The Universe - Part I
Thomas D. Le




Contents

Introduction

Chapter I

1.0  The Curiosity
2.0  The Ptolemaic System
3.0  The Renaissance and Post-Renaissance Theories and Contributions
4.0  The Stars
4.1    What Is a Star?
4.2    Characteristics of The Stars
4.2.1      Distance Measurement
4.2.2      Colors and Temperatures
4.2.3      Chemical Composition
4.2.4      Size, Mass, and Density
4.2.5      Brightness
4.2.6      Motions
4.2.7      Variable Stars
5.0   Galaxies
5.1   Star Clusters
5.2   Nebulae
5.3   Galaxies
5.4   Black Holes and Quasars
5.5   Wormholes

Chapter II

Advances in Science And Technology
1.0   Spectroscopy
2.0   The Telescope
3.0   The Periodic Table of The Elements
4.0   The Internal Structure of the Atom

Chapter III

Twentieth-Century Theories
1.0     The Steady-State Theory
2.0     The Big Bang Theory
2.1     A Brief History of Big Bang
2.2     Evidence for the Big Bang
2.3     Questions and Elucidations on the Big Bang

Conclusion

References

Introduction

My interest in astronomy went back to my high school days, when one night, I decided to find the North Star using what I had learned in a science class. I found it, and since then the dream of one day studying astronomy was embedded in my mind. But it was not to be, and I moved on to other things.

Yet this abiding interest remains. On my Web site, I have written about Mars exploration and the International Space Station, mostly to satisfy my own curiosity about space. But even Mars and the International Space Station are closer to home than we think.

The vast universe out there, extending to billions of light-years and still expanding, holds a great deal more mystery and wonder to our imagination and insatiable thirst for answers.

Where did all this universe come from? How did it come into being? Where it is going from here? Will it keep expanding forever, or will it someday contract to nothing? Where did matter come from? How did the galaxies, the stars, and the solar system form? How did life evolve?

All these questions and more have fascinated generations of inquisitive minds, who harnessed their energy and talent to accumulate a corpus of knowledge we now take for granted, and hold out hope that more light will be shed on the secrets of the universe.

And so the continuing saga of exploration and investigation keeps transfixing our minds, whether we are professional, amateur or lay people, for there is no more fundamental question than one that queries the origin of the universe.

This article offers a synoptic overview of the subject matter for the curious lay persons, touching upon different perspectives of the universe ranging from the Ptolemaic system to the current Big Bang theory, with sufficient information on astronomy and physics to appreciate the theories. For readers with a greater appetite the article includes a reference list of Web links for further research and study.

Consider this an adventure into a world of fascination and excitement as well as an intellectual journey of the first order. I hope you will come out with a greater sense of the hold the universe has on humans, and of our place in it. You will certainly gain a new perspective on our life and our own species, the one that asks the ultimate question, and continues to search for the answer.

I dedicate this work to an extraordinary person and friend of mine, Giang N. Trinh, D.Ph., for her interest in astronomy, and her urging and encouragement, without which it would probably never have seen the light of day.

Thomas D. Le
11 April 2003

Chapter I

1.0   The Curiosity

To paraphrase Carl Sagan, the late astrophysicist, we are made of star-stuff. By that he meant all the elements found in the cells and molecules in our bodies were made in the interiors of stars eons ago. It is quite a mind-boggling thought to realize that somewhere in the expanding universe, on a largely watery and rather puny planet, there evolved a form of life over some three million years that knows to ask grand questions about its own origin and learn how it all came to pass.

When you look at the clear night sky and see the myriad stars studding the firmament with varying degrees of light intensity, some merely shining, some twinkling, some clustered together, and some standing apart, what passes through your mind? The answer probably depends on your mood and your state of mind at the moment. You might be alone but serene, and are mystified by the vastness and awesomeness of the universe. You might be in a romantic mood, and see your lover in the brightest star, the blue-white Sirius most likely, hovering up there over the Northern Hemisphere all by itself, and eclipsing the rest. Or if you are like me, you will be wondering how all this universe has come about that is so immense, so powerful, so enthralling, so enigmatic, and so beautiful.

The universe has always held an awe-inspiring sway on man's imagination. History records this enormous hold that for thousands of years has inspired men from various civilizations throughout the world. Their observations have been put to diverse uses in religion, navigation, exploration, even in the conduct of war. In the Western world the question of the existence of the universe, simple as it was and is, has fascinated men, among whom were Hipparchus, Aristarchus, Eratosthenes, Ptolemy down to Copernicus, Kepler, Galileo, Newton, Einstein, Carl Sagan, Stephen Hawking and other contemporary scientists who devote their lives to penetrating its seemingly impenetrable veil of secrecy.

