Question

The mass of the Sun is \(2 \cdot 10^{30} \mathrm{~kg}\), and the Sun contains more than \(99 \%\) of all the mass in the solar system. Astronomers estimate there are approximately 100 billion stars in the Milky Way and approximately 100 billion galaxies in the universe. The Sun and other stars are predominantly composed of hydrogen; a hydrogen atom has a mass of approximately \(2 \cdot 10^{-27} \mathrm{~kg}\). a) Assuming that the Sun is an average star and the Milky Way is an average galaxy, what is the total mass of the universe? b) Since the universe consists mainly of hydrogen, can you estimate the total number of atoms in the universe?

Short answer

Question: Estimate the total mass of the universe and the total number of hydrogen atoms in the universe, given the mass of the Sun is \(2 \cdot 10^{30} \mathrm{~kg}\), the mass of a hydrogen atom is \(2 \cdot 10^{-27} \mathrm{~kg}\), and there are an estimated 100 billion stars in a galaxy and 100 billion galaxies in the universe. Answer: The total mass of the universe is approximately \(2 \cdot 10^{50} \mathrm{~kg}\), and the total number of hydrogen atoms in the universe is approximately \(10^{77}\).

Step-by-step solution

a) Calculating the total mass of the universe

Given the mass of the Sun (\(2 \cdot 10^{30} \mathrm{~kg}\)), and the number of stars in a galaxy (100 billion) and the number of galaxies (100 billion), we can assume that the Sun is an average star and the Milky Way is an average galaxy. To find the total mass of the universe, we can multiply the mass of the Sun by the number of stars in a galaxy, and then multiply this by the number of galaxies in the universe: Total mass of the universe = Mass of the Sun x Number of stars in a galaxy x Number of galaxies in the universe Total mass of the universe = \((2 \cdot 10^{30} \mathrm{~kg}) \times (100 \times 10^9) \times (100 \times 10^9)\) Total mass of the universe = \(2 \cdot 10^{30} \times 10^{20} \mathrm{~kg}\) The total mass of the universe is approximately \(2 \cdot 10^{50} \mathrm{~kg}\).

b) Estimating the total number of atoms in the universe

Since the universe consists mainly of hydrogen and we are given the mass of a hydrogen atom, we can estimate the total number of hydrogen atoms in the universe by dividing the total mass of the universe by the mass of a hydrogen atom: Total number of hydrogen atoms in the universe = Total mass of the universe / Mass of a hydrogen atom Total number of hydrogen atoms in the universe = \((2 \cdot 10^{50} \mathrm{~kg}) / (2 \cdot 10^{-27} \mathrm{~kg})\) Total number of hydrogen atoms in the universe = \(10^{77}\) So the universe contains approximately \(10^{77}\) hydrogen atoms.

Key concepts

Mass of the Universe

In astrophysics, the mass of the universe is a crucial concept that helps us understand the scale and nature of everything that exists. The universe is incredibly massive, consisting of countless stars, galaxies, and other celestial bodies. To estimate the mass of the universe, we start by considering an average galaxy, like the Milky Way, which consists of about 100 billion stars. If we assume the Sun is an average-sized star, with a mass of about \(2 \times 10^{30} \text{ kg}\), we can calculate the total mass.

By multiplying the mass of the Sun by the number of stars in an average galaxy and then multiplying by the number of galaxies (again around 100 billion), we get the total mass of the universe. This calculation gives us:\[2 \times 10^{30} \times 10^{20} = 2 \times 10^{50} \text{ kg}\]This estimation assumes that all stars are similar to the Sun in mass, which simplifies the real complexity of the universe, but provides a helpful approximation for understanding its immensity.

Hydrogen Atom Mass

Understanding the mass of a hydrogen atom is fundamental in estimating the mass distribution in the universe. Hydrogen is the most abundant element in the universe, making up about 75% of its normal matter. The mass of a single hydrogen atom is approximately \(2 \times 10^{-27} \text{ kg}\). This is calculated by taking both the proton and electron into account, although the electron's mass is negligible compared to that of the proton.

Hydrogen atoms serve as the building blocks of stars which, through nuclear fusion, transform into heavier elements over time. Knowing the mass of a hydrogen atom allows astronomers to make educated estimates about the amount of matter in the universe. To manage such large numbers, scientific notation is usually employed. For instance, expressing small or large quantities in powers of ten makes complex calculations more tractable.

Number of Stars in the Galaxy

In our galaxy, the Milky Way, there are estimated to be around 100 billion stars. These stars vary greatly in size, mass, and characteristics. Some are much larger and more massive than our Sun, while others are smaller and fainter.

Stars are made primarily of hydrogen gas, which condenses under gravity to form a star. Once there is enough pressure and temperature, nuclear fusion starts. This process fuels the star and leads to the production of various elements over the lifecycle of a star.

• Stars are usually born in clusters within nebulae.
• They can live for millions to billions of years depending on their mass.
• Some end their lives in supernova explosions, while smaller stars may become white dwarfs or neutron stars.

Understanding the number and variety of stars in our galaxy helps us get a sense of the vastness and diversity of the universe.

Galaxies in the Universe

The universe is composed of an astonishing number of galaxies, roughly estimated to be around 100 billion. Each galaxy is unique in terms of size, structure, and the types of celestial bodies it contains. Galaxies are massive systems bounded by gravity and generally comprise stars, star clusters, interstellar gas and dust, and dark matter.

There are several types of galaxies, such as spiral, elliptical, and irregular. Our galaxy, the Milky Way, is a barred spiral galaxy, meaning it has a central bar-shaped structure composed of stars. This wide range of galaxy types adds to the complexity and variety of the universe.

• Spiral galaxies, like the Milky Way, often have well-defined spiral arms.
• Elliptical galaxies are more rounded and three-dimensional without specific structure.
• Irregular galaxies lack a discernible shape and are often found near larger galaxies.

The study of galaxies helps astronomers understand the evolution of the universe from the Big Bang to the present day, offering insights into past processes and future developments.