A Few Things You Really Need to Know First
Steven Dutch, Natural and Applied Sciences, University
of Wisconsin - Green Bay
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I thought this was going to be about astronomy. There was all this chemistry
(From an actual CCQ Comment)
- Astronomy is Chemistry and Physics
- That's why the course is cross-listed with Physics
- Physics is how we know what the stars are, and how they work
- Chemistry is about what everything - including you - is made of
- I will try to keep the pain manageable - somewhere between waterboarding
and a root canal without Novocain
The Two Most Amazing Ideas in Science
The Sun is a Star
Imagine what this idea implies. The stars must be incredibly far away to be
so faint. If we understand the Sun, we can understand other stars.
This idea turns up in a joke:
Sherlock Holmes and Watson are camping and gazing at the sky. Holmes says: "Look
at the stars and tell me what you deduce." Watson replies: "The stars are suns,
and they must be very far away. Maybe they also have planets and life, and maybe
at this moment some being is looking up at us." And Holmes replies: "No, Watson,
you idiot. It means someone stole our tent."
Supposedly a computer picked that as the world's funniest joke, which is why
Letterman and Leno still use human writers.
We Are Made of Star-Stuff
About 60 chemical elements have been detected in the sun, yet the sun is only
capable of converting hydrogen into helium. The other elements must have formed
somewhere else, in earlier stars. Judging from its composition, the Sun is
probably a third-generation star. That is, two earlier generations of stars
formed and blew their matter into space to be incorporated into the Sun. The
Solar System formed from the same materials. That means all the heavier atoms on
Earth: the carbon in your cells, the silicon in your computer, the copper in
your house wiring, the gold in Fort Knox, all formed in long-dead stars.
What Do You Need to Build a House?
What Do You Need to Learn in College?
- Facts (Materials)
- Relationships (Plans)
- Processes and Events (Methods)
Example: The Sun
- Holds solar system together by gravity
- Supplies energy to planets
- Gets energy by nuclear fusion
- How planets absorb and retain heat
- How gravity and inertia combine to keep objects in orbit
In Science, Everything is Metric
- 1 centimeter = 0.4 inches
- 1 meter = 39.4 inches = 1 yard +
- 1 kilometer = 5/8 mile: 5 mi = 8 km
- 1 kilogram = 2.2 pounds
- Unit of time = second
All other quantities (force, pressure, energy, etc.) are combinations of kilograms, meters, and
seconds although the units may have names of their own. For example, the unit of
energy is called a joule, and its units are kilograms x meters2/seconds2.
A more familiar unit, the watt, is one joule per second.
U.S. is the only major country not using the metric system
- Your foreign customers will use metric. Your promotion may depend on
your being able to. Deal with it.
Important Metric Prefixes
- Nano = 1/1,000,000,000
- Micro = 1/1,000,000
- Milli = 1/1000
- Centi = 1/100
- Kilo = 1000
- Mega = 1,000,000
- Giga = 1,000,000,000
- Tera = 1,000,000,000,000
"A billion here, a billion there, and pretty soon you're talking real money"
Attributed to the late Congressman Everett Dirksen of
Illinois. According to one account, it was actually a misquote, but Dirksen liked it so much he never issued a
It's no accident that large numbers are called "Astronomical."
- Mass of Sun: 2,000,000,000,000,000,000,000,000,000,000,000 kg
- Distance to Alpha Centauri:
- Number of Stars in Milky Way Galaxy:
- Age of Universe: 13,000,000,000 years
Think of the way we write numbers:
- 1,2,3,4,5,6,7,8,9 (counting ones)
- 10,20,30,40,50,60,70,80,90,99 (counting tens)
- 100, 200,300 .... 900,999 (counting hundreds)
Each time we max out on nines, we go to the next larger power of ten.