I want to share with you my fascination with the cosmos as a layman, an average curious person who never ceases to be amazed at the mystery that enshrouds the genesis of the universe and, along the way, the origin of us all.

We will briefly go over theories that were advanced over time to account for observational data about the universe, and appreciate how far we as humans have gone in gaining an understanding of its mystery. Within the last hundred years along with progress in physics, chemistry, mathematics, computer science, astronomy, and cosmology, men have pieced together a compelling picture of the structure and evolution of the universe. And although a complete account still remains elusive, we now have the tools to probe deeper, and to widen our inquiry.

2.0   The Ptolemaic System

Inquisitive minds in the pre-scientific era had asked questions about the origin of the universe, and from their observations of the movements of heavenly bodies, had pondered over their meanings and applications to daily life. Ancient civilizations from Egypt through the Fertile Crescent to India and China have all made keen observations of the planets and stars, and formulated and systematized them into bodies of knowledge that were known as astronomy, astrology or astromancy. Pre-Greco-Roman Europe bore traces of this rudimentary science in cults, and places like Stonehenge in Britain still mystify us with queries about their astrological meanings. New World civilizations of the Aztecs, Incas, and Mayas also made their contributions.

I will not dwell on these observations. Instead I will take you on a brief but exciting adventure into the world of astronomy and cosmology through time.

The first attempt to measure the world dated back to the third century B.C., when the Greek astronomer Eratosthenes (c. 276-196 B.C.), who lived in Alexandria, Egypt, noticed that on the first day of summer in Syene (now Aswan) the sun was directly overhead. In Alexandria, however, the sun appeared slightly south of the zenith. Knowing the distance between these two cities and assuming that the sun's rays were parallel when they hit the earth, Eratosthenes was able, using simple geometry, to accurately calculate our planet's circumference to be 25,000 miles (40,000km).

But it was Claudius Ptolemaeus, better known as Ptolemy (c.100-170), whose 13-volume treatise The Almagest compiled the achievements of Greek astronomers to his day, who introduced the first general theory of cosmology, based largely on the works of perhaps the greatest of them all, Hipparchus (c. 190-c. 125 B.C.), who had discovered the precision of equinoxes and made the first catalog of stars. His geocentric model explained the movement of the seven "planets" of the known universe (the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn) through space around Earth. Since the ancient Greeks equated predicting the positions of the planets with understanding the universe, the distant stars were nothing more than a backdrop for planetary motion.

Ptolemy envisioned a perfect universe in which each planet moved in a circular orbit at a constant speed. To overcome observed difficulties such as changing speeds and the occasional east-to-west (as opposed to the normal west-to-east movement relative to fixed stars) or retrograde motion of the planets, he hypothesized that each planet moved in a small circle, called the epicycle, whose center described a larger circular trajectory, called a deferent, with Earth as its center. Since this scheme still fell a bit short, Ptolemy placed Earth slightly off-center of the deferent (which came a bit closer to being an ellipse), and had the epicycle move at a constant angular speed around a third point, called the equant, which is diametrically opposed to Earth from the deferent's center. This ingenious refinement allowed him to achieve reasonable, though imperfect, accuracy in his calculations.

Along with the Earth-centered view, the idea that Earth is flat remained in the public consciousness until Christopher Columbus' days, although the Greek philosopher Aristotle (384-322 B.C.) had argued convincingly for a spherical Earth from the apparent sinking or rising of the North Star (Polaris) depending on whether one travels south or north, and from the circular shadow of Earth against the Moon during a lunar eclipse. If Earth were a flat disk, its shadow would have been elliptical. The flat-earth myth was exploded once circumnavigation of Earth was accomplished in the 16th century.

Ptolemy's geocentric paradigm, which was undisputed for 1400 years, fit the Catholic Church's view of God's creation of the universe so perfectly that the Church adopted it as its canon, thus stifling further scientific inquiry for centuries.

3.0   The Renaissance and Post-Renaissance Theories and Contributions

It was not until the Renaissance, when classical ideas received renewed interest among philosophers and intellectuals, that modern scientific investigation into the cosmos began in earnest.

The Polish astronomer Copernicus (1473-1543), rejecting Ptolemy's cumbersome model, showed that computations of planetary positions would be far simpler by placing the Sun in the center of the universe, with Mercury, Venus, Earth, Mars, Jupiter and Saturn circling around (Uranus, Neptune, and Pluto had not yet been discovered.). Although this hypothesis had already been formulated by the ancient Greek astronomer Aristarchus (310-c.230 B.C.) of Samos 1500 years earlier, Copernicus gave it a modern impetus, and sparked a revolution in the science of the universe. This heliocentric concept envisions the daily movements of stars and other planets as a mere reflection of Earth's rotation on its own axis, and could explain the occasional retrograde movement of the planets in relation to Earth in a natural way. Since Earth moves at a faster speed than the outer planets, it periodically overtakes them, and they appear to move backward relative to the background. This is similar to the experience of a faster runner in an inner lane who sees his slower competitors in a farther outer lane moving backward as he passes them. By the same token, Mercury and Venus, which are closest to the Sun, never seem to stray too far from the Sun from Earth's vantage point. However, this model is still defective by Copernicus retaining the old notion that the planets move in circular orbits and at constant speeds. Like Ptolemy he had to devise a system of circles within circles for his calculations to be reasonably accurate.

