# General Astronomy/The Modern View of the Cosmos
## The Big Picture

The universe is a big place — too big for us to comprehend. But how big? Astronomers have struggled with this question for millennia, and their view of the known universe has steadily grown to immense and incomprehensible sizes. It’s an important question, and a basic part of our grasp of the universe itself. To study astronomy, it’s essential to understand what’s out there, how everything relates, and where we fit in the universe. The problem is that the size scales, the relative general sizes of classes of objects, are too foreign for things much larger than Earth. In a big universe, this can be a challenge. To tackle the problem, let's try to connect the familiar life-size world around us with the unfamiliar cosmic size scales.
If you're a student, you probably watch your instructor write on the chalkboard almost every day. The chalkboard is something you're much more familiar with than the whole universe because you can see it and touch it. You know the size of the board, the chalk, the markings, the eraser, and so on because they’re right at hand. How much bigger is the board than a dot made on the board with a piece of chalk? It turns out that the answer is about a thousand, for an average sized chalkboard, and a fair sized chalk dot.
Now let's consider something that's a thousand times the size of a blackboard. A blackboard is a few meters across, so we want to think about something a few kilometers across. That's something like the size of a small city. If a city is 1000 times larger than a chalkboard and a chalkboard is 1000 times larger than the mark on a chalkboard, that's a useful connection that helps us think about the size of a city: we can say that the chalkboard in the city is like the mark on the chalkboard.
In this way we will now step out from the city into the larger universe. With each step, we will consider something (very roughly) a thousand times larger than the last step. As we move out, each stop in our journey will be much smaller than the next, like a mark on a chalkboard.
A city is much larger than the blackboard we used as a reference point, but it's still something we are very familiar with. Many people drive across part of their home city and back again every day. It's possible to drive through most small cities in a half hour or so, even with stoplights, and it only takes a few hours to walk from one end to the other. As promised, the next step out will be much larger and farther from our everyday experience. Our next stop will have a size of several thousand kilometers, and that's the size of Earth.
In a car, you can drive across a city in less than an hour, even at a slow speed. If you could drive around the Earth at a speed of 60 miles per hour (100 kilometers per hour), going day and night over land and water, it would take a full 17 days. Remember, driving through a small city at 60 miles per hour would only take a few minutes. Seventeen days is much, much longer than a few minutes. The fastest jets, which have a top speed of about 2,000 miles (3,200 km) per hour, can make the trip around the world much faster. At that speed, you could circle the Earth in 11 hours. Even speeds like that will quickly become inadequate as we continue moving out into the universe.
The size of Earth is typical of the sizes of the rocky planets, the terrestrial planets, but planets made mostly of gas such as Jupiter and Saturn are larger by a factor of several to ten. In general, we can expect the same kinds of things to have similar properties. Given no other information about a planet, we might guess its radius to be the same as Earth's. If we knew that our imaginary planet were a much larger gas giant, we might change our estimate and guess that the planet has the same radius as say, Saturn.
This size scale represents the vast majority of human experience. Only a small number of people have ever been in Earth orbit, and these people remained very close to Earth. Most of the satellites launched remain very close to Earth. The shuttle, for example, orbits at an altitude of only a few hundred kilometers — a few percent of the radius of Earth. Some spacecraft are sent to other planets or to the Moon, but the majority stay at the scale of this step in our journey. Only 24 people — the Apollo astronauts — have ever left Earth's orbit to visit the next stop on our journey.
As we continue to move out, we reach a size of about 1000 times the distance around the Earth. The distance to the Moon is about 30 times the diameter of Earth, so the Moon is easily within reach in this step, but there's little else in the remaining distance. The nearest planets, Mars and Venus, are out of our reach. Aside from the Earth and Moon, we find the space in the neighborhood of Earth to be almost completely empty, with only the occasional passage of an asteroid or comet.
Although the Moon seems nearby when we consider the huge space surrounding the Earth-Moon system, we should remember that the Earth and Moon are really very far apart. If we could get in a car and drive to the Moon, the trip would take five months of driving nonstop — 24 hours a day and seven days a week. If our jet could go to the Moon, it would take five days to get there. These trips are becoming longer now, but they're still manageable. The trip by foot is much longer, though — a walk to the Moon would take nine years! Light travels faster than anything else in the universe. It has a speed of 300,000 kilometers (186,000 miles) per second. At this speed, light can travel to the Moon in just over one second. This distance, the distance light travels in one second, is called a light-second.
Another step out will extend our reach to most of the planets. We now encompass the bulk of the Solar System, the system comprising the Sun and all of the objects orbiting around it. This size scale is about five billion kilometers across, 30 times the distance between the Earth and the Sun. The distance from the Earth to the Sun is a convenient standard for measurement in the Solar System, so astronomers use the average Earth-Sun distance as a standard unit called the astronomical unit (AU). One astronomical unit is equal to about 93 million miles or 150 million kilometers. We can say that we are now working at a size scale of 30 astronomical units, or 30 AU for short. A box this size centered on the Earth would comfortably fit Saturn's orbit, but Uranus, Neptune and Pluto are still too far away. For much of human history, none of the Solar System objects outside of this box were known to exist.
Remember that our size scale has increased from the last step by a huge factor, a factor of 1000. Using our jet to take a trip from Earth to Saturn would take about fifty years. Light takes about 80 minutes to travel from Saturn to Earth, depending on where Earth and Saturn are in their orbits. Because it takes so long for light to make the trip from Saturn, the light we see from the planet at a given moment actually left 80 minutes ago. This means that we don't see Saturn as it is presently, but as it was 80 minutes ago. This also means that looking out into space is like looking back in time. The farther we look, the older the light. This is not very important for Saturn, but it will become more important as the size scale increases.
