One of the more difficult concepts for students of Astronomy 105 to comprehend is the great range in sizes of the many different types of objects needed to understand the planets. As we wind our way through the semester, we will talk about the smallest subatomic particles, and we will discuss the largest object in the Solar System: the Sun. Before we start on this path, however, it is important for you to become comfortable with the way we will express very large and very small numbers using something called "scientific notation".
To start this exercise, let's look at some familiar numbers: ten, one hundred, and one thousand.
The number ten is written as: 10
The number one hundred is written as: 100
The number one thousand is written as: 1,000
All three of these numbers are multiples of 10:
10 = 1 X 10
100 = 10 X 10
1,000 = 10 X 100 = 10 X 10 X 10
Back in high school you learned about the squares of numbers, for example 22 = 2 X 2 = 4. Here are some other examples:
32 = 3 X 3 = 9
42 = 4 X 4 = 16
52 = 5 X 5 = 25
10 2 = 10 X 10 = 100
etc.
The superscript two in these expressions is called the "exponent". The exponent can actually be any real number, but in this class we will be dealing with integers. Here are some other examples of integer exponents:
33 = 3 X 3 X 3 = 27
103 = 10 X 10 X 10 = 1,000
44 = 4 X 4 X 4 X 4 = 256
56 = 5 X 5 X 5 X 5 X 5 X 5
= 15,625
Now we see that we can express 1,000 as 103 and 100 as 102. How do we express 10? This way: 101. Scientific notation breaks every number down to two components, one of which is a power of 10 (that is 10 with an exponent). For example, let's look at the number 200:
200 = 2 X 10 X 10 = 2 X 102
Here are some other numbers:
500 = 5 X 10 X 10 = 5 X 102
3,000 = 3 X 10 X 10 X 10 = 3 X 103
6,000,000 = 6 X 10 X 10 X 10 X 10 X 10 X 10 = 6 X 106
(six million)
Ok, we have been dealing with very easy numbers. What about a number like 3,100? Well, simply break this number down:
3,100 = 310 X 10 = 31 X 10 X 10 = 31 X 102 .... but note that there is still another power of 10 we could remove:
3,100 = 310 X 10 = 31 X 10 X 10 = 3.1 X 10 X 10 X 10 = 3.1 X 103 because 3.1 X 10 = 31! Here are some other examples:
250 = 2.5 X 102
4,300,000 = 4.3 X 106
5,123 = 5.123 X 103
Ok, now we can handle the big numbers we are going to find in Astronomy 105, how about very small numbers? This is a little more confusing. Let's start with some easy examples: 0.1, 0.01, and 0.001. That is 1/10, 1/100, and 1/1,000:
0.1 = 1/10
0.01 = 1/100
0.001 = 1/1,000
Just like earlier, we can break-up the denominator (the bottom number of a fraction) into powers of 10:
0.1 = 1/(10)
0.01 = 1/(10 X 10)
0.001 = 1/(10 X 10 X 10)
The scientific notation way of expressing these numbers is through the use of exponents that are negative numbers:
0.1 = 1/(10) = 10-1
0.01 = 1/(10 X 10) = 10-2
0.001 = 1/(10 X 10 X 10) = 10-3
Alright, how do we express small numbers that are not even powers of 10? Just like their big cousins:
0.2 = 2 X 1/(10) = 2 X 10-1
0.013 = 13 X 1/(10 X 10 X 10) = 1.3 X 10 X
1/(10 X 10 X 10) = 1.3 X 10-2
0.0001587 = 1.587 X 10-4
That is all there is to scientific notation. Now, why do we need it? Because the numbers in astronomy span such a large range that it gets difficult to express them. For example the Sun is located 93,000,000 miles from Earth, and this is actually a very small distance compared to most of the distances encountered in astronomy. For example, the nearest star is located about 12,000,000,000,000 miles away! It is very cumbersome to write down all those zeroes, so we would use scientific notation to say that the Sun is located 9.3 X 107miles away from the Earth, while the nearest star is 1.2 X 1013 miles from Earth. Soon, we will find that we are too lazy to even write down these numbers, and will switch to measuring such distances using other "units" (such as "Astronomical Units"). Speaking of "units", we next need to talk about the metric system.