Although the Copernican model does not prove that Earth revolves around the Sun, the heliocentric view began to take hold in most of northern Europe at a time when the Ptolemaic system prevailed in southern Europe, where the Catholic Church was entrenched. His book Revolutionibus Orbium Coelestium (The Revolution of the Heavenly Spheres), published in 1543, the year of his death, was dedicated to Pope Paul III, conceivably with an intent to placate the religious authorities into accepting, or at least not condemning, his contrarian view.

It devolved on the Danish astronomer Tycho Brahe (1546-1601) and the German astronomer Johannes Kepler (1571-1630) to finally explain the secrets of planetary motion. Using Brahe's precise naked-eye measurements of the planets' positions over a twenty-year period from 1576 to 1597, his assistant and successor Kepler modified Copernicus' concept by introducing a slightly elliptical, as opposed to the circular, orbit with the Sun at one focus, and found that Mars' positions almost exactly matched the elliptical path. Other planets behaved similarly. This elliptical orbit became the accepted first law of planetary motion. The second law Kepler discovered was the varying speed at which a planet travels around the Sun, fastest when closest to the Sun, and slowest when farthest away. And the third law of motion calculates with precision the relation between a planet's distance from the Sun and the amount of time the planet takes to make one complete revolution around the Sun. The value of these three laws of motion lies in their predictive power, i.e., they allow accurate prediction of the positions of the planets.

Up till then astronomers were content with theorizing and hypothesizing on the basis of naked-eye observations of the sky with the aid of crude instruments such the quadrant. It was not until 1608 that the Dutch optician Hans Lippershey invented the telescope, which the Italian Galileo quickly adopted in what was later recognized as the first truly scientific observation of our planetary system.

Galileo Galilei (1564-1642), who had abandoned his training in medicine in favor of mathematics, quickly turned the recently invented telescope to the sky, and within months found mountains and craters on the Moon and dark spots on the Sun. His discovery of the four moons (58 at latest count) orbiting Jupiter shattered the ancient notion that Earth was the center of all motion. And his discovery of the phases of Venus, similar to the phases of the moon, challenged the Ptolemaic system, which could allow Venus to show only its crescent phase. Galileo's work had thus lent observational support to the Copernican system.

By 1610 Ptolemy's view had begun its decline as a credible theory at least in northern Europe. Galileo, being an Italian living the Catholic Church's stronghold, was forced before the Inquisition to recant his findings and renounce his endorsement of the Copernican model. But the heliocentric model was going to prevail.

Giving modern astronomy an important boost were the contributions of the Englishman Isaac Newton (1642-1727). He clarified the laws of motion, and invented the first reflecting telescope whose basic design still remains in use, the preeminent mathematical tool of science, calculus, and the law of universal gravitation. Until the advent of Albert Einstein's general theory of relativity in the twentieth century, all cosmological models were based on his theories.

Back in the eighteenth century astronomers had suspected that the Sun was only a part of a larger conglomeration of stars, called a galaxy later known as the Milky Way, with the Sun at its center. Our concept of the universe thus expanded to other stars beyond the solar system. One puzzling discovery was the large masses of fuzzy light, the nebulae, that lay beyond our galaxy. The 18th-century French astronomer Charles Messier had catalogued more than 100 of these objects. By the beginning of the 20th century using small and medium-sized telescopes, astronomers have catalogued more than 10,000, many of which were identified as interstellar clouds of gas and dust and star clusters. But most still remain a mystery. Immanuel Kant had hypothesized that nebulae were galaxies, but no proof was proffered until well into the twentieth century. Before long the Sun-centered view became rather parochial, and soon would be replaced by the broader "galactocentric" concept.

4.0   The Stars

Before discussing the progress in science and technology that gives astronomers the tools they need in their investigation, it behooves us to understand essentials facts about the cosmos, and its fascinating inhabitants, the stars and other celestial objects.