As before, we can use the speed of light as a measure of distance. A light-second is the distance light travels in one second. Likewise, a light-minute is the distance light travels in one minute. That means that Saturn is 80 light-minutes away. In the same way, we could write that Saturn is 1.3 light-hours away, and that's about the same as Saturn's distance from the Sun. Saturn's orbit is much bigger than Earth's orbit, which is only 8 light-minutes in radius. This is a striking and important fact about the Solar System — the rocky planets, the terrestrial planets, orbit close to the Sun and close to each other, but the giant gas planets, the Jovian planets, orbit at greater distances and have more widely spaced orbits.
The next step in our journey will encompass a distance of 30,000 AU, or half a light-year. Although this step completely encloses the planets, Solar System objects are found at much greater distances. These objects form the Oort cloud — a vast, sparse region of comets surrounding the Sun. The Oort cloud is almost empty, but it's there just the same. At this step we've only covered a piece of the range of influence of the Sun, and plenty of Oort cloud remains out of our reach. The Oort cloud is thought to extend out from the Sun as much as two light-years.
If we look just beyond this step, we find the nearest star, Proxima Centauri, at about four light-years. It will take Voyager 1 and 2 80,000 years to reach this star. (These ships, launched in 1977, have a speed of 51,500 km/hour.) As other stars enter into the picture, the Sun will no longer be the dominant source of gravity. This means that we can expect the solar system to really end as we begin approaching other stars.
Our next step out places us in a 500 light-year box. This size scale is easily large enough to fit the Sun, Alpha Centauri, and many other stars. In fact, about 250,000 stars are within 500 light-years of Earth. Astronomers refer to this region as the Solar Neighborhood. As we've seen, the stars in the Milky Way are very far apart, with vast stretches of mostly empty space separating them.
Stars in the Solar Neighborhood (and throughout space) are mostly small and faint. If these fainter stars were much farther away, they would be too faint to see from Earth. Much brighter stars are more rare, but they can be seen from much farther away. Because of this, two "kinds" of stars fill the sky as viewed from Earth: stars that are intrinsically faint but nearby, and stars that are bright and more distant.
As we continue outward in our journey, we see the random scattering of stars form into a pattern. Spiral structure emerges, and we see that the Earth, the Solar System, and nearby stars are collected together into an orderly system of stars called a galaxy. Our galaxy is called the Milky Way Galaxy.
Like the Solar System, the Galaxy is shaped like a flat disk, but the Galaxy is much bigger. Our galaxy contains hundreds of billions of stars, and the Solar System is only one member contained inside. The Sun is located in the spiral arms of the galaxy about two thirds of the way from the center, and it orbits around the center of the galaxy with all the other stars. If the Milky Way were fifty miles long, the Solar System would only be a dot the size of the tip of a ball point pen. In actuality, the Galaxy is 100,000 light-years across, but only a few thousand light-years thick.
As we start out towards the next step, we see other galaxies like the Milky Way begin to appear. Compared to stars in the Milky Way, galaxies are packed together much more closely, and collisions between galaxies are much more common. The Andromeda Galaxy, the nearest galaxy to the Milky Way, is 2.5 million light-years away and on a collision course for Earth. Don't panic, though, as the collision won't happen for another 3 billion years.
At a size scale not much larger than our last, we see that the galaxies are clumped together. These galaxy clusters typically have hundreds of galaxies and are millions of light years across. Galaxies orbit around the center of their clusters. The Milky Way is a member of the Virgo Cluster. It orbits near the edge of the Cluster, so we can see much of its center in a small region of the sky in the direction of the constellation Virgo. Presently, the Milky Way is moving away from the center of the Virgo Cluster. In the distant future, however, the Cluster's pull will slow the Milky Way and draw it inward.
Although our reach now includes many more objects, the size scale of galaxy clusters still does not represent an expansion over the last size scale by a factor of 1000. We have not fully reached the next step in our journey until we come to the scale of hundreds of millions of light years. At this scale, even the galaxy clusters form clusters. These groups of galaxy clusters are called superclusters. A supercluster may contain hundreds of thousands of galaxies. The Virgo Cluster is a member of a supercluster called the Virgo Supercluster.
Light from the edge of our 500 million light-year reach has traveled for 500 million years before reaching us. This means that we see the Virgo Supercluster as it was 500 million years ago. Five hundred million years can be a long time, but it isn't really long enough for the universe to have changed significantly. Even though the light is old, the universe at the edge of the Virgo Supercluster still looks much like the universe nearby.
As we continue out from the 500 million light-year size scale, we see older and older parts of the universe. As the distance becomes very large, we begin seeing billions of years into the past, and big changes in the Universe as a whole become important. Going further and further back, we see the formation of the first galaxy clusters, galaxies, and stars. Eventually, we see the universe so young that no stars have formed yet. Before the first stars formed, the Universe was cool and dense enough for the loose, unused gas in space to block visible light. Beyond this, we can't see any further. The contents inside this wall are called the Hubble volume, or the Observable Universe. There's no way to observe objects outside of this volume because the light from these distant objects hasn't reached us yet.
The Universe extends out infinitely, but our view is limited to the Hubble volume. Trying to visit the edge of the Hubble volume is impossible. You'll never reach it because it's only an illusion. If you tried to visit the location where we see the edge of the Hubble volume, you would see the universe around you as it is today, not billions of years ago, and you would see the edge of the Hubble volume all around you, billions of light years away.
Extending out further inevitably delves into the pages of theory and crosses the line dividing what we have seen and what we cannot see. Some have theorised that the universe itself does not comprise all of existence, and that there may be other universes with different physical laws existing together in clusters and groups in a multiverse.
As we go further and further out, many note that there must be an edge, an end, a border of reality. Others have speculated that the universe, or the multiverse it sits in, is simply infinite, and has no such boundaries. However, at this point in time, there can be no absolution, no definite answer to these questions.
Much remains unknown about what the Universe is like, but our picture has evolved dramatically since humanity first began asking questions about the world around it. Armed with curiosity and the tools of science, astronomers have investigated the heavens for centuries, and their work continues today.

