A Few Things You Really Need to Know First
Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
I thought this was going to be about astronomy. There was all this chemistry and physics!
(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.
- TheU.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 denial.
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:43,000,000,000,000 km
- Number of Stars in Milky Way Galaxy:400,000,000,000
- 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 as10 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
TheExponent = 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
To 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 buckshot!
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 humans.
- 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 adequate.
- Wavelength = distance between waves (λ: the Greek letter lambda)
- Frequency = number of waves per second
- 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 threats.
- 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 easily.
- 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 itself.
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 the mounting
- A sharp, moderately large image is far better than a fuzzy, very large image.
- 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 parts.
- 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 17 January 2020