Scientists exclusively use the metric system. The reason for this is that it is easy! The main unit of distance in the metric system is the "meter". In the English system you are familiar with, there are a variety of distance units, including inches, feet, and miles. Remember that a mile has 5,280 feet, and one foot has 12 inches, so one mile has 63,360 inches. Very hard to convert from one unit to the other. Not so in the metric system, as the bigger and smaller units are based on powers of ten:
1 mm = 1 millimeter = 1/1000 of a meter = 10-3
meters (or 1 meter = 1,000 mm)
1 cm = 1 centimeter = 1/100 of a meter =
10-2 meters (or 1 meter = 100 cm)
1 km = 1 kilometer = 1,000 meters = 103
meters
So, how many centimeters are in a kilometer?: 100 cm/m X 1,000 = 105 cm = 1 km
While there are a number of other named length/distance units in the metric system, we will mostly be using the mm, cm, m, and km. It is relatively straight forward (using a calculator) to convert between the English system you commonly use and the metric system with these simple conversion factors:
1 inch = 25.4 mm
1 foot = 304.8 mm = 0.3048 m
1 mile = 1,609.34 m = 1.609 km
The other metric system unit of interest to us for astronomy
is the metric unit for mass, the "kilogram", which is 1,000 grams. In the
English system we commonly associate "pounds" with kilograms, but this
is not really correct. The pound is a unit of force caused by the pull
of the Earth's gravity. Thus, while we normally say one kilogram = 2.2
lbs, this is not true everywhere! For example, you may have heard of "weightless"
astronauts in Earth orbit, or that an astronaut only weighs 34 lbs on the
Moon. But the mass of an astronaut does not change no matter what planet
or moon he is on, or even if drifiting out in space. I know this is confusing,
but
it is an important concept. We will talk about the
masses of objects in this class, and not their "weight". For example, the
mass of the Sun is 2 X 1030 kg, but to measure the weight
of the Sun in pounds we would need to put the Sun on a bathroom scale that is
located on the surface of the Earth!
A Trip through the Solar System
We are about to head off on a voyage of discovery this semester that will take us very far away. To use what we have learned today, let's hop into our car and head out into the Solar System to see where we are going, and to appreciate the size of the place in which we dwell. Let's say there is no speed limit and we can drive at 125 mph. 125 mph is equal to 200 kph. New Mexico is about 450 km from top to bottom. At 200 kph, it would take 2.3 hours to drive from Raton to El Paso (if the road was straight, and had no traffic!). If we wanted to drive our car to Washington, D.C, which is located about 3,200 km (2,000 miles) from Las Cruces, it would take 16 hours. If we wanted to drive our car all the way to Santiago, Chile (about 8,800 km from Las Cruces) it would take 44 hours--of course, the road to Chile is not straight, so it would probably take three times longer!
This is too slow, let's switch to a jet. A typical jet airliner travels at a speed of 1,000 kph. Thus it would only take 8.8 hrs to fly from El Paso to Santiago. Let's now fly our jet to the Moon (of course this is impossible with a normal jet--but pretend anyway). The Moon is 384,000 km from the Earth. It would take our jet 384 hours, or 16 days to fly to the Moon. Mars is one of the Earth's closest neighbors in the solar system, and can get as close as 35 million km (like summer, 2003). Let's hop in the interplanetary jet and take a trip to Mars. We better bring lots to eat, as this trip will take us 35,000 hrs, or 1,458 days = 4 yrs! Mars will have made two trips around the solar system in that time. Pluto is about 25 times further away, so it would take our jet 100 years to get to Pluto.
We must go faster. Ok, let's attach some big rocket engines to our jet. Using those on the space shuttle, we should be able to get to about 20,000 kph. Now a trip to Mars only takes 73 days, and Pluto is a mere 5 years away!