## Short History of the Universe

For time immemorial, humans have been intrigued by creation. Where did we, and the universe in which we live, come from? In the Rig Veda, it was proposed that before creation there was "neither existence nor non-existence." The Latin phrase ex nihilo nihil fit ("out of nothing comes nothing") sums up current human beliefs about origins.
The Qur'an contains the following verse regarding the origin of the universe: “Do not the Unbelievers see that the heavens and the earth were joined together (as one unit of Creation), before We clove them asunder?” [Al-Qu’ran 21:30]
Many possibilities have been considered by scientists over the millennia. Did the universe "happen" suddenly?… was it created quickly by God?… has it existed forever?… or is it in a constant state of creation, even now?
Just as we can use size scales to make rough comparisons of the sizes of objects in the universe, we can also use time scales to compare the periods of time over which events occur. For example, Comet Halley takes about 75 years to complete its orbit around the Sun, so we can say that the period of Comet Halley's orbit has about the same time scale as a human lifespan.

## The Origin of the Universe according to the Big Bang Theory

The universe is big in space, but it's also big in time. The age of the universe appears to be 13.7 billion years. Like huge space scales, a span of 14 billion years is hard to imagine for a person who will have a much shorter lifespan than that. To better understand very long time scales, we can "compress" long periods of time like the age of the universe into shorter periods such as a human lifetime.
A typical person will live around 80 years. That means that the Earth will go around the Sun eighty times over the course of an average lifetime. The human life time scale and the time scale of human history are far smaller than the time scale of changes in the universe. Astronomers have learned about how the universe as a whole came to be the way it is by studying only an instant of its existence. To get a clearer picture of how the cosmological time scales fit together, let's consider an imaginary astronomer whose life is "stretched out" to fill the entire history of the universe.
If a human lifetime were vastly longer than it is, the orbit of the Earth around the Sun might be too fast to be a useful way to measure age. Instead, it might be more practical measure time from something slower. The Sun takes 230 million years to complete an orbit around the Milky Way Galaxy. That means that a "Milky Way year" will be 230 million times longer than an ordinary year.
Let's suppose our old astronomer has a lifespan of 80 "Milky Way years" instead of 80 normal years. That way, the astronomer will live long enough to see events that happen on cosmological time scales rather than human time scales. The astronomer's life happens in extremely slow motion. His growth and his actions are slowed by a factor of 230 million. At this rate, it takes four normal months for the astronomer just to blink.
Astronomers have theorized that the universe was very small, hot, and dense when it began. Since then, it has expanded and cooled. At first, the universe contained almost entirely hydrogen and helium gas. The universe was very uniform, with no galaxies, stars or planets. We'll place our protagonist's birth at the time of the big bang.
Our astronomer was much too young to remember the early development of the universe after the big bang. By the time the astronomer was only two days old, atoms had formed in the universe and the universe had cooled enough for structure to begin forming in the gas that uniformly filled all of space. Remember, the imaginary long-lived astronomer measures time much more slowly — what the astronomer sees as two days amount to a million years of time on a normal clock. While a million years seems like an extremely long time, that's only a tiny part of the history of the universe.
Our astronomer's earliest memories of childhood will include the first formation of stars and galaxies, which began to occur when the astronomer was around five "Milky Way years" old. Galaxies would continue forming and developing well into the astronomer's teenage years, when the universe was billions of years old. Today, galaxies continue to evolve and change.
There are two schools of thought on how the Universe formed: "top down" and "bottom up". Top down theorists think that large clusters formed after the Big Bang, which later broke down into stars and galaxies. "Bottom up" theorists instead pose the theory that matter was originally dispersed fairly evenly by the Big Bang, later accumulating into stars and galaxies. Recent data from Hubble Deep Field photographs appear to support "bottom up" theories. The photos show young galaxies from up to 11 billion light-years away. These young, small galaxies, from early in the universe's history, support the theory that large structures formed out of smaller ones. The galaxies appear as faint blue blobs with vague spiral structures, 2000 to 3000 light-years across.
An important necessity for the appearance of life is heavy elements. Since only hydrogen and Helium gas were formed during the big bang, everything heavier than that had to be made in stars later. These other elements — all of the elements on the periodic table — were made in stars.
Stars use light elements like Hydrogen and Helium as their fuel. Like nuclear bombs, they use the power of the atom for energy. Stars are unlike nuclear bombs, however, in that most nuclear bombs get their energy from heavy atoms like Plutonium and Uranium. In a nuclear bomb, the energy comes from converting heavy elements into lighter elements. This process is called fission. In a star, the energy comes from converting the light elements into heavier elements. This process is called fusion. All of the material in the universe heavier than Hydrogen and Helium were made by fusion in a star.
An ordinary star can make many of the elements, especially the most important ones for life. It can't make all of the elements, though; it can't make anything heavier than Iron. The heavier elements were made in supernovae. A supernova occurs when a massive star reaches the end of its life. Supernovae are extremely bright and extremely hot. This is where the heaviest elements in the universe are made.
