranging from the lightest neutrinos to the heaviest elements formed in stars. For our calculation, we use the mass of an average particle of normal matter, which is \(10^{-27} \mathrm{kg}\). This includes protons, neutrons, and electrons. By dividing the total mass of the universe by the mass of a single particle, we can estimate the number of these particles that exist in the universe. This calculation gives us an idea of the sheer scale and quantity of matter spread across the cosmos.
Universe Calculations
Calculating the mass of the universe involves a couple of key multiplication steps. First, we calculate the mass of one galaxy by multiplying the number of stars per galaxy \(10^{11} \text{stars}\) by the mass of an average star \(2 \times 10^{30} \text{kg/star}\). This gives us \(2 \times 10^{41} \text{kg}\). Then, we multiply this result by the total number of galaxies \(10^{12}\) to get the total mass of the universe \(2 \times 10^{53} \text{kg}\). Finally, to find the number of particles, we divide this mass by the mass of an average particle \( \frac{2 \times 10^{53} \text{kg}}{10^{-27} \text{kg/particle}} = 2 \times 10^{80} \text{ particles}\).
Dark Matter Exclusion
In our calculations, we have excluded dark matter. Dark matter makes up about 27% of the universe's mass-energy content. It does not emit light or energy, making it invisible and detectable only through its gravitational effects. By excluding dark matter, our calculations focus solely on visible, normal matter. This provides a clearer understanding of the universe's mass without the complexities added by dark matter. However, to get a complete picture, dark matter must also be considered in broader astronomical calculations and models.

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Most popular questions from this chapter

Dark matter is different from normal matter because a. it doesn't emit light. b. it doesn't absorb light. c. it doesn't scatter light. d. all of the above

It is likely that most galaxies contain supermassive black holes, yet in many galaxies there is no obvious evidence for their existence. Why do some black holes reveal their presence while others do not?

The differences among various types of AGNs are caused by a. the type of the host galaxy. b. the size of the central black hole c. the amount of dark matter in the galaxy's halo. d. the viewing angle.

Name and describe a common, everyday object that appears so dissimilar when viewed from different angles that from these different views you might think it was actually a different object.

\(\mathbf{T} / \mathbf{F}: A\) spiral galaxy's dark matter is distributed spherically.
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