ASTRONOMY PHYS-1704: The Scale of the Cosmos – Space and Time

Introduction to Astronomy: PHYS-1704

• Definition of Astronomy: Astronomy is more than just the study of planets, stars, and galaxies; it is the study of the entire universe in which humanity resides.

• The Boundless Nature of Study: While humanity is currently confined to a small planet orbiting an average star, the study of astronomy allows us to transcend these physical boundaries. It helps define where we are in the universe and provides insight into what we are.

• The Scientific Space-Time Machine: Our imagination serves as the key to discovery, allowing astronomy to function as a space-time machine:     * The Past: We can travel back in time to observe the formation of the Sun and Earth, the birth of the first stars, and the ultimate creation of the universe.     * The Future: We can project forward to witness the eventual death of the Sun and the withering of the Earth.

Key Vocabulary and Definitions

• Star: A large, glowing ball of gas that generates heat and light through the process of nuclear fusion.

• Planet: A moderately large object that orbits a star and shines primarily by reflected light.     * Composition: Planets can be rocky, icy, or gaseous.     * 2006 Solar System Definition: To be classified as a planet, an object must orbit the Sun, be large enough for its own gravity to make it round, and must dominate the neighborhood around its orbit.

• Moon (or Satellite): An object that orbits a planet. A specific example is Ganymede, which orbits Jupiter.

• Asteroid: A relatively small and rocky object that orbits a star (e.g., the asteroid Ida).

• Comet: A relatively small and icy object that orbits a star. Comets typically feature a nucleus, a coma of escaping gas, a dust tail, and a plasma tail.

• Solar (Star) System: A star and all the material that orbits it, including its planets and moons.

• Nebula: An interstellar cloud consisting of gas and/or dust.

• Galaxy: A vast "island" of stars in space, held together by gravity and orbiting a common center (e.g., M31, the Andromeda Galaxy).

• Universe: The sum total of all matter and energy, encompassing everything within and between all galaxies.

• Atom: The microscopic "building blocks" of all chemical elements.

Our Cosmic Origins and Life Cycle

• The Big Bang and Expansion: The universe began in a hot, dense state called the Big Bang and has been expanding ever since.

• Galaxy Formation: Within a few billion years of the Big Bang, gravity caused local concentrations of matter to collapse into galaxies, while the universe continued its overall expansion.

• Cosmic Recycling Plants: Galaxies like the Milky Way function as recycling centers. Stars form from clouds of gas and dust; they shine using energy from nuclear fusion, which also creates heavier elements from lighter ones. When stars die, they return this processed material to interstellar space.

• Stellar Death: Massive stars explode at the end of their lives, scattering newly produced elements into space.

• Planet Formation: A star forms at the center of a collapsing cloud of gas and dust. Planets may subsequently form within the spinning disk that surrounds the young star.

• The Origin of Earth: The Earth was constructed from elements produced in stars that lived and died in the Milky Way before our solar system even formed. As the saying goes, we are "star stuff."

The Relationship Between Light, Distance, and Time

• The Finite Speed of Light: Light travels at a constant speed of approximately $300,000\,km/s$.

• Looking Back in Time: Because light takes time to travel, we see objects as they were in the past. The farther away an object is in distance, the further back we see it in time.

• Light Travel Times:     * Moon: $1\text{ second}$     * Sun: $8\text{ minutes}$     * Sirius: $8\text{ years}$     * Andromeda Galaxy: $2.5\text{ million years}$

• Seeing the Andromeda Galaxy: When we photograph Andromeda, we see it as it looked $2.5\text{ million years}$ ago. We will not be able to see what it looks like "now" for another $2.5\text{ million years}$.

• The Light-Year (ly):     * Definition: A light-year is a unit of distance, not time. It is the distance light travels in one year.     * Approximate Value: About $10\text{ trillion km}$ (or $6\text{ trillion miles}$).     * Mathematical Derivation of 1 ly:         1. In $1\text{ second}$, light travels $300,000\,km$.         2. In $1\text{ minute}$ ($60\text{ seconds}$): $300,000\,km \times 60 = 18\text{ million } km$.         3. In $1\text{ hour}$ ($60\text{ minutes}$): $18\text{ million } km \times 60 = 1.08\text{ billion } km$.         4. In $1\text{ day}$ ($24\text{ hours}$): $1.08\text{ billion } km \times 24 = 25.92\text{ billion } km$.         5. In $1\text{ year}$ ($365\text{ days}$): $25.92\text{ billion } km \times 365 = 9.46\text{ trillion } km$.         6. Final constant: $1\,ly = 9.46 \times 10^{12}\,km$ (or $9,460,000,000,000\,km$).

Limits of the Observable Universe

• The Age Conflict: If the universe is $14\text{ billion years}$ old, we can see objects up to $14\text{ billion light-years}$ away.

• The 15 Billion ly Limit: We cannot see a galaxy $15\text{ billion light-years}$ away because looking that far involves looking to a time before the universe existed. Even in principle, nothing is visible at that distance.

• Observable Radius: For a universe estimated to be $13.8\text{ to } 14\text{ billion years}$ old, our observable universe is limited to a radius of approximately $14\text{ billion light-years}$.

The Cosmic Calendar

• Concept: Devised by Carl Sagan, the cosmic calendar compresses the entire $13.8\text{ billion year}$ history of the universe into a single calendar year.

• Time Scale: One month on the calendar represents approximately $1\text{ billion real years}$.