Thus 2845 means (2 x 1000) + (8 x 100) + (4 x 10) + 5
We can write 1000 as
10 x 10 x 10 = 103
The small digit (the exponent) is the number of times we multiply 10 to get the
number. If we have some multiple of a power of ten, we just write the multiplier
times the power:
500,000 = 5 x 100,000 = 5 x 105
Exponent = Number of Digits - 1
If it's a round number, Exponent = Number of Zeros
Using scientific notation:
- Mass of Sun: 2 x 1030 kg
- Distance to Alpha Centauri:
4.3 x 1013 km
- Number of Stars in Milky Way Galaxy: 4 x 1011
- Age of Universe: 1.3 x 1010 years
Normally we write numbers so the multiplier is between one and ten, but
it's not essential. Sometimes it makes numbers more understandable if we
keep the power of ten consistent. For example, in comparing distances, we
might say the Moon is 0.4 x 106 km away, the Sun is 150 x 106
km away and Pluto is 6000 x 106 km away.
Working With Scientific Notation
Multiplication and Division
100,000 x 10,000 = 1,000,000,000
105 x 104 = 109
To Multiply, Add Exponents
100,000,000/1000 = 100,000
108 / 103 = 105
Divide, Subtract Bottom Exponent from Top
There are no easy rules for addition and subtraction. We just have to
write the numbers out and do the math:
105 + 104 = 100,000 + 10,000 = 110,000 = 1.1 x 105
100 / 10,000 = 1/100 = .01
102 / 104 = 10-2
Negative Exponents mean numbers less than 1
.01 = 1/100, so 10-2 = 1/102
Exponent = -1 x (Leading Zeros) -1
.00362 = 3.62 x 10-3
And Now The Most Confusing Part
10 = 101
.1 = 10-1
10 x .1 = 1
101 x 10-1 = 100= 1
Therefore Anything to the Zero Power = 1
"But How Can it be 1 When It's 0??!!"
Another Way to Look At It
1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 10 = 101
1 = 10 no times = 100
.1 = 1/10 = 10-1
.01 = 1/(10 x 10) = 10-2
.001 = 1/(10 x 10 x 10) = 10-3
The zero is just a label, a counter. We don't actually calculate
with it. This is by no means the only time zero is just a label. A magnitude
zero star is not invisible, but very bright. A size zero dress is tiny, but
still exists. And you definitely would not want to get hit with size zero
Distances in Astronomy
- Wisconsin is 500 kilometers in maximum dimensions
- United States is 4000 kilometers across
- Earth is 12,500 kilometers in diameter and 40,000 kilometers around
- The round number for the circumference of the earth is no accident.
The metric system defined the kilometer so that the distance from
equator to pole would be exactly 10,000 kilometers.
- The Moon is 400,000 kilometers away
- The Sun is 150 million kilometers away
- Pluto is 6,000,000,000 (six billion) kilometers away.
- Alpha Centauri is 40,000,000,000,000 (40 trillion) kilometers away
- The galaxy is about 1,000,000,000,000,000,000 kilometers across
- The edge of the visible universe is about
13,000,000,000,000,000,000,000,000,000 kilometers away
- Obviously we need a better unit of measurement
- One light-second is the distance light travels in a second, 300,000 km
- The Earth is .13 light-seconds around
- The Moon is 1.3 light-seconds away
- The Sun is 500 light-seconds or 8.3 light-minutes away
- Pluto is 20,000 light-seconds or about six light-hours away
- Alpha Centauri is 130,000,000 light-seconds or 4.3 light-years away
- One light year = 300,000 x 60 x 60 x 24 x 365 = about 10,000,000,000,000
(ten trillion) kilometers.
- 1013 kilometers is a good approximation
- Alpha Centauri is 4.3 light years away
- The Orion Nebula is about 1500 light years away. When you see the Orion
Nebula, the light left about when the Roman Empire fell.
- The Milky Way galaxy is about 100,000 light years across
- The Andromeda Galaxy is about 2.2 million light years away. You can see
this galaxy with the unaided eye on a clear night. You are looking at light
that left when the ice ages were just beginning and there were no modern
- The edge of the visible universe is about 13 billion light years away.
Two Useful Factoids
- One day = 86,400 seconds
- One year = 31.5 million seconds
Scientists use the Celsius (Centigrade) scale
- 32 F = 0 C (Water freezes)
- 212 F = 100 C (Water boils)
- -40 F = -40C (Scales Equal)
- One C degree = 1.8 F degrees
- All atomic motion stops at -273 C (Absolute Zero)
- C = (9/5)(F-32)
- F = (5/9)C + 32
The Kelvin Scale starts at Absolute Zero
- K = C + 273
- For Stellar temperatures, makes little difference.