All of the material needed to make rocky planets was made in stars, and some of it was made in supernovae. This means that planets couldn't exist until there had been enough time for a star to completely go through its life cycle and become a supernova. The material would then be ejected back into space, and would form a new star, possibly with planets. It also means that everything in the world, including you, came from a star. As the astronomer Carl Sagan said, "We are star stuff."
The Sun and the Earth formed about four and a half billion years ago, when our long-lived astronomer was 37 "Milky Way years" old. A solar system forms relatively quickly, and ours probably only took about 100 million years. The Sun and the planets formed from a cloud of sparse gas in the Milky Way, which condensed down and coalesced. After this happened, the Earth was very hot. It was a completely molten ball of rock, and had melted so thoroughly that its consistency was similar to water. Certainly, no life could have existed on the very young Earth.
Soon, however, the conditions on Earth became suitable for life. For our carbon-based type of life to develop, a planet needs to have
* organic matter (the material from which DNA is made),
* liquid water,
* a source of energy, and
* appropriate temperatures.
Earth had all of these fairly early in its history. Scientists aren't sure when life first appeared on Earth, but some evidence dates the earliest life at three and a half billion years ago, when our astronomer was 47 "Milky Way years" old.
Evidence suggests that life appeared almost immediately once the necessary conditions were satisfied on the young Earth, but the first inhabitants of the new planet showed no strong predisposition for evolution to more advanced life forms. More than two billion years passed before primitive, single celled microbial organisms advanced to become multicellular life. Once it did, however, advanced life took rapid hold. This period of rapid development in the complexity of life is called the Cambrian Explosion.
The Cambrian Explosion occurred when our astronomer was 56 "Milky Way years" old. Ten years had passed on our slowed cosmological clock. This period of history was, in some sense, the most profound step in the development of intelligence on Earth.
Since the Cambrian Explosion, things have become very interesting on Earth. The astronomer was barely a year older by the time the primitive multicellular creatures had developed to become the dinosaurs, which were unimaginably more complex and advanced by comparison. We have now come into recent times, as the appearance of the dinosaurs occurred only twelve months before this instant in our astronomer's life.
We can see now that we must occupy a tiny, tiny part of the cosmic timeline. By what standard could the time of the dinosaurs possibly be considered recent? By a cosmological standard. The dinosaurs had a short stay on Earth. They disappeared 65 million years ago, or four months ago by the astronomer's clock. This gave mammals the chance to rise to dominance.
The first humans appeared on Earth only eight hours ago by our astronomer's clock. Civilization accounts for only a small fraction of this time. The first system of writing, and the first evidence of civilization, dates to only 6000 years ago, or fifteen minutes ago by our astronomer's clock. In the lifetime of the universe, all of culture and all of written history could fit into a coffee break!
Periods more similar to the human life span become even smaller in our comparison with the cosmic timescale. It was only very recently that people first endeavored to learn about the world using science in the way we understand it today. These first scientists, who considered observation and experimentation to give the last word on the nature of the universe, lived only about four hundred years ago, or one minute ago on our cosmic clock.
As we come progressively closer to the present, our lives seem progressively more ephemeral and fleeting. How long will our society, our culture, and our ideas endure in the long run? Only time will tell. At the current rate, it does not appear to be long before something must happen to stop the downgrade of society.
We can say little about what might happen on Earth in the next thousand years, let alone the next million years or the next billion years. Meanwhile, the Milky Way will continue on its normal course, a course which happens to be headed straight for a collision with the nearest neighboring galaxy in about 12 "Milky Way years." This is unlikely to be the disaster for Earth it might appear to be — a collision between any stars during a galactic merger is actually extremely improbable. The Solar System will simply take up residence in the new galaxy created in the aftermath of the collision.
Five billion years from now, the Sun will have used up its fuel and will die. At this point, about 20 billion years after the big bang, the long-lived astronomer will be 80 years old. The Earth will no longer be able to support life after the Sun dies, and the Solar System will become rather desolate. The universe as a whole will continue long after the death of both the Sun and our astronomer, but it too will slowly die, eventually becoming cold and empty as it continues to expand.
Looking back over the scales of the universe and seeing humanity's role, unimaginably small in both space and time, one might wonder whether science has painted a bleak, depressing, and hopeless picture for humanity. Some would say so, while others find comfort in the majesty and grandeur of the universe, and the possibilities that the future might bring. For now, the future of humanity in this universe, as chaotic and vast as it is, remains uncertain.
Summary of Events 230 million years = 1 year :
| Event | Real time scale | Compressed time scale' |
| Formation of structure begins | 1 million years after big bang | 2 days |
| Earliest stars and galaxies form | 2 billion years after big bang | 6 years |
| Sun and Earth form | 9 billion years after big bang | 37 years |
| First evidence of life on Earth | 10 billion years after big bang | 47 years |
| Advanced life forms on Earth | 500 million years ago | 57 years |
| First dinosaurs | 230 million years ago | 58 years |
| Dinosaurs become extinct | 65 million years ago | 4 months ago |
| Humans appear | 200,000 years ago | 8 hours ago |
| Writing is developed | 6000 years ago | 15 minutes ago |
| Modern scientific thought | 400 years ago | one minute ago |
| Present day | 13.7 billion years after big bang | 59 years |
| Human lifetime | 80 years | ten seconds |
| Milky Way collides with Andromeda | 17 billion years after big bang | 71 years |
| The Sun dies | 20 billion years after big bang | 80 years |