• Key Milestones:     * January 1 (Midnight): The Big Bang occurs.     * Late February / Early March: The Milky Way Galaxy starts to coalesce (estimated age up to $13\text{ billion years}$).     * Mid-August: Our solar system begins to form.     * Late September: Primitive life emerges on Earth.     * Mid-December: Complex living structures, such as invertebrate life, form.     * December 25: Dinosaurs roam the Earth.     * December 30: The end of the dinosaur era ($65\text{ million years}$ ago).     * December 31 (Late evening): All of recorded human history occurs.         * 11 seconds ago: Egyptian pyramids were built.         * 1 second ago: Copernicus convinces humanity that Earth orbits the Sun.         * 0.14 seconds ago: Elizabeth II becomes Queen of England.         * 0.04 seconds ago: A typical 18-year-old student was born.         * 0.023 seconds ago: Canada won 2002 Olympic Gold in hockey.         * 2 millionths of a second ago: You started reading these notes.

Our Cosmic Address

To identify our physical place in the universe, we use a hierarchical address:

1. Planet Earth: A rocky planet.

2. Solar System: Consists of objects orbiting the Sun.

3. Milky Way Galaxy: Our home galaxy, containing over $100\text{ billion stars}$.

4. Local Group: A cluster of about $40\text{ galaxies}$, including the Milky Way and Andromeda.

5. Local Supercluster: Also known as the Virgo Supercluster; a collection of galaxy groups.

6. The Universe: The sum of all superclusters, filaments, and voids.

Exploring Spatial Scales (Powers of Ten)

• 10 Meters: The starting point (e.g., a garden at the CERN visitor center).

• 10 Kilometers ($10^4\,m$): Covers the area of the Large Hadron Collider (LHC).

• 1,000 Kilometers ($10^6\,m$): Shows the entire planet Earth (diameter $\approx 13,000\,km$). The atmosphere is thinner than a strand of thread at this scale.

• 1,000,000 Kilometers ($10^9\,m$): Shows Earth and the Moon. The Moon's diameter is $1/4$ of Earth's, and its average distance is $380,000\,km$.

• Astronomical Unit (AU): Defined as the average distance from Earth to the Sun.     * $1\,AU = 1.5 \times 10^8\,km$ (or $1.5 \times 10^{11}\,m$).     * Venus is $0.7\,AU$ from the Sun.

• Solar System Scale: Light takes $8\text{ minutes}$ to reach Earth but over $4\text{ hours}$ to reach Neptune. Pluto orbits mostly outside Neptune but is no longer a major planet.

• Interstellar Scale: Stars are isolated. If the Sun were a golf ball in Vancouver, the nearest star would be a golf ball in Calgary.

• Local Neighborhood:     * Diameter of $≈ 17\,ly$.     * Proxima Centauri: The nearest star, located $4.2\,ly$ away.

• Galactic Scale:     * The Milky Way is a cloud of stars, gas, and dust bound by gravity.     * Diameter: Approximately $100,000\,ly$ (or $1,000\text{ quadrillion km}$).     * Sun's Position: Roughly two-thirds of the way from the center to the edge.

• Intergalactic Scale:     * The Milky Way is just one of many billions of galaxies.     * Local Group: A region $17\text{ million ly}$ in diameter containing a few dozen galaxies.

• Large-Scale Structure:     * Superclusters: Clusters of galaxies grouped together.     * Filaments and Walls: Long chains of superclusters.     * Voids: Regions nearly empty of galaxies, approximately $150\text{ million ly}$ in size.     * "Soap-Bubble" Appearance: Luminous matter mostly exists on the surfaces of these cosmic bubbles.

Spaceship Earth: Constant Motion

We are never "sitting still." Humanity is subject to multiple levels of motion:

1. Rotation: Earth rotates on its axis once per day.     * Speed: Over $1,000\,km/h$ ($1,667\,km/h$ at the equator).     * Calculation: $\text{Circumference } (40,000\,km) / \text{Time } (24\,h) = 1,667\,km/h$.

2. Orbit of the Sun: Earth revolves around the Sun once per year.     * Speed: Approximately $100,000\,km/h$ ($103,680\,km/h$).     * Details: Average distance of $1\,AU$; axis tilt of $23.5^{\circ}$ toward Polaris.

3. Local Solar Neighborhood Motion: The Sun moves randomly relative to nearby stars.     * Speed: Relative speeds of more than $70,000\,km/h$.

4. Galactic Rotation: The entire Milky Way rotates.     * Speed: The Sun travels at $800,000\,km/h$ (or $777,600\,km/h$) around the galactic center.     * Period: One rotation takes approximately $230\text{ million years}$.

5. Motion Within the Local Group: The Milky Way moves toward the Andromeda Galaxy.     * Speed: Approximately $300,000\,km/h$.

6. Universal Expansion: All galaxies outside the Local Group are moving away from us.     * Hubble's Discovery: The more distant a galaxy is, the faster it races away.     * Metaphor: Like raisins in an expanding cake; the space between them (the "dough") expands.

Questions & Discussion

• The Invisibility of the Sun: On a scale of $1,700\,ly$, the Sun is too faint to be easily located.

• Interstellar Clouds: Although these clouds are thinner than the best laboratory vacuums on Earth, they are critical because they give birth to new stars.

• Mystery of Galactic Mass: Most of the Milky Way's light comes from stars and gas in the disk, but detailed study reveals most of the mass resides in the halo (above and below the disk), suggesting the presence of dark matter.

• Photographing the Galaxy:     * Question: Does NASA plan to launch a spacecraft to photograph the Milky Way from the outside?     * Answer: No. Even a spacecraft moving close to the speed of light would take tens of thousands of years to reach a sufficient vantage point.

• The Red Sox Question:     * Scenario: Is the phrase "The Red Sox haven't won in light-years" logical?     * Answer: No, because a light-year is a unit of distance, not time.