Lesson 1

1 :: “Truly Ancient Ideas”

An introduction to the standard “big bang” model and the observations, taken over the past several centuries, that have helped us understand the origins of our universe.

Your Place in Space

This course exists for you. You are strongly encouraged to go to the class Message Board and introduce yourself and tell us something about what you hope to learn through this class. While there, you will have an opportunity to meet your instructor and fellow students and start talking!

NOTE: I could not save the animations included in this course.

The First Days

Two forces have shaped man’s view of the universe: our day-to-day knowledge of how things work and the philosophical framework we use to understand why things should (or shouldn’t) work the way they do. The evolution of science is coupled with revolutions in our thinking, with science and philosophy alternately inspiring and deriding one another. In no area of science is this clearer than in the field of cosmology, where new knowledge often requires us to rethink how we view the entire universe.

Cosmology — the study of our cosmos, and the universe(s) it contains — is a field that has undergone rapid evolution over the past century. Large telescopes and detectors sensitive to colors invisible to our eyes have allowed astronomers to probe distance and time scales unimagined by our not-so-distant ancestors. At the same time, scientists have used high-energy colliders in Europe and America to shatter atoms into their most basic units of mass and energy. In this course I will attempt to define our place in space by reviewing these observations of the very large and the very small. I do not claim that the picture that will emerge in these lessons (as well as in the course text, Timothy Ferris’ The Whole Shebang) will be complete, but it does make testable predictions.

Like all sciences, cosmology is a field best understood through discussion. You will get the most out of this course if you participate in the online Message Board. Through active dialogue, you will encounter ideas that you might not have thought of on your own, and you will gain better insight into complicated topics. Even the greatest cosmologists of our era — Stephen Hawking and Steven Weinberg included — work in collaboration with their peers. Each lesson will include an assignment and set of questions to guide you in selecting which topics are the most important.

In the Beginning . . .

The story of cosmology begins with the first human civilizations. The earliest cosmologists were priests trying to predict the motions of the planets, eclipses, and solstice and equinox days in order to determine festival dates and find the best times for planting and harvesting. Although they were among the best naked-eye astronomers of all time, these early observers lacked the philosophical framework necessary to use their observations to learn about how the universe works.

The early Greeks were among the first to try to create a physical model of the universe. From the shape of the Earth’s shadow on the moon, the Greeks knew that Earth is a sphere. (See Figure 1-1.) This knowledge, coupled with Plato’s philosophical view that the sphere is the most perfect geometrical form, led to the first geocentric, or Earth-centered, model of the universe. Devised in the fourth century B.C. by the astronomer Eudoxus and the philosopher Aristotle, this model hung the sun, moon, and planets on a series of nested spheres that rotated around the Earth at different rates inside the celestial sphere of stars. Although philosophically comfortable, this model didn’t make useful predictions about planetary motions or eclipse dates and could not explain why Mars, Jupiter, and Saturn appear to move both east-to-west (prograde) and west-to-east (retrograde) relative to the stars.

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Figure 1-1: If the Earth were flat, it would cast an oblong shadow on the moon. A spherical Earth is required to make a circular shadow. (Graphic by Pamela L. Gay, copyright 2002)

It was nearly 600 years before mankind came up with a usable model of the solar system. In second century A.D., Ptolemy added epicycles to the geocentric model. In his system, the planets moved in perfect circles, attached to perfect spheres, that all rotated at different rates around the Earth. This model could recreate the observed prograde and retrograde planetary motions. No one — especially Ptolemy — believed that this complex system was anything more than an abstract mathematical model. Nevertheless, this model did make reasonable predictions and maintained its usefulness for 1,400 years.

The Center Moves From Earth to Sun

The cumbersome and imprecise nature of Ptolemy’s model led Nicolaus Copernicus to rethink the Earth’s place at the center of the cosmos in the early 16th century. Inspired by the Neoplatonic sun worship of the Renaissance, Copernicus created a sun-centered, heliocentric model of the solar system. His model did three things: It explained the prograde and retrograde motion of the planets, it moved the Earth out of its special location in the center of the universe, and it expanded the size of the universe. In a geocentric or Earth-centered model, the size of the system must be small enough that it can rotate once every 24 hours without the stars flying off of it from centrifugal force. In the heliocentric or Sun-centered model, the celestial sphere no longer rotates, eliminating this concern. Since the Earth does move, the proposed celestial sphere must be enlarged to explain why stars don’t appear to change in size or location as the Earth orbits the sun. With the Earth and other planets orbiting in concentric circles, prograde motion becomes nothing more than the planets literally moving east-to-west on their orbits relative to the stars. Retrograde motion is explained as a change in our perspective as the Earth catches up to and passes an outer planet.

