Away from city lights on a clear, moonless night, the naked eye can see 2000-3000 stars. As you look at the stars, your mind may group them into different shapes of patterns. People of nearly every culture throughout history have looked at the stars and given names to shapes they saw and invented stories to go with them. The pattern that the Greeks named Orion, the hunter, was seen by the ancient Chinese who called it a supreme warrior named Shen. The Chemehuevi Native Americans of the California desert saw the same group of stars as a line of three sure-footed mountain sheep.

The patterns of stars seen in the sky are usually called constellations, although more acurately, a group of stars that forms a pattern in the sky is called an asterism. Astronomers use the term constellation to refer to an area of the sky, which contains all the stars and other celestial objects within that area. The International Astronomical Union (IAU) divides the sky into 88 official constellations with exact boundaries, so that every place in the sky belongs within a constellation. Most of the constellations in the northern hemisphere are based on the constellations invented by the ancient Greeks, while most in the southern hemisphere are based on names given to them by seventeenth century European explorers.

A good way to learn more about the consellations is to use Google Sky for Google Earth, web-based Google Sky, or Stellarium, which are all free, to look at the constellations. You can turn on and off the constellations and zoom around the sky to find as many as you want. If you would like to learn more about a particular constellation, search for it in Wikipedia where you can learn about the stars in it, its history and mythology.

With Google Sky for Google Earth you can click on each of the stars in a constellation to get more information about each one including the history of its name, its surface temperature, type of star, and distance from Earth. Although the stars in a constellation appear close to each other in the sky from Earth, they are not necessarily close to each other in the universe and are often very different types of stars and other objects. 

Stellarium gives information about each object in a constellation including the name, type, magnitude, location and distance. It also has a constellation art button you can turn on and off to help you visualize the characters the Greeks imagined in the sky.

Angular Measure in the Sky

An important part of astronomy is knowing where to point a telescope and keeping track of the positions of objects in the sky. To to this, astronomers use angular measure.

An angle is the opening between two lines that meet at a point and angular measure describes the size of an angle in degrees, designated by the symbol °. A full circle is divided into 360° and a right angle measures 90°. One degree can be divided into 60 arcminutes (abbreviated 60 arcmin or 60'). An arcminute can also be divided into 60 arcseconds (abbreviated 60 arcsec or 60").

Astronomers use angular measure to describe the apparent size of an object. The angle covered by the diameter of the full moon is about 31 arcmin or 1/2°, so astronomers would say the Moon's angular diameter is 31 arcmin, or the Moon subtends an angle of 31 arcmin. 

If you extend your hand to arm's length, you can use your fingers to estimate angular distances and sizes in the sky. Your index finger is about 1° and the distance across your palm is about 10°.

The Small-Angle Formula

The angular sizes of objects show how much of the sky an object appears to cover. Angular size does not, however, say anything about the actual size of an object. If you extend your arm while looking at the full moon, you can completely cover the moon with your thumb, but of course, the moon is much larger than your thumb, it only appears smaller because if its distance. How large an object appears depends not only on its size, but also on its distance. The apparent size, the actual size of an object, the distance to the object can be related by the small angle formula:

D = θ d / 206,265

D = linear size of an object

θ = angular size of the object, in arcsec

d = distance to the object

An Example:

A certain telescope on Earth can see details as small as 2 arcsec. What is the greatest distance you could see details as small the the height of a typical person (1.6 m)?

d = 206,265 D / θ = 206,265 × 1.6 m / 2 = 165,012 m = 165.012 km

This is much less than the distance to the Moon (approximately 384,000 km) so this telescope would not be able to see an astronaut walking on the moon. (In fact, no Earth based telescope could.)

Some calculations to try:

1. The average distance to the Moon is approximately 384,000 km. The Moon subtends and angle of 31 arcsminutes, or about 1/2°. Use this information and the small-angle formula to find the diameter of the moon in kilometers.

2. At what distance would you have to hold a quarter (which has a diameter of about 2.5 cm) for it to subtend and angle of 1°?