How To Convert In Your Head
Centigrade to Fahrenheit:
Double the temperature, subtract the first digit of the result, add 32.
Example: 30 C: 2 x 30 = 60. Subtract 6 = 54. Add 32 = 86 F
This is a good approximation but can be a degree off.
Fahrenheit to Centigrade:
Just reverse the steps above. Subtract 32, add the first digit of the result,
divide by 2.
Example: 86 F: Subtract 32 = 54. Add 5 = 59. Divide by 2 = 24.5. Note it's off
by half a degree.
If you have some math skills, you might want to see if you can figure out why
these methods work.
When you're talking the thousands of degrees on the surface of a star, or the
millions in the center of a star, who cares about 32 degrees? For these
extremes, F = 9/5 C and C = 5/9 F.
Light is made up of waves
- Oscillating electrical and magnetic fields
- Collectively called Electromagnetic Radiation
- Speed = 298,000 km/sec (symbol:
c). For many purposes, approximating it as 300,000 kilometers per second is
- Wavelength = distance between waves (λ: the Greek letter lambda)
- Frequency = number of waves per
- One hertz (Hz) = 1 wave per second
- Wavelength x Frequency = c
- AM = 1000 kHz = 1,000,000 Hz. c = 300,000 km/sec = 300,000,000
m/sec, so λ = 300,000,000/1,000,000 = 300 meters.
- FM = 100 MHz: λ = 3 meters
- Infrared: λ = 1 m - 7 x 10-7 m (700 nm). Infrared is given
off by warm objects and we sense it as heat.
- Visible light: 700 - 400 nm
- Ultraviolet: 400 - 1 nm. UV is mostly blocked by the upper atmosphere
but causes sunburn and skin cancer.
- X Rays: 1 - .01 nm. Given off by high energy collisions between atoms
- Gamma Rays: <.01 nm. Given off by radioactive decay
There are many processes that produce various kinds of electromagnetic
radiation besides the familiar examples cited.
- Red = 700 nm (4 x 1014 Hz)
- Green = 550 nm
- Indigo (we need a
vowel for the mnemonic)
- Violet = 400 nm (7 x 1014 Hz)
Some people use the mnemonic Roy G. Biv to remember the sequence.
Visible Light and the Eye
- Infrared absorbed by molecular vibrations
- Ultraviolet absorbed by
electrons around atoms
- Atmosphere is transparent to visible light because it's in a narrow
"in-between" energy range.
- That's why we
see in this range: it provides maximum information for finding food and avoiding
- Maximum solar output is green light
- Maximum eye sensitivity is
also green light: no accident that it matches the sun's maximum output.
Measuring in the Sky
Sizes and positions in the sky are measured in terms of angles.
The angular size of an object is the angle between two lines from our eye to
opposite sides of the object. The angle between the pointer stars of the Big
Dipper is about 5 degrees, or we say the Pointer Stars subtend or span
an angle of five degrees. The Sun and Moon subtend angles of about half a
degree, and the best the human eye can resolve is an angle of about 2 or 3
minutes of arc. (A degree = 60 minutes). Even Venus at its largest is barely a
minute of arc across, so the planets all appear as points of light.
- 1 degree = 60 minutes (60')
- 1 minute = 60 seconds (60")
Size and Distance
- A one degree object is 60 times its diameter away (57.3, to be more exact, but
60 is a useful rule of thumb). One degree is the apparent size of a quarter
5 feet away.
- A one minute object is 3400 times its diameter away. One minute is the
apparent size of a quarter a football field away.
- A one second object is 200,000 times its diameter away. One second is
the apparent size of a quarter three miles away.
- A Refractor uses lenses to create an image. The largest refractor in the
world is the 40-inch (just over a meter) telescope at Lick Observatory in
California. It is very difficult to make lenses that large that are
optically perfect so refractors have pretty much reached their limits.