4.1   What Is a Star?

The universe is full of giant clouds of gas and dust. As a massive and enormous interstellar cloud of dust and gas, mainly hydrogen, begins to contract under gravity, the atoms of gas and dust particles become denser, heat up to very high temperatures, take on a globular shape, and glow. A star is born. Contraction continues until hydrogen in the center is converted into helium by nuclear fusion, and generates outward pressure that counterbalances the inward gravitational pull. At this point the star stops shrinking, and maintains a stable life for millions or billions of years. Massive hot blue stars may reach this stage in hundreds of thousands of years whereas cooler yellow and orange stars may take millions of years. This process of nuclear reaction continues as long as there is enough hydrogen fuel to keep it going. When it has spent much of its fuel supply the star's core begins to lose its stability. Its core contracts until it reaches up to 100 million degrees C, and its gas pressure expands the overlying layers and make the star shine even brighter. When the hydrogen supply in the core is almost consumed, fusion continues in the outer layers, expanding the star further. The enormous surface of the star radiates sufficient light to transform it into a red giant or supergiant. In the meantime if the core's temperature is high enough, helium fuses into heavier carbon atoms. When the temperature reaches 3 billion degrees C, iron and other heavy metallic elements form. This is the end for the star. Iron is too heavy an element to fuel the nuclear reaction. After this thermonuclear reaction has used up all the hydrogen fuel, its core can no longer support the heavy outer layers, and the red giant collapses upon itself. The nuclei of its atoms are compressed together so tightly that the star shrinks to a hot white dwarf. Its interior begins to cool. However, due to residual heat the white dwarf may continue to glow faintly for another billion years. Eventually even the core becomes cold, and the star becomes dark and dies. Another possible scenario is violent death: the red giant may contract into a red variable star called nova before its collapse, and may even eject much of its overlying layers as a supernova, and shines as brightly as an entire galaxy before the final collapse. The matter thrown out by the supernova in its cataclysmic demise is used in the formation of new stars. Over billions of years, this process repeats itself as heavier elements are thus cooked up in the stellar furnaces, and form the building blocks of life. We are made from these fundamental building blocks.

Our Sun has been burning its fuel for 4.5 billion years, and is estimated to last another 5 billion years before it becomes a red giant and consumes the entire solar system. We still have plenty of time to put our earthly affairs in order!

4.2   Characteristics of The Stars

When peering at a star, astronomers are interested in determining its distance, diameter, mass (total amount of matter), density, surface temperature, chemical composition, motion, and formation. Beyond individual stars, they investigate galaxies, novae, nebulae, black holes, quasars, pulsars, and other exotic objects.

4.2.1   Distance Measurement

To measure astronomical distances, scientists use different units, such as the astronomical unit (AU), the light-year, and the parsec. For short distances within the solar system, the astronomical unit is the average distance from Earth to the Sun, or 93 million miles (about 150 million km). Longer distances are measured in light-years, a light-year being the distance traveled by light at the speed of 186,000 miles (300,000 km) per second for 365 days, or nearly 6 trillion miles (10 trillion km). The Sun is only 8 light-minutes from Earth, that is, it takes eight minutes for the Sun's rays to reach us. At the 1983 Conference Generale des Poids et Mesures, the SI (Systeme International) defines the meter as the distance traveled by light in a vacuum for 1/299,792,458 of a second, making the speed of light 299,792,458 m/s in a vacuum.

In 1838 the German astronomer Friedrich Wilhelm Bessel (1784-1846) first proved Earth's motion around the Sun by effecting a precise measurement of a small displacement of the nearby star 61 Cygni in relation to more distant stars. He thus estimated the distance to that star to be 65 trillion miles, or about 11 light-years. This displacement of a star is called parallax, a basis which astronomers use in measuring stellar distances. It is half the angle opposite the long axis of Earth's orbit, which serves as a baseline for a triangle with the two sides being lines of sight from a point on Earth to the star taken six months apart, i.e., on opposite sides of its orbit. The parallax is greater for a nearer star than for a distant one. In addition to light-years, astronomers use the parsec (coined from parallax of one second), defined as the distance at which a star would have a parallax of one arc-second. A parsec is about 3.26 light-years, about 20 trillion miles, 3.085678x1013 km, or roughly 206,000 AU. Using the parallax, the distances to two other stars, Alpha Centauri and Vega, were determined. Alpha Centauri, the second brightest star in the Southern Hemisphere sky, and its invisible neighbor Proxima Centauri are about 25 trillion miles away. In the following decades more distances to the stars were calculated, and the universe became larger than scientists had expected.