Answers:

1. The diameter of the Moon is about 3,463 km

2. You would have to hold it at a distance of 1.43 meters.

Powers of Ten

The distances and sizes of of the objects astronomers study vary from very small, including atoms and atomic nuclei, to very large including galaxies, clusters of galaxies and the size of the universe. To describe such a huge range, astronomers need a way to avoid confusing terms like "a billion trillion" and "a millionth". Astronomers use a system called powers-of-ten notation, which consolidates all of the zeros that you would normally find attached to very large or small numbers such as 1,000,000,000,000 or 0.0000000001. All of the zeros are put in an exponent, which is written as a superscript, and indicates how many zeros you would need to write out the long form of the number. So for example:

10⁰ = 1

10¹ = 10

10² = 100

10³ = 1000

10⁴ = 10,000

and so on.

In powers-of-ten notation, numbers are written as a figure between one and ten multiplied by a power of ten. So for example, the distance to the Moon of 384,000 km can be re-written as 3.84 × 10⁵ km. Notice that 3.84 is between one and ten. The same number could accurately be rewritten as 38.4 × 10⁴ or 0.384 × 10⁶, but the preferred form is to have the first number be between one and ten.

Very small numbers can also be written using powers-of-ten notation. The exponent is negative for numbers less than one and indicates dividing by that number of tens. So for example:

10⁰ = 1

10^-1 = ¹/₁₀ = 0.1

10^-2 = ¹/₁₀ × ¹/₁₀  = 0.01

10^-3 = ¹/₁₀ × ¹/₁₀ × ¹/₁₀  = 0.001

10^-4 = ¹/₁₀ × ¹/₁₀ × ¹/₁₀ × ¹/₁₀ = 0.0001

and so on.

Once again, numbers are written as a figure between one and ten multiplied by a power of ten. So for example, a number like 0.00000375 would be expressed as 3.75 × 10^-6.

A few websites offer demonstrations of powers-of-ten and the scale of the universe.

Astronomers use many of the same units of measurement as other scientists. They often use meters for length, kilograms for mass, and seconds for time. However, the distances and sizes in the universe can be so big, that astronomers have invented more units to describe distance.

Astronomical Units:

Distances in the solar system are often measured in astronomical units (abbreviated AU). An astronomical unit is the average distance between the Earth and the Sun:

1 AU = 1.496 × 10⁸ km = 93 million miles

Jupiter is about 5.2 AU from the Sun and Pluto is about 39.5 AU from the Sun. The distance from the Sun to the center of the Milky Way is approximately 1.7 × 10⁹ AU.

Light-Years:

To measure the distances between stars, astronomers often use light-years (abbreviated ly). A light-year is the distance that light travels in a vacuum in one year:

1 ly = 9.5 × 10¹² km = 63,240 AU

Proxima Centauri is the nearest star to Earth (other than the Sun) and is 4.2 light-years away. This means light from Proxima Centauri takes 4.2 years to travel to Earth.

Parsecs:

Many astronomers prefer to use parsecs (abbreviated pc) to measure distance to stars. This is because its definition is closely related to a method of measuring the distances between stars. A parsec is the distance at which 1 AU subtends and angle of 1 arcsec.

1 pc = 3.09 × 10¹³ km = 3.26 ly 

For even greater distances, astronomers use kiloparsecs and megaparsecs (abbreviated kpc and Mpc).

1 kiloparsec = 1 kpc = 1000 pc = 10³ pc

1 megaparsec = 1 Mpc = 1,000,000 pc = 10⁶ pc

 

 

The equatorial coordinate system is what astronomers use to keep track of the positions of objects in the sky. Astronomers imagine that the Earth is surrounded by a large sphere called the celestial sphere. The Earth's equator and the plane of the Earth's orbit are projected onto this sphere. 

The plane of the Earth's orbit is called the ecliptic when it is projected onto the imaginary celestial sphere. Because the Earth's axis of rotation is at a 23.5° to the plane of the Earth's orbit, the celestial equator and the ecliptic are also at a 23.5° angle to each other.

The plane of the ecliptic and the plane of the celestial equator intersect only twice a year, once on about March 21st of each year, and once on about September 22nd. The points on the celestial sphere where this occurs are called the vernal equinox (in March) and the autumnal equinox (in September).