Today we begin our journey to attempt to understand the Solar System in which we live. But
before we talk about what modern astronomers know, it is important to look
back to see where astronomy came from, because much of the language and
structure of astronomy owes itself to ancient ideas, beliefs, and traditions.
Before we do so, however, you must
purge your mind of what you know, or think you know about the Solar System.
Pretend we are prehistoric cave people. Back some 20,000 years or so, humans
were not arranged in complex societies (about the time the last ice age
ended). They basically were "hunter-gatherers".
A nomadic lifestyle. We do not know much about their belief systems because
they left few traces of their existence, as they rarely stayed in one place
long enough to leave a significant record of their presence (though they
did leave some traces, such as the cave paintings
at Lascaux,
dating from 17,000 years ago). Some term them "intelligent animals".
For these people, the world was a mysterious place, for they could not
comprehend the real reasons why most natural events happened. For example, how
do you think they felt during a thunderstorm? Did they do something to bring on
such a storm? Even though they did not understand much about the Universe,
they certainly soon became aware of certain astronomical events and cycles.
Obviously, they knew about night and day. The Sun, whatever it was, would
always rise in the East (even though they may not have had a word for East!),
travel across the sky, and set in the West. They understood that there then
would be a period of darkness before the Sun would again rise.
They certainly also became aware of the Moon and the stars. The Moon would
slowly move amongst the stars while constantly changing its appearance. They
would probably be able to predict the time of full Moon, as at these times
it would be bright enough at night to allow them to hunt (or to be hunted!).
These people might have been aware of the yearly seasonal cycle. There would
be times of cold weather, and times of warm weather. Various types of food,
such as fruits and vegetables, would be abundant during the warm times of
the year. During some times of the year, different types of game animals
would be migrating, and they would probably follow them. While we do not have
any clear evidence for this type of knowledge among the prehistoric peoples,
we know from studying existing tribes of people on this globe that such
traditions are still alive and well, and probably remain relatively unchanged
in the intervening eons.
For
reasons that are not yet completely clear, some 15,000 years ago, agriculture
appeared on the scene. Various types of animals were domesticated, and
humans began to purposely grow food, instead of merely "collecting"
it. Before the development of agriculture, the Universe was more difficult
to understand because you would have had to always be "on the move", and
it was difficult to recognize the repeated cycles and patterns of celestial
motions. There was not much time for reflection. With the rise of agriculture,
and we include ranching and fishing in this term, food was not so hard to come
by. With experience, you could grow sufficient quantities of grain to get you
through the winter. Or you could dry fish and other meats, or use your live
animals for food during the winter. Some years you might end up with more of a
particular type of food than you needed to survive the winter---you could trade
this with a neighbor to get some different type of food. Thus, people were now
able to stay in one place, and now could pay more attention to natural
cycles. These cycles were especially important for agriculture--you had to know
when to plant your seeds, or when to move your sheep to better grazing
lands.
The development of agriculture leads to the origin of astronomy. For example, you would quickly notice harbingers of the coming spring by watching the motion of the Sun and stars. Fisherman would notice how the movements of the Moon would affect the tides. With sufficient observation you would notice that there was a predictable pattern: a certain number of days would have to elapse between when the Sun would again rise at a particular spot on your horizon. You would develop a system that would allow you to predict when it was time to plant your grain. You would devise a calendar. The beginning of each new cycle may have been cause for a celebration---the first "New Year's" celebrations.
Of course, it became quite clear that just because it was officially "spring", it did not mean it was warm enough to plant your grain. The weather was only partially tied to the motion of the Sun in the sky--some years were good, some years were bad. A bad year might lead you to suspect that you had done something to upset nature, you may have angered the Sun for example. It is not too hard to envision the early rise of religion to attempt to understand these events, and with that, various ceremonies designed to placate these celestial beings. With these developments, we get a new type of profession: the priest. A person who's sole job it was to understand and read the signs of nature, and of course, to keep track of time so that all of the necessary ceremonies occurred on schedule to keep the gods happy. Of course, it was also the priest's job to suggest remedies when things went unexpectantly wrong.