4.2.2   Colors and Temperatures

Stars appear in different colors even to our unaided eye. In a spectrum analysis hot stars emit more light at the blue end of the spectrum, and cooler stars emit more light at the red end, very much what we experience in daily life. A blowtorch is hottest when its flame becomes blue-white. White light is decomposed by a glass prism into a spectrum of colors ranging by decreasing order of their wavelengths from red through orange, yellow, green, to blue, indigo, and violet. The spectrum of an element carries distinctive lines across the color band. These lines help observers to identify the chemical elements present in the stars. Astronomers group stars into seven classes according to their spectral lines. Class M, red stars such as Antares and Betelgeuse with a surface temperature of about 3,000 C; Class K, orange stars, e.g., Arcturus, Aldebaran, with a surface temperature of about 4,000 C; Class G, yellow stars, e.g., Sun and Capella, with a surface temperature of about 6,000 C; Class F, white-yellow stars, e.g., Canopus, Procyon, with a surface temperature of about 7,500 C; Class A, white stars, e.g., Sirius and Vega, surface temperature of 8,000 C to 11,000 C; Class B, blue-white stars, e.g., Rigel, Spica, surface temperature of 15,000 C to 30,000 C; and Class O, blue stars, e.g., Zeta Puppis, surface temperature of above 30,000 C. This classification shows that as hot as the Sun seems to us on Earth, it is only moderately so and therefore not very luminous.

4.2.3   Chemical Composition

Stars are composed of the same elements we have on Earth, but in very different proportions. Most stars consist primarily of hydrogen and helium with only about one percent of heavier elements such as iron, calcium, sodium, titanium, and other elements. Our sun is about 70 per cent hydrogen, 28 percent helium, with about 60 other elements forming the remaining 2 per cent of its mass. Most stars differ among themselves more in their temperature than in their composition.

4.2.4   Size, Mass, and Density

Stars vary in size from smaller than Earth to Epsilon Aurigae, which is about 2 billion miles in diameter. Our sun is an average star with a diameter of 864,000 miles as compared to Earth's 8.000 miles, and an average density 1.4 times that of water. Its mass is more than 300,000 times that of Earth. The red supergiant Betelgeuse has a density about one ten-millionth that of the sun. At the opposite end, the white dwarf star that accompanies Sirius is so dense one teaspoonful of it weighs about a ton.

Variation in mass is less pronounced. Stars range in mass between ten times the sun's mass to about one-fifth of its mass. Most stars range close to the sun.

4.2.5   Brightness

The true brightness of a star depends on its size and surface temperature, and its apparent brightness also depends on its distance. The star's brightness is defined as its magnitude. Its apparent magnitude is its brightness as observed by the eye, or photography. Before the invention of the telescope astronomers distinguished six classes of magnitude, with first-magnitude stars being the brightest and sixth-magnitude barely visible to the unaided eye. Today the 200-inch telescope at Mount Palomar can photograph twenty-fourth magnitude stars with less than a billionth the apparent brightness of Betelgeuse. Since the ratio of brightness between two consecutive magnitudes is 2.5, a first-magnitude star is 100 times as bright as a sixth-magnitude star. Astronomers assign positive numbers with decimals for greater precision to less bright stars and negative values to stars with apparent magnitude brighter than first-magnitude stars. Thus, first-magnitude stars may have magnitudes between 1 and 0: Rigel 0.15, Capella 0.09, and Vega 0.04. The brightest star in the sky Sirius has the apparent magnitude of -1.6, and Alpha Centauri -0.27. The full moon's magnitude is -12.6 while our Sun's is -26.5.

The star's apparent magnitude indicates how bright it looks to us, not how bright it really is. Its true magnitude or luminosity cannot be determined directly because we cannot place stars at the same distance from Earth. Astronomers standardize calculations by defining the absolute magnitude as the apparent magnitude a star would have at a distance of 10 parsecs or 32.6 light-years. By this measure Betelgeuse has a high absolute magnitude of -5.8 whereas our sun's absolute magnitude of 4.8 makes it barely visible at 10 parsecs. Most stars are even less luminous than our sun.

In general we would expect hotter stars to be more luminous. We would expect blue or blue-white stars to have high luminosity and absolute magnitude. Sirius and Vega are hot blue-white and very luminous. Yet Capella and Arcturus with absolute magnitude of -1 and high luminosity are red stars. They are known as red giants. Supergiants include blue-white Rigel, white-yellow Canopus, and the red supergiants Antares and Betelgeuse. Red supergiants are the largest of all; they have to be in order to be luminous. Betelgeuse is so large that it consists mostly of near-vacuum. At the opposite extreme, less luminous stars are called dwarfs, which we expect to be red, orange or yellow stars. Again there are exceptions. White dwarfs are so dense a teaspoonful weighs about a ton, as mentioned above.