## Scientific Notation

In previous sections, we discussed some numbers that were very large. In astronomy, the appearance of such huge numbers is common. This is one reason astronomers and other scientists use scientific notation when working with very large or very small numbers. Scientific notation is a system for writing and working with numbers that makes it much easier to deal with numbers that are very small or very large.
For example, the Milky Way Galaxy contains roughly three duodecillion tons of material. That is a rather cumbersome number. (Astronomers would never actually write this. Instead, they would say that the Milky Way contains one trillion times the mass of the Sun, which is somewhat easier. We'll use this much larger number for our demonstration.) You could also write this number as
    3 000 000 000 000 000 000 000 000 000 000 000 000 000 tons,
but that's even worse. Scientific notation makes the number much more compact and readable:
    3 × 10$^{39}$ tons.
This number is verbally expressed as "three times ten to the 39 power tons." This is numerically equivalent to the first two expressions.
A number written correctly in scientific notation has two parts. The first is a number greater than or equal to 1 and less than 10 (but it can be either positive or negative). This is sometimes called the mantissa. The second part is the number ten raised to a whole number power. The exponent of the second number is called the power. Some examples of numbers written correctly in scientific notation are:
    2 × 10$^{18}$
    -1.4 × 10$^2$
    7.656 × 10$^{-4}$
    2.1 × 10$^0$
These, on the other hand, are not valid examples of numbers written in scientific notation:
    0.1 × 10$^4$ is wrong because the mantissa is less than 1
    12 × 10$^3$ is wrong because the mantissa is not less than 10
    8.4 × 10$^{2.2}$ is wrong because the power is not a whole number
Remember that
    10$^n$ = 10 × 10 × 10 × ... for n times,
which means that ten raised to n power is the same as 10 multiplied by itself n times, which is the same as a 1 with n zeros written after it. For example, 10$^3$ is 10 × 10 × 10, or 1000. That means that our earlier number, 3 × 10$^{39}$ tons, is equivalent to
    3 000 000 000 000 000 000 000 000 000 000 000 000 000 tons,
which is a three followed by 39 zeros. A number written in scientific notation with a negative power corresponds to a small number. For example, the number 1 × 10$^{−3}$ is written as 0.001 in conventional notation. In general,
    10$^{-n}$ = 1/10 × 1/10 × 1/10 × ... for n times.
* These are the steps in converting a large number expressed in scientific notation into standard notation. Write the mantissa and find the location of the decimal point, and shift the decimal point by the number indicated in the power. Here, the power is 9, so the decimal is moved nine digits to the right.
* These are the steps in converting a small number expressed in scientific notation into standard notation. The steps for converting a small number are the same as for a large number, but the decimal point should be shifted to the left instead of to the right.
Since scientific notation relies on powers of ten, it's simple to convert a number from scientific notation to standard notation or vice versa. To convert a large number (with a positive power) from scientific notation to standard notation, first identify the decimal point in the mantissa, then shift the decimal to the right by the number indicated by the power. To convert a number from standard notation to scientific notation, just reverse these steps. Find the decimal point in the number, and move it until the number is at least 1 but less than 10. Count the number of places you moved the decimal point and use that number as the power. If you moved the decimal point to the left, make the power positive. If you moved the decimal point to the right, make the power negative.
Scientific notation also makes it simpler to do multiplication and division. To multiply two numbers in scientific notation, multiply the mantissas and add the powers:
    (3 × 10$^4$) × (4 × 10$^{-2}$)
    (3 × 4) × 10$^{4-2}$
    12 × 10$^2$
    1.2 × 10$^3$
In some cases, such as the one shown here, you may need to shift the decimal point again ensure that the number is in correct scientific notation. It should never be necessary to shift the decimal point by more than one digit. When dividing numbers in scientific notation, divide the mantissas and subtract the powers:
    ${\frac {3\times 10^{4}}{4\times 10^{-2}}}$
    $(3/4)\times 10^{4+2}$
    0.75 × 10$^6$
    7.5 × 10$^5$
Here also, it may be necessary to shift the decimal point and change the exponent.
Scientific notation makes it easy to compare numbers that have very different values because all the zeroes have been replaced with the much more readable exponent. Numbers with a greater exponent are always bigger than numbers with a lesser exponent.
If one of the exponents is bigger than the other by more than a couple, the difference between the two is clearly very big. Recognizing a huge difference between two numbers can sometimes be a very useful insight, so it often makes sense to take a moment to develop an intuitive feel for a math problem before attacking it. In some cases, it's useful to see roughly by how much one number is larger than another. Scientific notation makes this much simpler. For a rough estimate, you only need to find the difference in the exponents. For example, 10$^7$ is greater than 10$^3$, since 7 - 3 = 4.
    Some tourists in the Chicago Museum of Natural History are marveling at the dinosaur bones. One of them asks the guard, "Can you tell me how old the dinosaur bones are?"
    The guard replies, "They are 73 million, four years, and six months old."
    "That's an awfully exact number," says the tourist. "How do you know their age so precisely?"
    The guard answers, "Well, the dinosaur bones were seventy three million years old when I started working here, and that was four and a half years ago."
    (From the Science Jokes Web page )
In science, measurements are never perfect and numbers are never exact. As a result, every measurement we make has some uncertainty associated with it. Scientific notation makes it easy to express how precisely a number is known. Suppose a paleontologist discovers ancient dinosaur bones and finds that they are 73 million years old. Of course, the paleontologist doesn't know exactly how old they are. Maybe they're 73,124,987 years old, but the paleontologist only knows the age within 1 million years, so the age is written as 73,000,000 years, or 7.3 × 10$^7$ years. Either of these expressions imply that the bones aren't exactly 73 million years old, but are 73 million years old, give or take a million years.
But what if the paleontologist knows the age within 200,000 years, and is sure that the bones aren't, say, 73.4 million years old? In that case, the standard notation is ambiguous — the number is still written as 73,000,000 years. In scientific notation, we can write the number as 7.30 × 10$^7$ years. If we write this, we mean that the third digit is significant. The paleontologist might have calculated that the bones are 72,954,332 years old, but it would be useless to report these numbers, since the error on this measurement was 200,000 years. The extra digits are insignificant. The number of significant figures in a number are a reflection of the precision expressed in the number. In this case, the number of significant figures is three. The first significant figure is 7, the second is 3, and the third is 0.
Scientific notation gives the trailing digits written after the decimal point of a number special meaning — they tell that the number is exactly 7.30 × 10$^7$ years. This is unlike the usual use of numbers in mathematics, where trailing zeroes after the decimal point have no special meaning.
In the story about the museum guard, the guard hadn't thought about the precision of the age of the bones. It doesn't make sense to add the four years to 73 million years because the uncertainty in the age quoted to the guard was a lot more than 4 years. When working with numbers that have uncertainties, we must be sure not to express better precision in the results of our arithmetic than we had in the first place.
When doing arithmetic, numbers being added or subtracted are treated differently from numbers being multiplied or divided.
    When multiplying or dividing numbers with uncertainties, make sure that the answer has as many significant figures as the least precise of the original numbers.
For example, in (2.3 × 10$^3$) × (1.21 × 10$^2$), the number 2.3 × 10$^3$ has two significant figures and the number 1.21 × 10$^2$ has three significant figures. The result should have two significant figures: 2.8 × 10$^5$. We assume that there was some uncertainty in the measurement that gave us 2.3 × 10$^3$, and this leads to some uncertainty in the result of the computation.
Addition and subtraction work differently. When adding 23.14 and 2.2, for example, the number 2.2 has uncertainty beginning in the tenths place. This uncertainty makes it pointless to report the hundredths place in the sum. To see this, try adding some uncertainty to 2.2 and see how this affects the sum.
    When adding or subtracting numbers with uncertainties, round the result to the last significant place of the original number with the greatest uncertainty.
For example, 2.3 × 10$^3$ + 1.1 × 10$^2$ can be written as
    2300 +110 2410
But we don't know the real value of the tens place in 2.3 × 10$^3$, so we really only know the answer to the hundreds place. We should write
    2300 +110 2400
or 2.3 × 10$^3$ + 1.1 × 10$^2$ = 2.4 × 10$^3$. This may seem incorrect, but we're really only rounding off. Since we don't know the result to better than two significant figures, it makes no sense to report the extra digits — that would be like the museum guard who tells visitors that the dinosaur bones are 73 million and four years, six months old.
Almost every number has a unit of measurement attached to it. The number we used as our first example carried units of tons, and we expressed the age of the dinosaur bones in years. The units a number carries are part of the number itself. Units can also be multiplied or divided just like numbers.
As an example, consider a simple equation:
    distance = velocity × time.
Suppose you drive in a car with a speed of 100 kilometers per hour (60 miles per hour) and you go in a straight line for one hour. The distance you will travel is
    $\mathrm {distance} =100{\frac {\mathrm {kilometer} }{\mathrm {hour} \!\!\!\!\!\!\!\!/}}\times 1{\mathrm {hour} \!\!\!\!\!\!\!\!/}$
or 60 miles. We have cancelled hours as though it were a number.
This trick is also useful when you need to convert units. If you have a result in one system and you'd like to convert to another, you can set up a ratio, such as 1,000 meters/1 kilometer. Since 1,000 meters is equal to 1 kilometer, the ratio 1,000 meters/1 kilometer equals one. Because of this, multiplying any number by 1,000 meters / 1 kilometer will not change the value of the number. If we want to know what 100 kilometers is in meters, we can write
    $100\mathrm {\ kilometers} \!\!\!\!\!\!\!\!\!\!\!\!\!\!/\,\,\,\,\,\,\,\,\,\,\,\times {\frac {1000\ \mathrm {meters} }{\mathrm {kilometer} \!\!\!\!\!\!\!\!\!\!\!\!\!\!/}},$
or 100,000 meters.
Other units of measurement used in astronomy are kilograms (mass), Newtons (force), and Joules (energy).