Unfortunately, in adhering to the Platonic belief that the circle or sphere is the perfect geometric form, the Copernican model was unable to reproduce the exact motions of the planets or times of eclipses. In desperate attempts to fix these shortcomings, Copernicus cluttered his heliocentric models with epicycles, creating a system more cumbersome and less accurate than Ptolemy’s. It would take a radical change of thought to create an accurate model of our solar system.

Kepler

Briefly, Kepler’s three laws of planetary motion are these: (1) Each planet revolves around the sun in an elliptical path, with the sun occupying one of the foci of the ellipse. (2) The straight line joining the sun and a planet sweeps out equal areas in equal intervals of time. (3) The squares of the planets’ orbital periods are proportional to the cubes of the semimajor axes of their orbits. You can see the laws in action at:

http://observe.ivv.nasa.gov/nasa/education/reference/orbits/orbit1.html.

Gravity and Orbits

From Newton: A force (F) is related to the acceleration or deceleration (a) of a mass (m). Mathematically: F = ma. Planets moving in ellipses constantly accelerate toward the sun. Think of it this way: A fired cannonball will move forward and down. The faster the cannonball is shot, the further it will go before gravity pulls it to Earth. If you shoot it hard enough, it will orbit because it falls at the same rate that the Earth is curving away. Planets are like the cannonball, falling towards, but never into, the sun (see Figure 1-5).

Observations Change the Picture

Kepler’s Laws

The best way to create an accurate theory is to base it on accurate data. It would take the detailed observations of astronomer Tycho Brahe to convince the 17th-century mathematician Johannes Kepler that the circle was not the correct geometric form to use to model planetary motions. Kepler was first and foremost a mathematician, and he knew that the circle was a special kind of ellipse (see Figure 1-2). By fitting non-circular ellipses to the orbits of planets, he was able to find orbital solutions that correctly predicted planetary positions.

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Figure 1-2: This drawing shows the best way to draw an ellipse. In the solar system, the sun is located at one focus of the ellipse. (Graphic by Pamela L. Gay, copyright 2002)

A planet’s orbital speed is greatest when it is nearest to the sun, and Kepler determined that planets sweep out equal areas in equal time (see Figure 1-3). Similarly, a planet with a smaller orbital axis (a) has a shorter orbital period (P), with:

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Although Kepler could not directly measure the planet’s exact orbital sizes, he was able to measure the ratio simply by using this equation and Brahe’s observations of orbital periods.

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Figure 1-3: Planets move quicker when closer to the sun and sweep out equal areas in equal amounts of time. (Graphic by Pamela L. Gay, copyright 2002)

Kepler created the first accurate model for planetary motion. Unfortunately, he couldn’t explain why the planets move. Up through the 1500s, scientists believed that all objects tend to stay at rest. They observed that objects in motion eventually came to a stop and that unmoving objects did not begin to move on their own. This raised the question: Why do the planets continuously move?

Finding Cause for the Effects

Further observations were required. In the early 1600s, Galileo Galilei slid blocks across surfaces of varying smoothness and noted that rough tables caused objects to decelerate faster than smooth tables did. He reasoned that if a surface were completely smooth — frictionless — objects would continue moving forever. This led to the theory of inertia: An object in motion tends to stay in motion in a straight line, and an object at rest tends to stay at rest, unless acted upon by an external force.

This explains why planets keep moving, but why don’t they fly off their orbits and move off on straight lines deep into the celestial sphere? In 1687, Sir Isaac Newton published the answer in Philosophiae naturalis principia mathematica. He determined that the external force that kept the planets on ellipsoidal orbits was the tug of gravity. The same force that explains why an apple falls to the ground also explains why the moon continually “falls” around the Earth (Figure 1-4).

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Figure 1-4: The moon is pulled towards the Earth by gravity, but stays in orbit because its tangential motion carries it forward faster than it falls down. (Graphic by Pamela L. Gay, copyright 2002)

The work of Kepler, Galileo, and Newton began a new era of observational science. No longer would scientists try and match data to theory. Instead, observations would become the driving force behind new theories describing our universe.