4.2.6   Motions

Stars in our galaxy rotate with the galaxy at high speeds that vary with their distances from the center of the galaxy. However, Vera Rubin (1928- ) has shown in her study of star motion that stars' velocities remain fairly constant irrespective of their distances to the galaxy's center, and that most spiral galaxies contain about ten times more mass than is visible. The first finding contradicts our knowledge of planetary motion in our solar system, where velocities decrease with distances from the Sun. The second finding is startling in that the universe contains much more invisible matter than we ever suspected, dark matter. More about this in the discussion of the Big Bang theory below. Star motion may be described in two ways. Proper motion, the rate of change of the star's position relative to each other, can be detected by comparing two different photographs taken years apart of the same star among the same background stars. Their vast distances from us guarantee that very few stars move appreciably over short periods of a few years. However, proper motion will be much more appreciable in 50,000 years. By analyzing shifts of spectral lines astronomers can measure radial velocity, the rate at which a star moves away from or toward us. Most radial velocities range between 20 to 30 miles per second although 60 miles per second have been observed with some stars.

4.2.7   Variable Stars

Variable stars, so called for their varying brightness, include eclipsing variable stars, pulsating stars, and cataclysmic or eruptive stars.

Eclipsing variables are binary systems in which one star eclipses the other during each pulsation period, alternating between increase and decrease in light output. Beta Lyrae is one such eclipsing variable.

Pulsating stars expand and contract in regular cycles and change brightness accordingly. Expansion corresponds to cooler temperatures whereas contraction causes the star to become hotter and brighter. Cepheid variables (named after the constellation Cepheus) are regular in their pulsating patterns. Delta Cephei, the prototype for Cepheid variables, has regular periods ranging from one to several days. The longer a cepheid's period is, the greater is its absolute magnitude. It is this reliable relationship that astronomers use to calculate the distances to galaxies containing the cepheid, given that cepheids are bright and widely distributed.

Cataclysmic or eruptive variables are faint stars that explode into sudden outbursts thousands or hundreds of thousands of times as bright as before. Many such stars are novae, binary systems made up of a white dwarf and a red giant. Gravity exerted by the white dwarf draws matter from the less dense red giant toward it. Over hundreds or thousands of years enough material has accreted to trigger a thermonuclear explosion. For several days the star increases its brightness by as many as 10 magnitudes before slowly fading away. The detonation occurs again when enough material has been accumulated. Nova Cygni 1975 and Nova Herculis 1934 are two such well-known novae.

Occasionally a violent explosion flares with such brilliance, approaching hundreds or thousands of times that of a nova, that it is called a supernova, and its absolute magnitude is as great as that of an entire galaxy. One such convulsive supernova was observed in 1054. During the explosion most of the star's matter was lost, and it became an expanding cloud of gas now known as the Crab Nebula in the constellation Taurus. What remains after the giant explosion of this supernova is a core of hot neutrons (giving it the name of neutron star) thirty kilometers across, spinning rapidly, and emitting radio waves and visible light, flashing 30 times per second. Hence the name pulsating star, or pulsar. Other supernovae were recorded in 1572 by Tycho Brahe, and in 1604 by Johannes Kepler. In 1987 the Canadian astronomer Ian Shelton found Supernova 1987A, which over a period of three months reached magnitude 3, at which it was almost as luminous as all the other stars in the Large Magellanic Cloud. Within a year Supernova 1987A had faded to naked-eye visibility.

5.0   Galaxies

5.1   Star Clusters

Clustering occurs among stars when they are close together to form distinctive groups that move together. About 600 star clusters have been identified that fall into two classes. Open or galactic clusters, generally numbering in the tens or hundreds, consist of younger stars, and are called open because they are widely scattered, and galactic because they are found in our galaxy. The Pleiades, the Hyades are part of some 500 open clusters. Globular clusters, about 150 in number, are scattered throughout the sky, and when seen through a large telescope appear to be huge aggregations of up to a hundred thousand stars, some 15 billion years old, as old as the universe, all located in the core of the Milky Way. Stars in globular clusters consist mostly of light elements such as hydrogen and helium while younger stars in the open clusters also contain heavier elements such as calcium and iron. M22 in Sagittarius is a globular cluster.

5.2   Nebulae

Many fuzzy, blurred patches of light that lie among stars once thought to be nebulae have been resolved by large telescopes into galaxies. In 1923 and 1924 with the help of the 100-inch reflector at Mount Wilson, California, Edwin Hubble was able to resolve the Andromeda Nebula into individual stars. By comparing the nebula's apparent magnitude with its absolute magnitude, he estimated the nebula's distance at close to one million light-years. Nebulae are made up of cosmic dust and gas that do not have light of their own. Bright nebulae receive light from stars within them or in the neighborhood. Some bright nebulae are reflecting nebulae because starlight reflects off their dust. Others are ionized by intense emission of ultraviolet radiation from close stars, and glow as emission nebulae. The Great Nebula in Orion (M42, short for Messier's Catalog, Object No. 42) and the Lagoon Nebula (M8) are good examples. Dark nebulae have no nearby stars or background stars to give them light, and are thus called coal sacks. One such dark nebula, studied by the British astronomer John Herschel (1792-1871), lies in the southern sky by the Southern Cross. One of the best-known dark nebulae is the Horsehead Nebula in the constellation Orion.