## The Scientific Method

The results of scientific thought have played an important role in shaping the world into what it is today. This is true not only because of the influence technology has had in our lives, but also because of the change science has brought to the way we think. Scientific thinking has permeated all aspects of our lives, fundamentally changing the way we see the world. It is science's "way of thinking," the scientific method, that forms its heart. Although "scientific thought" or "science" is sometimes taken to refer to the entire body of scientific theories and knowledge including chemistry, biology, physics, and so on, the term science strictly only refers to the process by which these theories and ideas are examined.
The scientific method is fundamental to the investigation and acquisition of new knowledge based upon physical evidence. Scientists use observations, hypotheses, and logic to propose explanations for natural phenomena in the form of theories. Predictions from these theories that can be reproducibly tested by experiment are the basis for developing new technology.
Although scientific progress is often described as a linear scheme that allows a single scientist to proceed from a state of relative ignorance to a state of knowledge, the scientific method is really much more complicated than this. The scientific method is not a recipe. It requires intelligence and imagination. Science is not the lifeless execution of step-by-step instructions, but a creative and inspired process. Over the past half-century, philosophers, historians, and sociologists of science have established a more complete model describing the ways science is actually practiced.
The modern description of scientific progress gives much more importance to the role of the scientific community. It is impossible for a single person working in isolation to engage in science. This is because of the central role of peer review as a means of correcting error, bias, and self interest. Human nature prevents even a well intentioned scientist from doing anything other than confirming preconceived ideas when working in isolation. Because science is closely tied to a community, progress is usually scattered, proceeding from many stages and different directions at once.
In a new area of scientific exploration, scientific progress is slow at first. Investigators reach out in search of a basic description of how their area of inquiry works. This inquiry is motivated by observations of some interesting phenomena manifested in reality. The observations and experiments undertaken by scientists in a developing field are typically dictated by the scientists' interests and by convenience. The scientists have no heritage of successful experiments and little common ground. Because of this, new pursuits in science lack direction and are wanting of a broad common ground that will unite scientists and prescribe the course of scientific research.
As the new field advances, an underlying set of principles begins to take hold and gain widespread acceptance. These principles become the common ground of scientists in the new field, the basis of a paradigm. With a paradigm in place, researchers no longer need to start from scratch when interpreting the results of new experiments. Instead, they address a specialized audience that works under a common paradigm, and they describe their work in the context of that paradigm. They are no longer unguided in the direction of the work — the paradigm dictates which experiments might be useful in further exploring the questions of their field. An established paradigm is therefore an extremely valuable asset in the pursuit of science.
In the presence of an established paradigm, the normal course of scientific research begins. Scientists seek to clarify the understanding of their area of research by formulating theories grounded in their paradigm and by making relevant observations that test the theories and further clarify the paradigm. The observations give greater insight into the paradigm and test the agreement of theories and paradigms with reality. The theories discern previously unseen details in the paradigm and in nature, and guide the method of new observations.
For the normal course of scientific progress, these methods are extremely efficient. In some cases, however, a scientific discipline might be founded on a paradigm that is fundamentally incorrect. This presents a problem, since the paradigm underlying a discipline is deeply valued by the practitioners in the discipline. Such was the case in astronomy during the scientific revolution of the Renaissance. From the times of Aristotle, it had been thought that the Earth was at the center of the Universe, with everything else moving around it in circles. Eventually, observations of the positions of the planets made Aristotle's model inconsistent with reality. As time passed, it became increasingly difficult to modify Aristotle's paradigm to agree with observations. The prospect of a new and completely different paradigm became ever more attractive, and the new idea of a Sun-centered universe took root.
It is almost always the case that some observations cannot be explained by existing scientific theories, but a gap between knowledge and theory is hardly sufficient to produce a paradigm shift. In The Structure of Scientific Revolutions, Kuhn claims that scientific revolution is only possible when the dominant paradigm of a field is in a state of crisis. Only once it becomes apparent that the ideas tied to the paradigm are irreconcilable with observations does it begin to appear sensible to pursue completely new explanations.
When scientists consider theories, either as candidates for a new paradigm or as elaboration for an existing paradigm, they evaluate theories on the basis of a number of criteria that have proven over the years to be relevant indicators of usefulness. These criteria were described by the philosopher of science Karl Popper in his book, The Logic of Scientific Discovery.
The central goal of science is to produce theories that are consistent with reality. Science approaches this goal by testing a theory for validity, and discarding or modifying the theory if observations can't be shown to agree with it. The use of an approach like this requires that theories be falsifiable. In order for a theory to be scientific, it must be relevant to observable aspects of reality. It must be possible, at least in principle, to make observations that would be inconsistent with the logic of the theory. Said otherwise, the theory must make non-trivial predictions that can be tested by a set of observations. If scientists find that a theory's predictions are incorrect, the theory is falsified. A central property of scientific theories is that they can never be proven, but they can eventually be disproved. This fact makes it essential that a theory make specific, useful predictions before it can be examined scientifically.
The need for falsifiability implies a need for theories that make clear predictions. Theories that make strong predictions are said to have a high predictive power. A theory with high predictive power makes bold, clear and testable predictions. Theories with high predictive power are more highly valued in science because they are more easily falsified. Scientists consider theories that have not been falsified despite strong predictions to be more reliable, whereas a theory that makes fewer predictions or less bold predictions tends to be received with more skepticism.
The requirement that scientific theories have strong predictive power leads to the surprising notion that an implausible theory should be preferred over a plausible theory. This is because the claims made by the implausible theory are bolder and more subject to being falsified. In order to succeed, a scientific theory must make a prediction that would not be expected otherwise. If a theory makes a seemingly wild claim that turns out to be correct, the theory is very well supported. This mechanism for developing scientific ideas by creating and testing the predictions of a model is the foundation of science.
A final requirement of scientific theories is that they be as simple as possible while still accurately describing nature. This requirement was famously stated by the English logician and Franciscan friar William of Ockham. He stated the requirement, in Latin, as
    Numquam ponenda est pluritas sine necessitate,
which translates roughly as
    Assertions should not be multiplied unnecessarily.
This maxim is widely known as Ockham's Razor. It is a very useful principle, but also one of the most misused doctrines in science.
Ockham's razor warns us that, when two theories make identical predictions, the theory that relies on fewer assumptions is more likely to be correct. The razor is based on the principle that reality is unlikely to conform to our presuppositions. In the absence of evidence, it's often wiser not to speculate.
When creating theories or distinguishing between competing theories, scientists rely on two distinct types of reasoning: inductive reasoning and deductive reasoning.
Inductive reasoning works from the specific to general. It involves making observations and building generalizations on the basis of observations. For instance, you might observe the sunrise every day for a year, and you notice that this Sun rises more or less in the east every time. You might conclude that the Sun always rises in the east. Inductive reasoning involves drawing conclusions from a limited sample of information. You have no way of knowing that the Sun won't rise in the west tomorrow. Still, a pattern will become apparent as observation continues, and year after year of observation makes it compelling to imagine that the Sun must always rise in the east. If the pattern remains very consistent, it can be considered reliable even if the underlying cause isn't obvious. Should a theory ever be presented that predicts that the Sun will always rise in the east, that theory will be well supported. On the other hand, if a theory predicts that the Sun will sometimes rise in the east and sometimes in the west, that theory will be disfavored by the observations even though it isn't disproved in a strict sense. Notice that it is possible, though unlikely, for inductive reasoning to discredit a correct theory or support an incorrect theory. Although it is a powerful and essential tool in science, inductive reasoning must be treated with skepticism when based on a very limited sample of observations.
Deductive reasoning works from the general to the specific. It is based on logical arguments (syllogisms). An example of deductions invented by the author Lewis Carroll is provided below:
    All lions are fierce.
    Some lions do not drink coffee.
       Therefore, some fierce creatures do not drink coffee.
Unlike inductive reasoning, deductive reasoning is perfectly reliable if you have made correct assumptions and applied correct logic. Because deductive reasoning is absolutely reliable when used with good assumptions and proper method, it is easy to place undue trust in claims made on the basis of deductive reasoning. It is important to remember that these claims also require careful examination to check that the assumptions are good and the reasoning is valid. In reality, deductive reasoning is as much subject to error as inductive reasoning. Only the sources of error differ.

## What People do in Astronomy

Astronomy like all sciences is a social activity in which people are constantly discussing new ideas, interpreting data, and arguing with each other over what observations mean. Astronomers can broadly be divided into two groups. Observational astronomers specialize in building instruments such as telescopes, and spacecraft, and take raw data and process them into meaningful results. Theoretical astronomers often also known as astrophysicists take the results that observational astronomers provide and attempt to create physical models which explain the data that observers see and provide ideas of the directions that observers should go into. Theoretical astronomers increasingly rely on computer models and often are skilled at programming.
Astronomy is rather unique in that a lot of the data is provided by amateur astronomers. The data needed in some fields such as variable star astronomy or comet discovery can be gathered by instruments well within the budget of an interested hobbyist.

### Peer review

A central part of the scientific process is peer review which occurs at several stages in the process, and creates what H.H. Bauer calls a knowledge filter. In the peer review process, a proposal or a journal article is given to a group of referees who anonymously submit their comments on the proposal. While the referees will sometimes communicate with each other, they are not intended to reach a consensus on the quality of work. In addition, the referees usually do not have the final authority to decide on the fate of a proposal, but instead given their opinions to an editor or project director who does have the final authority and on occasion overrides the opinions of the referees.
The opinions of the referees are usually made available to the submitter, and often contain suggestions for improvement to the submitter. This is considered crucial for the scientific process as it allows the submitter to receive feedback on his or her proposal and improve it. In some cases, the submitter is encouraged to resubmit their proposal after making changes, and this often develops into an anonymous communication between the referees and the submitter.