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Figure 1-5: If you shoot a cannonball hard enough, it will go into orbit! (Graphic by Pamela L. Gay, copyright 2002)

The Doppler Effect

All waves — sound waves, light waves — are affected by motion. When an object moves toward an observer the waves get compressed, and the observer either hears a higher-pitched noise or sees a bluer light (i.e., blue-shifted). If the object moves away from the observer, the waves spread out, causing a lower pitch noise or redder light (i.e., red-shifted). Astronomers see fast-moving distant galaxies as more red-shifted than slower moving nearby galaxies. To see an example of this, go to:

http://www.control.co.kr/java1/masong/doppler.html

The Modern View

Our initial description of the universe portrayed it as unchanging and infinite. Novae and comets come and go, and stars are forming and dying, but the overall nature of the universe was considered static and eternal.

Olber’s Paradox

This led to a paradox. If the universe has always been more or less the same, why is the sky dark? If the universe is infinite in size, every direction in which a person looks will eventually run into a star. If the universe is infinite in age, the light from every star will have had time to reach Earth. This implies that the sky should glow with the light of a billion billion suns. The problem is that even the most sensitive images taken with the Hubble space telescope show stars and galaxies as just small bright patches on a vast dark canvas (Figure 1-6). Heinrich Olber first popularized this paradox in 1826, and it bears his name. To explain the dark night sky, the universe must be finite in age, finite in size, or both.

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Figure 1-6: If the universe is infinite in time and space, the sky should glow with the light of a billion billion suns (left). In reality, the sky is composed of stars and galaxies spattered on a dark background (right). (Graphic by Pamela L. Gay, copyright 2002)

In 1917, astronomer Vesto Slipher pointed the Lowell Observatory telescope at 25 of the nearest galaxies and measured their radial velocities using Doppler shifts. (See the sidebar for more about the Doppler effect.) Much to his surprise, 21 of the galaxies were moving away from the Milky Way! In 1929, Edwin Hubble was able to measure the distances to these and other bright galaxies, and discovered that there is a relationship between the recession rate of and distance to far away galaxies, with more distant galaxies moving away faster. With almost everything moving away, the idea of an unchanging universe began to crumble.

Universal Expansion

To explain the observed recession of all distant galaxies, cosmologists turned to Einstein’s general theory of relativity. First published in 1916, this theory describes a dynamic universe in which everything is either expanding or contracting. Einstein was not pleased with the aesthetics of this result, and halted the universe with a “cosmological constant” that cancelled out the expansion. This philosophically driven alteration to his theory was unnecessary and is often referred to as “Einstein’s Mistake.”

If the entire universe is expanding, observers in every galaxy will see all other distant galaxies moving away. Closely spaced galaxies will appear to move apart slowly because there is less intervening material to expand. More distant galaxies, separated by larger expanses of expanding space, will move apart faster. This expansion implies that in the past the universe was condensed into a single point. The explosion of the universe from a singularity was given the name “The Big Bang” by Sir Fred Hoyle, one of the theory’s early detractors. It was not until the 1940s that the big bang became widely accepted.

The big-bang model explains the observed expansion and has made predictions that we’ll discuss in the next lesson. It also explains Olber’s Paradox. With the big bang, the universe is not infinite in size, so every line of sight does not end in a star. And it is not infinite in age, so light, which travels at a finite speed, has not had time to reach us from objects that are located in the most distant corners of space.

Moving Forward

From the geocentric model of Aristotle and Eudoxus to modern cosmology’s standard big-bang model, we have had to rethink our place in the universe. No longer are we at the center. No longer is everything destined to stay the same forever. Instead, we are now just one more planet, orbiting one small star, in a backwater galaxy that is part of a magnificent and evolving universe.

To learn more about the scientists mentioned in this lesson and others, you are encouraged to explore this biographical link:
http://www-history.mcs.st-andrews.ac.uk/history/BiogIndex.html.

Assignment: Starting Out

Read the preface and Chapter 1 of The Whole Shebang: A State-of-the-Universe(s) Report by Timothy Ferris. What single subject (think along the lines of biology, geography, philosophy, algebra, physics, geometry, and so on) do you think was (is?) most important to cosmologists working to model the solar system and greater universe? There isn’t necessarily a single right answer.

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