5.3   Galaxies

Galaxies are huge systems of dust, gas, and billions of stars held together by gravity, and separated from each other by millions of light-years. Before powerful telescopes resolved them into galaxies in the 1920's they were called spiral nebulae. In 1926 Edwin Hubble classified galaxies into three main categories: spirals, barred spirals, and ellipticals. About seventy-five percent of bright galaxies have a spiral configuration consisting of a lens-shaped central disk populated by millions to billions of stars, and two spiral arms extending out of the center from opposite sides of the nucleus, and holding millions of young, hot stars, and bright emission nebulae. Open star clusters are distributed throughout the disk. Spiral galaxies range from 15,000 to 150,000 light-years in diameter. Typical spirals include the Andromeda (M31), the Whirpool (M51), and our Milky Way. About one-third of spirals show attributes of barred spirals, in which bright stars and ionized gas of the nucleus extend out to thousands of light-years in a straight bar on each side of the center. From the end of the bars spiral arms sweep back around the nucleus. Elliptical galaxies range from football-shaped to spherical, have no arms, and contain almost no gas or dust. The largest ellipticals measure at least 100,000 light-years in diameter, and may contain 10,000 billion stars. Large ellipticals such as M84 and M86 in Virgo make up about twenty percent of bright galaxies. Other types are lenticular galaxies with nuclei like spirals but no spiral structure, containing mostly old stars and very little gas. Finally there are irregular galaxies, so-called for their indistinct shape, making up about 5 percent of bright galaxies. The Small and Large Magellanic Clouds belong in this category.

At the beginning of the twentieth century, the Milky Way, also called the Galaxy, was thought to have 100 million stars and extend only a few thousand light-years across. In 1917 the American astronomer Harlow Shapley at Mount Wilson Observatory, California, showed that our solar system was farther out toward the edge of the Milky Way, some 50,000 light-years, later revised to 30,000 light-years, from its center, and that the Milky Way was the universe. Today we know the universe has 100 billion galaxies, each having an average of a hundred billions stars. And the Milky Way is a flat spiral galaxy with a wide bulge in the center, 1,500 light-years thick, with arms extending to 100,000 light-years, and containing some 200 billion stars. The Milky Way is only one among billions of galaxies in the universe. Around its disk a halo of older stars stretches out to another 150,000 light-years. Each star and nebula in our galaxy orbits its center, and follows its own independent path. The Sun, an average-sized star on one of the spiral arms, makes one complete orbit in about 240 million years. What is at the center of the Milky Way? It is still a mystery, but scientists now think they found a strong source of radio emission known as Sagittarius A*, or a black hole with the mass of millions of suns.

Galaxies are distributed unevenly in the universe and are separated by great distances. Our galaxy is one of a conglomeration of some 30 galaxies called the Local Group, with the Milky Way and the Andromeda (M31) being the largest. And the Local Group is part of a supercluster of galaxies which includes the constellations Coma Berenices and Virgo, the latter 65 million light-years distant and containing 2,500 galaxies. Galaxies within a cluster are bound together by gravity, but the clusters themselves are pulled away from each other by the expansion of the universe.

5.4   Black Holes and Quasars

Stars owe their brilliance to the process of thermonuclear reaction going on in their cores. When a star exhausts its hydrogen nuclear fuel in millions or billions of years, the energy produced by nuclear fusion is no longer able to counteract the inward pull of gravity, its core collapses, and its overlying layer caves in upon itself creating a cataclysmic implosion. In 1971 John Archibald Wheeler named the resulting object a black hole. The star crosses into its event horizon and disappears. The event horizon is the black hole's radius beyond which no light escapes; and any event taking place inside it cannot be detected. It is a point of no return. All known laws of physics break down inside the event horizon, including Einstein's gravitational laws. However, not all stars collapse into black holes. A star with a mass less than 1.4 times that of the sun forms a white dwarf. A star between 1.4 and 3 solar masses becomes a neutron star. If a neutron star gets to around 3 solar masses the force of gravity overwhelms the outward pressure, and it keeps contracting to a tiny mass and collapses into a black hole. Stars greater than 3 solar masses become black holes. A black hole can also be produced by compression from outside forces, such as that hypothesized as the primordial black hole at the origin of the universe, or a singularity. A singularity is a region in spacetime (i.e., 4-dimensional space, three dimensions for space and one for time) in which gravitational forces are so strong no light can escape from it. It marks the point of infinite spacetime curvature, in other words, a point of zero volume and infinite density. Einstein's general relativity requires that a singularity be formed under two circumstances: first, during the creation of a black hole, such as at the death of a star, when it runs out of fuel and collapses upon itself crushed by gravitational interaction, and second, under certain reasonable assumptions, an expanding universe like ours must have begun as a singularity. This hypothesis is the Big Bang theory discussed below.