### Getting what you need

A lot of the work in astronomy involves getting access to resources, which include:
* money
* for observers, telescope and equipment time
* for theorists, computer time
In order to get these resources, astronomers typically write grant proposals which outline the amount of money, telescope, and computer time needed.
Grant proposals typically undergo peer review by the granting agency which includes feedback on how well it fits the priorities of the funding agency, how likely the committees think it is to advance the frontiers of knowledge, and how essential the resource being allocated is to the researcher. Typically, a set portion of telescope or supercomputer time will be made available to the institution that hosts or funds the resource, giving scientists affiliated with that institution priority use over that resource. The remaining time is then made open for research proposals from researchers from other institutions. In the case of ground based telescope time, the most precious and highly sought after time is dark time during which the moon is new and the dimmest objects can be seen.
In some cases, such as building a new telescope, supercomputer center, or funding a new spacecraft, astronomers must lobby funders such as charitable foundations and legislators for money to finance a certain activity. The lobbying for research facilities can be extremely intense as having a facility sited at your institution gives your institution priority access to the facility, as well as prestige, and makes your institution a destination for researchers.

### The life of an observational astronomer

Typically, in an observing run, you wake up at about 3 p.m. During the day the technicians will have installed the instruments that you need for a nights observing run. You go to the telescope at 3 p.m., check to see that everything is installed correctly, since you don't want to wake someone up at 3 a.m. if something breaks, you then spend the next two hours before sunset taking some calibration shots.
After the sun starts setting, your first goal is to find the object that you are trying to photograph. You can punch in the coordinates into the computer, but that will only point the telescope in the general area of the sky that you are interested in. The next thing that you have to do is to take out your star atlas, and look for a pattern of stars that is close to the thing that you are looking for. This is a lot like driving in a strange city when you are looking at the monitor and then trying to match the patterns you see with the patterns on the chart.
So you've now found the object you are looking for. In between these measurements, you take some snapshots of a calibration device. If you are looking at spectra, you take picture of a fluorescent lamp that has lines in certain known positions. If you are measuring brightness, then you need to take some pictures of a star whose brightness is known.
So after a night of all of this, you now have some data on hard disk, and you go to sleep. The next few weeks is where the hard part comes in. You see you have a lot of raw data, but it's not very useful to anyone. The problem is that none of the data has been calibrated. So you spend the next few weeks taking the data, subtracting the black levels, correcting the white levels, stretching and shrinking the picture so that you know what the frequencies of your spectra are. You might also be spending your time doing things like trying to correct for the effects of dust in the galaxy. Through it all, you are probably using an astronomy package called IRAF, which like all big software packages has its cute bugs and idiosyncrasies. At the end of all of this you have a paper, and are ready to publish.
Observational astronomers are often at the mercy of things that are outside of their control. Weeks if not months of effort at setting up an observing run can be destroyed if it happens to be cloudy or raining on the night of the run.

### The life of a theorist

Unlike observers, theorists are creatures of the day. The typical theorist spends their days reading papers trying to understand how to model a particular type of phenomenon. Once they have a model, the goal then is to try to get testable predictions from that model, and this often means programming a computer to calculate the consequences of that model. There are occasional flashes of inspiration, but most of the time is spent very slowly and methodically trying to understand the consequences of a model, and to slowly and methodically program the model into a computer and systematically remove the bugs from the model.
There are also a lot of social interactions as theorists argue and debate what a particular observation means, and as theorists and observationalists share ideas about the latest data.

### Letting people know about your research

There are a number of channels through which scientific results are made known. The primary means that astronomers use to make others aware of current research are through preprints which are papers uploaded through web servers such as the Los Alamos Preprint Server at http://www.arxiv.org/ or through conference proceedings in which scientists announce their results either through lectures or poster papers. Astronomers are also constantly travelling between departments to give talks on their research at seminars, astronomy lunches, and journal clubs.
Although it has been supplemented by preprints, peer reviewed publication in the primary literature is still considered an essential part of publicizing research. This literature consists of articles in journal such as Astrophysical Journal or Astronomy and Astrophysics. Because of the length of time, typically several months, necessary to go through a peer review, research results are typically shared with the community through preprints before peer review is complete. Nevertheless, astronomers still generally submit their papers to peer review even after the results have been released to the research community, because the interaction between anonymous referees and the paper submitter improves the quality of the work and insures the community that the paper does not have any obvious errors.
Once an astronomy paper is available for publication, it can be accessed through the Astrophysics Data System at http://adswww.harvard.edu/ Increasingly, raw data from sky surveys is being made available on the web.
One shortcoming of the primary literature is that it reports on individual research results without providing context. As such it is difficult for someone who is not actively involved in research in a particular area to understand the relevance of the work. To deal with this problem, primary literature is summarized and combined into the secondary literature, where it will be read by a broader audience of scientists. The secondary literature is a synthesis of the results of recent research in a field. The body of secondary literature includes periodic reviews of progress, such as the Annual Review of Astronomy & Astrophysics, professional books, and other research summaries.

### How to be an astronomer

Most astronomers major in either physics or astronomy as an undergraduate and then go to graduate school where they work on the Ph.D. under the supervision of a dissertation advisor. The main challenges in becoming an astronomer are to master the language of mathematics and physics, and to gain experience in working through the scientific process.
After graduate school, an astronomer typically works as a post-doctoral fellow before getting a job either as a professor at a university or a researcher at a laboratory. Because of the large number of graduates gaining Ph.D.'s, people with astronomy degrees are increasingly found outside academia. They work in science related fields, as computer programmers for software companies and even on Wall Street.
Astronomy also is open for amateur astronomers. Most of the data for variable stars is accessible via a telescope which is affordable by hobbyists, and amateurs provide important observational data.

### Notes

[2] There are some exceptions to the practice of releasing research results before peer review is complete, and this involves a trade-off between speed and completeness.
When a result is believed likely to be controversial (such as the possible discovery of microfossils on Mars), the researchers may choose to keep the finding secret until peer review is complete so that the result will likely withstand challenges after it is released. Another case where results are kept until peer review is complete involves releasing large datasets such as sky surveys. In this case, the delay introduced by peer review is small in comparison to the benefits of having a through review before announcing the results.

### Discussion questions

1) Visit either the Los Alamos preprint site or the Astrophysics Data Service and find a paper. How is the paper structured and what concepts in this text book do you find in the papers?
2) Look at the schedule of several university astronomy departments on the web. What is being discussed? How are different astronomy departments different from each other and how are they the same?