With the rise of priests came more careful observation of natural cycles. The earliest records of "calendars" appear to be various alignments of stones, and of pre-historic buildings. Most of these are of the "horizon-intercept" kind, they were aligned with where the Sun (or Moon) rose (or set) along the local horizon. One example you are almost certainly familiar with is Stonehenge. Activity at the site of Stonehenge appears to date back to 7,000 BC, but the construction of the main parts of the monument appear to have begun around 3,000 BC. The various structures we see today at Stonehenge appear to be carefully aligned with the horizon locations ("azimuths") of the risings and settings of the Sun and Moon at various extremes in their motion (furthest south, furthest north, etc.). During this time, similar structures were being constructed elsewhere in the world, in both the Middle East (Babylon and Egypt), and in the far east (India and China). Later, such structures arose with the Mayan/Aztec culture in the Americas (reaching their peak circa 200 AD, though archeological evidence suggests their culture began about 1500 years before it reached its peak).
The first actual "calendars", as we would recognize them, appeared on the scene about 6,000 years ago (here is an excellent site on ancient calendars). The Chinese calendar appears to have begun in 2637 BC (go here for more on Chinese calendars), while the Egyptian calendar (from which our modern calendar arose) appears to date from 4236 BC! These calendars even had systems to account for the fact that the year is not exactly 365 days long (why we have "leap" years like 2008).
As observations became more careful and accurate, cycles were noticed, as well as other phenomena: the discovery of the planets, and their motions. The appearance of comets, and "new stars" were noted. Of course, to keep track of all of this, writing had to be developed, as well as mathematics. With these developments, ancient cultures were able to predict astronomical motions and events well into the future---the most extreme case probably occurred in Mayan culture, with some events recurring on cycles that had periods of 3 million years!
Thus, its pretty clear that the origin of astronomy (and science in general) can be traced back to the rise of agriculture.
Let us look more closely at the ties between astronomical
events and agriculture.
One of the most important dates for any farmer is the time of year that is
best suited for planting their crops. If you plant your seeds when it is still
too cold outside, it is likely that the seed will rot, and you will not
get a very good crop of grain. If you wait too long, until the weather is
hot, you also might get a very poor sprout rate because it is now too dry
for your seeds to germinate (more mature plants are better at seeking water
than little seedlings). In warmer areas, it is the coming of the rainy season
that is more important than other factors, as they rarely have killing frosts
in tropical and sub-tropical regions. It would be of great value if you knew
how to predict the rainy season.
Thus, early farmers were keen skywatchers and observers of nature's cycles.
One example shown in our textbook (fig 3.1). A carved bone from central
Africa dating to 6500 BC showing pictographs of the crescent Moon. They
observed that the crescent Moon, when it was close to setting on the
western horizon, had different orientations throughout the year. And during
those times of the year when it set so that the crescent set oriented exactly
on the horizon (the two "horns" of the crescent set at the same time), the
rainy season would be near its mid-point. Therefore, they could watch
how the setting crescent Moon progressed over the year, and have a good
indication of when the rainy season would begin--the time to plant your seeds.
Another example that you may have heard of is that of the ancient Egyptians
and the flooding of the Nile. Every summer, the Nile river in Egypt
begins its annual flooding. When the river was high, they could irrigate
their crops and begin their farming season. Unbeknownst to the early Egyptians,
the reason the Nile flooded at this time of year was that heavy rains in
Central Africa fell every June and July. The Egyptians noticed that the
flooding of the Nile corresponded to the appearance of the star Sirius (the
brightest star in the nightime sky) rising in the Eastern sky just before the
Sun--after being invisible for several months. They used this rising to
portend the coming floods, and developed a calendar to help them predict the
annual flood. The start of this calendar was based on the
regular appearance of Sirius in late July each year.
Sirius is a real beacon, it is the brightest star in the sky, and only is
exceeded by the Sun, the Moon, and the planets Venus and Jupiter in brightness.
In fact, the Egyptians believed that summer was hot because the star Sirius
and the Sun were lined-up, and their combined heat intensified that of the
Sun alone. The star Sirius is in the constellation of Canis Major, the
"great dog". This is also why Sirius is sometimes referred to as the "dog
star", and why we have the "dog days of summer". A 5,000 year old tradition
that has made it to modern times.