Albert Einstein's general theory of relativity suggests that a black hole, with its enormous density of matter compressed into a tiny volume, has such tremendous gravity that light inside it cannot escape to be seen. The British theoretical physicist Stephen Hawking (1942-), of Cambridge University, showed in 1974 that black holes can radiate energy. He believes that matter or energy can be created from "empty" space for there is no such thing as empty space, according the uncertainty principle. The quantum vacuum is filled with particles and antiparticles that appear briefly and disappear quickly. Consider this scenario, thought of by some physicists as "pop-science," but still accepted as a heuristic: If a pair of virtual particle-antiparticle forms near the event horizon, three possible scenarios exist if they don't annihilate each other first. Firstly, the pair falls into the black hole. Secondly, the pair escapes from the edge of the black hole. In the third scenario, one virtual particle falls into the black hole, restores the conservation of energy by taking on a negative charge to be absorbed by the black hole, which then loses further mass and shrinks. The remaining particle becomes real to be a source of radiation to the outside observer. Hawking calculated that the energy radiation is very small, of the order of 6 x 10-8/M Kelvin, where M is the black hole's mass in terms of solar masses. This phenomenon is known as Hawking radiation, still not observed because the only known black holes are so hot this radiation is undetectable.

Because of its invisibility a black hole is very difficult to detect. Detection therefore has to depend on other phenomena. First, although the star is no longer visible, its gravitational field remains as strong as before the collapse, and its planets continue to orbit about, as if about nothing. Next, the black hole's powerful gravity pulls dust and gas particles from nearby stars with such enormous speed and force that X-rays are emitted in the process. Astronomers have detected several binary star systems with strong X-ray emission, in which one star orbits its massive, invisible companion. Cygnus X-1, a strong invisible X-ray emitter, has a blue supergiant star orbiting it. The M87 galaxy harbors a supergiant black hole with 2 billion times the mass of the sun. The last technique of black hole detection is referred to as gravitational lensing. When a massive object, in this case a black hole, passes between Earth and a star, the black hole acts as a refracting lens bending the star's light rays and focusing them to Earth, where an observer sees the star brighten. Einstein's theory of relativity suggests that the star's light follow the path of bent time and space, bent by the black hole's gravity.

Today astronomers believe most galaxies and all quasars have a black hole at their cores. The first evidence was discovered in 1974 with the detection of a strong source of radiation, called Sagittarius A*, emanating from the center of the Milky Way. Quasars, short for quasi-stellar radio sources, were discovered in the early 1960s in the cores of distant galaxies. Astronomers were puzzled over their luminosity and their strong radio emission from a region about the size of our solar system. They emitted great energy by burning up to trillions of times the energy of the Sun, or up to a thousand large galaxies. Maarten Schmidt used Hubble's Law to deduce their great distances from the observation that their spectrum was highly redshifted. Most astronomers now believe that quasars lie in the centers of young galaxies, where supermassive black holes attract passing stars and gas clouds to form accretion disks around the black holes, emitting both intense visible light and radio waves.

5.5   Wormholes

This is still in the domain of science-fiction. Imagine a light beam traveling between two points in curved spacetime. It would take longer if it had to take to normal path between two points. Now imagine a "bridge" connecting two regions of spacetime, providing a shortcut. The light beam going through this shortcut would get to its destination in far shorter time. This bridge, now called a wormhole, was proposed in 1935 by Albert Einstein and Nathan Rosen, who realized it was allowed by general relativity. Any shortcut would raise the possibility of time travel. Until recently physicists believed wormholes exist only briefly, and anyone entering one would fall into a singularity. Quantum effects would destroy the wormhole before a space traveler could enter it. However, more recent calculations show that with "negative energy" an advanced civilization could prevent the wormhole from crushing itself out. Stephen Hawking, at first was not convinced that time travel would be possible, but since then he has come around, and thought only that it would be impractical.

If a black hole rotates and/or have charge, you can fall in without hitting a singularity. It could conceivably join up with its exact opposite, the white hole, and form a tunnel called the wormhole. Whereas there is evidence that a black hole exists, a white hole is only the result of a mathematical symmetry of the equations of general relativity that describe the black hole. The while hole is something like a mirror image of the black hole, with opposite properties. If nothing inside the black hole can escape, the white hole ejects anything that "falls" in it. In reality, there is no white hole. But the idea is tantalizing that if you can tunnel through a black hole to a white hole and emerge to the other side of the spacetime curvature, you have in effect traveled through time!



The Universe, Part II Mars Mars Exploration Rover Spirit Mars Exploration Rover Opportunity Quantum Mechanics The Multiverse Mathematics of Finance, Financial System Mathematics of Finance, Problems

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