## Dark Matter and Dark Energy

Dark matter is invisible, but has been postulated from its apparent influence on visible matter. It is one explanation for the observed strength of gravity needed to hold galaxies and clusters of galaxies together. Without considerably more mass than can be detected with telescopes, roughly 10 times more, these systems should simply fly apart. The dark matter theory hypothesizes that matter exists that emits little or no radiation and therefore is not observable with telescopes. Dark matter might also be needed to explain the cosmic microwave background (CMB) power spectrum. Some proposals for explaining dark matter are, for example, particles like weakly interacting massive particles (hypothetical WIMPs) or neutrinos, or massive compact halo objects (MACHOS), or ordinary matter that is hidden somehow, or modified gravity (MOND, MOG, f(R)), or some combination of these things.
Another hypothesis, dark energy, has been proposed to explain the surprising observation that the expansion of the universe is getting faster. This acceleration of the expansion was discovered by measuring a certain type of supernova, called type Ia, in surveys of galaxies. Type Ia supernova are used since they all have the same absolute brightness. (We will discuss why they have the same absolute brightness, and how they are used to measure distances, in a later chapter, General Astronomy/The Death of High Mass Stars). This makes them very useful for measuring distances. It had been anticipated, before the measurements were made, that the expansion of the universe would be decelerating, due to the gravity of all the matter. Dark energy is postulated to explain the apparent repulsive force pushing things apart. Ongoing research efforts are to measure the expansion rate more accurately, and discover the nature of dark energy.
Dark matter is generally accepted to exist, though questions remain. It is probably not regular matter made of protons and neutrons (baryonic matter). That is because a higher density of ordinary matter during the nuclear reactions occurring in the first few minutes of the universe (known as big bang nucleosynthesis), would be expected to produce different abundances of light elements and their isotopes, like deuterium, than are actually observed. Another problem for ordinary matter is that the "clumpiness" of the observed galaxies and the cosmic background radiation is not what would be expected from predictions. Other considerations tend to disfavor neutrinos as dark matter as well.
Alternatives to the dark matter hypothesis are new forces or modified gravity theories. There is speculation that there is another large-scale force that is keeping our universe together. Another possible explanation is to think of space as a gas-and-space solid. If you place two objects apart from each other then pressurize the area, the two objects will be forced towards each other. This reverses our current ideas of gravity from an object having a pull on other object, to an object being pushed from all directions. (An object alone has no movement, but two objects create an uneven pressure pushing the objects together.)
An estimated 23% of the matter in the universe is dark matter. Ordinary matter only makes up 4% of the universe. The remaining 73% is an even more mysterious, repulsive "dark vacuum energy".
The most popular theory right now is that the repulsive force is actually a property of space itself: it is caused by waves of energy, created by particles and anti-particles popping into existence and then annihilating each other with no net effect. Early in the universe, when there was not much space, the effect was small compared to gravity. But as the galaxies moved apart, the effect became greater.
History and Ideas of Composition
Dark matter was first proposed in 1933 by Swiss astrophysicist Fritz Zwicky to explain the orbital motions of galaxies in clusters. He observed that there was apparently much more mass in a cluster of galaxies than just the visible objects, like stars, gas, and dust. So there was something unseen adding to the mass of the cluster. Later, when X-ray telescopes became operational, they revealed a cloud of hot hydrogen gas between the galaxies, accounting for part of the missing mass. Beginning in the 1960's, Vera Rubin discovered that contrary to Kepler's law that objects orbiting around a central body move slower the farther away they are, that in fact the orbital speed of stars in galaxies remains roughly the same beyond a certain distance from the galaxy core. So there has to be some extra matter, either in the flat disk of galaxies or in a spherical halo around the galactic core. Building on Zwicky’s work she concluded that this extra mass was dark matter. The term dark matter refers to matter that is perceived to be present because of its effect on the objects around it. While the composition of dark matter is still unknown, scientist have proposed some possible candidates that dark matter could be. They are:
* Ionized gas — Emits thermal free radiation which cannot be observed.
* Dust — Emits radiation and is made up of elements heavier that helium.
* Main Sequence Stars — Could be an ingredient, but could not be sole component of dark matter because a great portion of them would be visible.
* Black Holes — Are highly unlikely because they would disrupt the binary separations of dark matter. However, not much is known about the explosions that produce black holes, so it is still an option.
* White Dwarfs — When forming, white dwarfs produce many intermediate-mass elements (He, N, Ne, C, O) or halo gas, which is not visible.
* Neutrinos — Unlikely, but they do have enough mass to be a candidate.
* WIMPS or Cold Dark Matter — Weak interacting particles, though they do move at nonrelativistic speeds.
A more in-depth flow chart depicting how the above suggestions are connected is picture below taken from Modern Cosmological Observations And Problems (140). http://ned.ipac.caltech.edu/level5/Bothun2/Figures/dm1.gif

## Reionization

The cosmic background radiation was formed when protons and electrons combined to form atoms. The trouble is that we know that the matter between galaxies today is ionized (i.e. it's separate protons and electrons) with clumps of hydrogen atoms. We know this because when we look at all but the most distant galaxies, we don't see the spectra lines of hydrogen. So at some point the hydrogen in the universe reionized. The notion was that starlight caused the hydrogen in the universe to reionize, but the latest observations seem to indicate that this reionization occurred before the first stars were there.

## Galaxy Formation

The idea is that galaxies started from tiny fluctuations in density that formed after the big bang. By assuming that the universe consists mainly of cold dark matter, you can almost get the clumpiness that you see with the current galaxies. But there are still puzzles. There is an annoying lack of tiny galaxies, and the rotation curve that cold dark matter predicts, isn't quite the one that we see.

## Before the Big Bang

Now to get really speculative, there have been some papers written recently that try to figure out what happened before the Big Bang. One of the strange ideas is that the universe is merely one plane in a multidimensional space, and that what happened was that two membranes in a multidimensional space collided causing a massive expansion in three of the dimensions. This is all really speculative, but the weird thing is that it isn't totally disconnected from observation. The idea is that you can use this model to predict the initial expansion of the universe, and this might have some effects on the ripples that you see in the cosmic microwave background. The big problem is that the matter that began expanding had to have always existed, yet, because of the predictable nature of the elements, it had to have had a definite, external force to set it in motion that could decide when to start the "chain reaction". Something cannot just be in a stable form, or even an unstable form, forever and finally explode, it has to go in a cycle. In other words, consider the following. Out of nothing, a theretofore nonexistent dense mass spontaneously emerged, which erupted in an enormously powerful fireball by its own theretofore nonexistent energy to spontaneously and immediately create from this chaos the defined fundamental forces of physics and the subatomic fundamental particles, which eventually organized themselves into a variety of atomic species, then into molecules, and then into a diverse assortment of inorganic matter that gravitationally assembled itself into this highly structured and precisely ordered universe. We all know that this is ridiculous, but it is equally ridiculous to say "a theretofore stable mass spontaneously became unstable".
With all of these puzzles, its not clear what is going to happen next. There is a lot of data coming in, and it may be that with new data, it will be possible to make our models of the universe work with minor tweaks here and there, and we can go on in the mode of what Kuhn calls "normal science." It's also possible that one day there will be some observation which is like Galileo seeing the phases of Venus — some observation that makes absolutely no sense in the current paradigm of things, and this will force people to fundamentally change how they view the universe.

## Discussion Questions

1) Find an old astronomy textbook, and compare it with a very recent one. What mysteries in the old astronomy textbook are now believed to be resolved, and what facts and statements in the old astronomy textbook are now believed to be incorrect?