Astronomy is probably the oldest of the sciences with beginnings that can be traced as far back as 3000 B.C. for Western Civilizations.  We have, in some respect, always observed the “heavens”.  At first we thought that our lives were under the influence of the planets and stars, this was the pseudo-science of astrology.   Eventually, modern astronomy displaced these ancient ideas (although we still check our horoscopes from time to time).  With the invention of telescopes, both optical and radio, along with sophisticated computers and other devices we have sat out to explore both the seen and unseen universe.

This program, through the School of Galactic Radio Astronomy (SGRA) at Pisgah Astronomical Research Institute, is designed to inform, instruct, and through hands on real time research, give students the ability to explore the Universe.

We would like to point out that math is the language of physics and, as such, the language of astronomy (better referred to as astrophysics).  We use the SI system (abbreviation for Systeme International d’Unites) a modified version of the metric system.  There are three base units with which you should be familiar along with several prefixes as listed in the table below (this is not an all inclusive list).

Base Units:

Length: meter (abbreviated m)
Mass: gram (abbreviated g)
Time: second (abbreviated s)

Prefixes include:

tara  (abbreviated T):   a million million
giga (abbreviated G):   a billion
mega (abbreviated M):  a million
kilo (abbreviated k):  a thousand

milli (m): one thousandth
micro (u): one millionth
nano (n): one billionth
pico (p): one trillionth

## Chapter 1: Measurement and Directions in Space

### A.  The Scale of Things: Distance Measurement

“Immense” would probably be a fitting description of the scale of distances in space.  While we have little trouble measuring such things on Earth, even measurement within our Solar System can be great.  For example the distance to our own Moon is 384,297 km (about 30 times the diameter of the Earth), and that’s the closest object to us.  The distance to our Sun is almost 150,000,000 km (around 390 times the distance between the Earth and Moon).

One problem you may have noticed is how we write such large numbers without running out of paper.  The answer: we abbreviate. Using scientific notation (also referred to as powers-of-ten notation) we can represent large numbers by using a multiplier and power of ten.  Let’s work our way up to how we do this.

Using numbers that are whole powers of 10 (numbers containing only a 1 and 0's) such as 100, 1000, or 1,000,000 we can see that:

100 = 10 x 10 or 102
1,000 = 10 x 10 x 10 or 103
1,000,000 = 10 x 10 x10 x 10 x 10 x 10 or 106

We can just as easily go in the other direction:

0.1 = 1/10 = 10-1
0.01 = 1/100 = 10-2

Carrying this idea one step further, we can express any number in scientific notation by first determining the exponent, the power to which the number must be raised. For a number larger than 1, the exponent is the number of digits after the 1.  For a number smaller than 1, the exponent is a negative, with its value equal to the number of places the 1 is to the right of the decimal  (note the examples above).

Unfortunately, not all numbers are simple powers of 10.   Let’s use the distance of 384,297 km between the Earth and Moon as our example. The preferred form for writing any large number is to always have the first number followed by a decimal point, 3.84297; followed by at least 2 numbers to the right of the decimal point (we’ll use 3 numbers for greater accuracy), 3.843 (“rounding” is sometimes necessary); followed by the exponent (multiplier in powers of ten), 3.843x 105. Our exponent of 5 tells us the actual long hand form of the number is in the 100,000's. Our rounded short-hand version (3.843 x 105) tells us that the number is 384,300 km.

A few other examples of scientific notation:

The size of an atom: 10-10meters

A human body cell: 5 x 10-5 m

Human: 1.8 m

Planet Earth: 1.3 x 107

Distance from Sun-Earth: 1.5 x 1011

The system works the same for very small numbers: write the number as a multiplier and a power of ten with a negative exponent.  The number 0.005 would be expressed as 5.0 x 10-3. Here we count the places to the right of the decimal point in order to determine the exponent.

### B.   The Scale of Things: Astronomical Distances

Astronomers use much the same measurements as do other scientists.  Distances are measured in kilometers (abbreviated km); mass is measured in kilograms (abbreviated kg ), and time is measured in seconds (abbreviated s).  Because of the great distances covered in space, however, other units of measure have been devised.

The astronomical unit (abbreviated AU) is used when measuring distances within our Solar System.  One AU is equal to the average distance between the Sun and Earth, so,

1 AU = 1.496 x 108 km = 93 million miles

The light year (abbreviated ly) is used when measuring distances outside our Solar System.  One ly is equal to the distance light travels in one year or 9.46 x 1012 km (9,460,000,000,000 km in long hand). The star closest to the Earth, Proxima Centauri is approximately 4.3 ly away.

The parsec (abbreviated pc) is the final distance measurement we’ll discuss. This is used to measure the farthest distances.  One parsec is equal to  3.26 ly (3.09 x 1013 km).  The distance to Proxima Centauri is 1.32 pc.

Let’s put it all together once more from astronomical unit to light year to parsec and back.

1 AU = 1.58 x 10-5 ly = 4.85 x 10-6 pc

1 pc = 3.26 ly = 206,265 AU

By now you should appreciate the use of scientific notation instead of long hand for writing astronomical distances.  Keep in mind that for even greater distances you can use the prefixes kilo and mega, meaning 1000 and 1,000,000, respectively (one example of this is the distance from Earth to the center of our galaxy, that’s equal to 8 kiloparsecs).

### C.   Lost (and Found) in Space:  Astronomical Coordinate Systems

Ancient civilizations believed the stars, planets, and other heavenly bodies existed at the same distance from Earth, a somewhat two-dimensional approach.  All of these points of light were thought to rest on a transparent sphere, with Earth at its center, and was referred to as the “celestial sphere”.  While we are aware that space is three-dimensional, we still use the idea of the celestial sphere as a means of charting the night sky.

In order to construct a meaningful coordinate system (sometimes referred to as a “referent system”) a few more details are added.  The celestial equator is a projection of Earth’s equator onto the sphere, and the celestial meridian is a projection of Earth’s meridian onto the sphere.   The celestial meridian is an imaginary line drawn from the celestial north pole, through a point overhead referred to as the zenith, then to the celestial south pole.  Remember, the poles are the points of rotation for Earth.

Now, let’s add the finishing touches.  By drawing a series of lines, both north-south and east-west, we’ve added what appear to be lines of longitude and latitude (refer to a globe of Earth to refresh your memory) to our celestial sphere.  The lines of latitude are declination and the lines of longitude are right ascension.  These are the references we utilize when locating objects in space.   (See illustration below.)

One more detail and our system will be complete.  Declination (abbreviated D) is measured in degrees, arcminutes, and arcseconds. For example,  8o 12 06 is a point of declination and is read as “eight degrees, twelve arcminutes, six arcseconds”.  Right ascension (abbreviated RA) is measured in hours, minutes, and seconds.  For example, 5h  14m 32.2s is a point of right ascension and is read as “five hours, fourteen minutes, thirty two point two seconds.   Putting these two coordinates together gives us the position of the star Rigel in the constellation Orion.