- Reflecting telescopes use curved mirrors to create an image. They can be
made in very large sizes, limited mostly by the ability of engineers to
design mounts capable of holding them. All the largest telescopes in the
world are reflectors. They do suffer from the problem of having an
obstruction in the light path to divert the image somewhere for viewing or
photography. This affects image quality a bit, but not severely.
- Compound telescopes of many designs use lenses and mirrors to create
images. They can be much more compact than other telescope designs or cover
wider fields of view. Most large reflectors actually are built to route
light to various destinations for different purposes and employ additional
lenses or mirrors as a result.
What Most People Think a Telescope is For
What Astronomers Think a Telescope is For
- Astronomers rarely look through large telescopes visually
- Virtually all large telescopes are used solely for photography
- Telescope time is a fiercely competitive resource
- Modern large telescopes are $100 M +, built by consortiums of
universities and governments
- Nowadays many telescopes are in remote places and operated by remote
control, so many astronomers never even visit the telescope they're using.
- Altazimuth mounts rotate horizontally (azimuth) and vertically
(altitude). They are simple and easy to build but don't follow the stars
- Equatorial mounts have one rotation axis parallel to the earth's axis.
They can follow the stars easily with a single motion, and can be fitted
with direction indicators for finding objects in the sky easily.
Because equatorial mounts are off-balance, really large telescopes no longer
use them. Really large telescopes are just too massive. It is now practical to
build altazimuth mounts for really large telescopes and use computerized
controls to locate and track objects in the sky.
All Telescopes Are Limited By The Wave Nature of Light
- When light passes through a lens, secondary ripples radiate away from
the edges of the lens. This process is called diffraction.
- Diffraction also happens when light reflects off a mirror. In fact it
happens every time light encounters a boundary.
- The diffracted light interferes with the main image, reinforcing some
light and canceling out other light
- An absolutely perfect telescope image of a star consists of a
bright central ring and progressively narrower light and dark rings. An
astronomer seeing such an image would be overjoyed. This image is the result
of diffraction and interference and is far larger than the image of the star
All telescope images are inherently fuzzy and this limitation is caused by
the nature of light itself. A rough rule of thumb is that a telescope can
resolve angles in seconds roughly equal to 10 divided by the diameter of the
telescope in centimeters. Thus a 10-meter telescope (really huge) can resolve
objects as small as .01 second of arc. That's equivalent to a quarter 300 miles
away, but at the distance of Pluto, it corresponds to a feature 300 kilometers
across. At the distance of Alpha Centauri, it corresponds to 2,000,000
kilometers - bigger than the star itself.
Bottom Line on Telescopes
- Magnification is vastly overrated
- Magnification magnifies defects in the optics and unsteadiness in
- A sharp, moderately large image is far better than a fuzzy, very
- Images are inherently fuzzy because of the nature of light itself
- This sets an absolute limit on magnification (rule of thumb: maximum
useful magnification = 20 x
diameter in cm)
- If we want detailed images of the planets, we have to go out there
physically and get them. No Earth-bound telescope, however large or
perfect, can equal a small telescope close to another planet.
- To learn about the stars, we have to build really humungous
telescopes (already being planned) or use indirect methods.
How to Use a Telescope
- The first planet to observe is the earth. Set the telescope up in the
daytime and practice aiming the telescope, finding objects (not the
Sun!) and focusing it. Sight in distant objects on the ground (trees,
buildings, etc.) and get familiar with how the telescope works. Generally if
you have an object more than a few hundred yards away in focus, the
telescope is properly focused for the sky.
- Many telescopes invert the image. This is disconcerting when looking at
the ground but is not a problem in astronomy.
- Never aim the telescope at the Sun unless you know exactly what
you're doing. Never look at the Sun directly without adequate eye
protection. Even indirect methods of observing the Sun can damage the
telescope itself. A couple of seconds of focusing the sun can melt plastic
- Do not expect images like you see in textbooks. Those images
are taken by large telescopes or spacecraft, and may be the result of many
hours of exposure. Also, film and imaging chips respond to faint colors
differently than the eye.
- In a small telescope, objects will be tiny
- Colors will be subtle
- Contrast will be low
- Observing is a skill that takes time to learn. The more you observe,
the more you will learn to see.
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Created 7 July 2008, Last Update
22 May 2010
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