A Few Things You Really Need to Know First

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay

Warning!

I thought this was going to be about astronomy. There was all this chemistry and physics!
(From an actual CCQ Comment)

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.

Effective Study

What Do You Need to Build a House?

What Do You Need to Learn in College?

Example: The Sun

In Science, Everything is Metric

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.

Important Metric Prefixes

Astronomical Numbers

"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."

Scientific Notation

Think of the way we write numbers:

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:

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

Tiny Numbers

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

Light Distances

Light Years

Two Useful Factoids

Temperature

Scientists use the Celsius (Centigrade) scale

Conversion

The Kelvin Scale starts at Absolute Zero

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.

About Light

Light is made up of waves

Electromagnetic Spectrum

There are many processes that produce various kinds of electromagnetic radiation besides the familiar examples cited.

Visible Light

Some people use the mnemonic Roy G. Biv to remember the sequence.

Visible Light and the Eye

Measuring in the Sky

Sky Angles

Sizes and positions in the sky are measured in terms of angles.

Size in the sky

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.

Angles

Size and Distance

Telescopes

Telescope types

  1. 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.
  2. 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.
  3. 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

Popular view of telescopes

What Astronomers Think a Telescope is For

What astronomers value in a telescope

Surprising Facts

Telescope Mounts

Telescope Mounts

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

How Diffraction affects telscope images

  1. When light passes through a lens, secondary ripples radiate away from the edges of the lens. This process is called diffraction.
  2. Diffraction also happens when light reflects off a mirror. In fact it happens every time light encounters a boundary.
  3. The diffracted light interferes with the main image, reinforcing some light and canceling out other light
  4. 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

How to Use a Telescope

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Created 7 July 2008, Last Update 17 January 2020