Speaking of constellations, groups of stars for which ancient people
constructed mythologies (stories), the Egyptians had only about one dozen.
To the ancient Egyptians, most heavenly bodies (besides the Sun and Moon)
were just not very important to them. One of the most important of their
constellations, however, was the one we call Orion. The Egyptians called this
constellation "Osiris", the "God of Light". The mythology of the constellation
of Orion/Osiris can be found in this online set of Sky charts for Astronomy 110, where you will
find a set of sky charts for each month. The constellation of Orion is
highlighted for the month of February. In January and February Orion is
visible in the southeast
right after sunset. By 9pm, during those months it is high in the sky towards the south, and
Sirius will be below, and left (southeast) of Orion (the belt of Orion points
to Sirius). To see Orion during the Fall semster requires you to go out
very early in the morning (before sunrise in September). By December it
rises at sunset.
Most of the other constellations in the sky come down to us from the Greeks
and Romans. The mythologies of these constellations are usually tied to
the Greco-Roman gods and/or their heroes. But some of the stories go further
back than the Greeks. One of these is the mythology of Perseus (the
constellation highlight for December). You can read about the mythology in
the online sky charts pages, along with that of the associated costellations of Andromeda,
Pegasus, Cepheus, Cassiopeia, and Cetus. Perseus is famous for slewing the
Medusa (for a more complete version of the story, go
here),
who's gaze could turn you into stone.
The Greek mythology for Perseus is at least 2,500 years old, but the story has
more ancient roots, possibly going as far back as 4,000 yrs ago, back to
Babylonian/Sumerian times by linkage to the ancient hero Gilgamesh.
With more freedom of time afforded by agriculture, people had
more time to devote to skywatching. This allowed for a rich history of
stories about the origin of the constellations as well as assigning them
various "powers". For if a star like Sirius could cause the Nile to flood, why
wouldn't the position of the Sun or Moon in some constellation predict some
other event equally important to humans (like the birth or death of kings)? Besides the Sun, Moon,
and stars, the ancients were aware of five other objects that moved against
the sky: the planets. Each planet had its own peculiar motion. The planet
Mercury moved through the sky very quickly, and was always located close to
the Sun. While Jupiter, the king of the Gods, moved at a more leisurely pace
(completing one circuit of the sky in 13 years).
It did not take too long before the association of the planet with one or
more gods lead to predictions about what the movement of a particular planet
meant in terms of human beings. This is the subject of Astrology. Astrology
is the prediction of various human traits or events to individuals depending on where
the planets, Sun and Moon are in the sky at the time of their birth. Given
your astrological classification, then the movement of these objects through
time can then be used to forecast events in your life.
Astrology is called
a pseudoscience, as it uses elements of science (such as the real motions of
planets among the stars) to make predictions that are too general to be
tested in a scientific way. For example, today your horoscope may say
"today is a good day to make new friends". How do you quantify this? When
is it a bad day to make new friends?
Astrology is relatively harmless if you do not take it too seriously. But
would you want your surgeon to decide to postpone an important operation
because Mars was in Aquarius? Or start a war because the stars tell
the President it is the right time to do so? Astronomers have to spend time debunking
astrology because the general public confuses it with what they do. But
astronomy is a real science, it follows something called the scientific method.
1) Make an observation (or set of observations) about some aspect of our universe.
2) Propose a tentative explanation, called a hypothesis, that appears to be consistent with the observations you have made.
3) Use your hypothesis to make predictions about this particular phenomenon.
4) Test the predictions by conducting specific experiments to test this hypothesis in every conceivable way (or make additional observations that allow you to confirm your predictions-since not every target for observation can be actively experimented on!).
5) Examine if your hypothesis explains all of the observations. If it does not, modify the original hypothesis if possible, or go back to step #2 and start again.
We will talk some more about the rise of modern science and the scientific method during the next class. This will lead to the first treatment of the celestial objects as physical objects, and not metaphysical objects.