For further information about the ecliptic, please consider watching the following videos:

Stargazing: The Ecliptic Line

The Relationship of the Celestial Equator and the Ecliptic

Celestial Coordinates:

To denote the positions of objects in the sky, astronomers use a system based on the celestial sphere. The use two measurements, right ascension and declination. Right ascension (abbreviated RA) is similar to longitude and is measured in hours, minutes and seconds eastward along the celestial equator. The distance around the celestial equator is equal to 24 hours.The right ascension of the vernal equinox is 0^h 0^m 0^s.

Declination is similar to latitude and is measured  in degrees, arcminutes and arcseconds, north or south of the celestial equator. Positive values for declination correspond to positions north of the equator, while negative values refer to positions south of the equator. The declination of the north celestial pole is 90° 0' 0" and the south celestial pole's declination is -90° 0' 0". Declination at the equator is 0° 0' 0".

The position of an object is stated with the right ascension first, then the declination. For example, the bright star Sirius' position is RA: 6h45m8.9s Dec: -16°42'52.1". The position of Betelgeuse is RA: 5h55m10.3s Dec: +7°24'25.4".

The advantage of the equatorial coordinate system is that it expresses the position of a star or galaxy in a way that is independent of the observer's position on Earth. However, the right ascension and declination of a given object change slowly over time, mainly due to a phenomenon called precession. This happens because both the ecliptic and the equator are slowly moving, as a result of tidal forces from the Sun, Moon and planets. The main effect is from the Moon and (to a lesser extent) the Sun, which makes the celestial pole orbit around the ecliptic pole once every 26,000 years.  So along with the RA and Dec of an object, you will usually see the date, expressed in years, when those coordinates were approximately valid.  This date, or "epoch", defines the precessing equator and equinox used to construct the star catalog.  Common examples are B1950.0 and J2000.0, where the B and J stand for slightly different sorts of year.

The changes to the coordinates happen slowly enough that successive generations of star catalog are 50 years apart. However, the most recent star catalogs, which are equinox J2000.0, will probably be the last in the sequence:  there are unlikely ever to be equinox J2050.0 catalogs, because of the adoption of the International Celestial Reference System (ICRS). The ICRS broke the connection between catalog positions and the Earth's motion, and is defined instead by a set of quasars.  For continuity, the ICRS was set up to be a good approximation to the equinox J2000.0 system, so in effect the catalog RA,Dec system has been frozen at J2000.0.

To Try:

Stellarium and Google Sky both tell you the coordinates of celestial objects. For practice you can try using one of the programs to find the following:

1. What are the coordinates of the star Rigel?

2. What are the coordinates of the star Vega?

3. What is located at RA: 20h41m25.9s Dec: +45°16'49.2"

4. What is located at RA: 5h16m41.4s Dec: +45°59'52.4"

Answers:

1. RA: 5h14m32.3s Dec: -8°12'05.9"

2. RA: 18h36m56.3s Dec: +38°47'01.9"

3. Deneb

4. Capella

Solar Time and Sidereal Time

Solar time is based on the position of the sun. Local noon in solar time is the moment when the sun is at its highest point (the upper meridian) in the sky. Solar time is what the time we all use where a day is defined as 24 hours, which is the average time that it takes for the sun to return to its highest point.

The Earth does a full rotation each day, but because it is also traveling on its orbit around the sun, it has to rotate about 1° more than a full 360° to get from one solar noon to the next. However, the stars are so far away, that the Earth's movement on its orbit makes only a negligible difference to their apparent direction. Sidereal time is based on when the vernal equinox passes the upper meridian. This takes approximately 4 minutes less than a solar day. 

1 sidereal day = 23 hours, 56 minutes, 4.1 seconds

Sidereal time is useful to astronomers because any object crosses the upper meridian when the local sidereal time is equal to the object's right ascension. Knowing when an object will near the meridian is useful because when an object is high in the sky, the distorting effect's of the Earth's atmosphere are minimized.

Now that you know how to find your way around the sky, you are ready to try to following activities:

• How to plan an observing session using Stellarium
• How to observe using the Real Time Control Interface (RTI)
• Any of the observing activities