# Orientation

If you want to learn a science, astronomy is the place to start. For most of what we do in this class higher mathematics is not a prerequisite (although being comfortable with numbers is helpful). Astronomy is a science based on geometrical, and often very visual, models. You will find that it's important to be able to visualize 3 dimensional spatial concepts, but often this is enough to have amazing predictive power toward understanding how the sky will behave. Such predictive power is the goal of all science.

We must develop a common understanding and vocabulary for describing the visible universe. Much of our observational exercises in this class will be aimed at illustrating and testing these geometrical models of the positions and motions of the stars and planets.

Astronomy would be pretty easy, and pretty dull, if the Earth stood still. In fact, the Earth has several different motions which astronomers long ago struggled hard to understand. One of these motions is the Earth's rotation on its axis; another is the Earth's revolution, or orbital motion, around the Sun.

Background Reading: Stars & Planets, p. 13 & 14 (Star positions); p. 16 & 17 (Appearance of the sky), p. 19 (The star charts).

### ROTATION

If you watch the night sky for a few hours, you will see that the stars appear to rotate about a fixed point in the sky, known as the north celestial pole (which happens to be near the star Polaris). This motion is due to the Earth's rotation. As the spin of the Earth carries us eastward at almost one thousand miles per hour, we see stars rising in the east, passing overhead, and setting in the west. The Sun, Moon, and planets appear to move across the sky much like the stars.

Because of the Earth's rotation, everything in the sky seems to move together, turning once around us every 24 hours. Ancient astronomers explained this phenomenon by supposing that the Sun, Moon, planets, and stars were attached to a huge celestial sphere, centered on the Earth, which rotated on a fixed axis once per day. Of course, this sphere does not really exist; the Sun, Moon, planets, and stars all fall freely through space, and only appear to move together because of the Earth's rotation. Nonetheless, we still use the concept of the celestial sphere in talking about the positions of stars.

The celestial pole is 21.3° above the horizon as seen from Oahu. The point on the horizon directly below the celestial pole is north, while the opposite direction is south. If you face north, west is on your left and east is on your right. Finally, the Zenith is the point exactly overhead.

Since the apparent rotation of the celestial sphere is due to the actual rotation of the Earth, the north celestial pole is exactly overhead as seen from Earth's north pole. Likewise, every point on the celestial equator is exactly overhead from some point on the Earth's equator.

### REVOLUTION

Over the course of a year, the Earth makes one complete orbit about the Sun. As a result, the Sun seems to move with respect to the stars, appearing in front of one constellation after another, as shown in the diagram on p. 12 of Stars & Planets. After one year, the Sun is back where it started. The Sun's annual path across the sky is called the ecliptic. Traditionally, the ecliptic was divided into twelve equal parts, each associated with a different constellation of the zodiac. The planets also appear to move along the ecliptic, although, as we will see, they don't always move in the same direction as the Sun.

The night sky is just that part of the sky which we see when the islands of Hawaii have turned away from the Sun. As we orbit the Sun, different constellations are visible at different times of the year. In January, for example, the evening sky is still dominated by winter constellations like Orion and Taurus; by April, these constellations will be low in the western sky, and summer constellations like Cygnus and Saggitarius will be rising in the east. You can get a 'sneak preview' of the summer sky by staying up late, thanks to the Earth's rotation. For example, the constellations visible at 8 pm in late April can also be seen at 2 am in late January.

The Earth's axis of rotation is not exactly parallel to its axis of revolution; the angle between them is 23.5°. As a result, the ecliptic is inclined by the same angle of 23.5° with respect to the celestial equator. This misalignment causes seasons; when the Sun appears north of the celestial equator the Earth's northern hemisphere receives more sunlight, while when the Sun appears south of the celestial equator the northern hemisphere receives less sunlight.

If we could view the Solar System from a point far above the north pole, we'd see the Earth revolving counter-clockwise about the Sun and rotating counter-clockwise on its axis. The other planets would likelwise revolve counter-clockwise around the Sun, and most would also rotate counter-clockwise. In addition, the Moon would appear to orbit the Earth in a counter-clockwise direction, as would most other planetary satellites.

### TIME

In this class, we will use a 24-hour clock instead of writing 'am' or 'pm'. Since our class meets in the evening, most of the times we will record are after noon, and the 24-hour time is the time on your watch plus 12 hours. For example, our class starts at 19:00 (= 7:00 pm + 12:00), and ends at 22:00 (= 10:00 pm + 12:00). Sometimes we need to record the date and the time together; for example, our first class begins at 01/13/05, 19:00.

Astronomers everywhere in world use a single time system to coordinate their observations. This system is called Universal Time, abbreviated as UT or UTC. (Greenwich Mean Time, abbreviated GMT, is the same thing as UT.) Universal Time is exactly 10 hours ahead of Hawaii time. To convert 24-hour Hawaii time to UT, you add 10 hours; if the result is more than 24, subtract 24 and go to the next day. For example, our first observing session (weather permitting) will be at 01/20/05, 19:00, or 01/20/05 , 05:00 UT. To convert from UT to Hawaii time, subtract 10 hours; if the result is less than 0, add 24 and go to the previous day. For example, observers in Honolulu can see the star eta Leonis occulted, or hidden by the Moon, at 4/29/04, 8:35 UT; that's 4/28/04 22:35 Hawaiian time.

As a rule, we will use Hawaii time in this class, and write times and dates without any time zone. The 'UT' symbol will be used to indicate universal time.

### ALL-SKY CHARTS

Astronomers represent the appearance of the entire sky as seen at some particular place and time by drawing circular all-sky charts. Unfortunately, it's hard to show the appearance of the sky on a flat piece of paper, so reading an all-sky chart and relating it to what you see in the sky is a little tricky. For example, these charts distort the patterns of stars near the horizon, so you may find it hard to recognize constellations from an all-sky chart. The only way to correct this distortion is to break the sky up into several separate charts (this approach, used in The Sky Tonight, helps to find the constellations). For some purposes, however, it's very convenient to show the entire sky in one chart, so you should learn to read these charts. All-sky charts for each month of the year appear in Stars & Planets, starting on p. 24.

To read an all-sky chart, hold it in front of you with the side labeled 'N' at the top. Now imagine you are lying flat on your back with your head pointing north; then east will be on your left, south at your feet, west on your right, and the Zenith right in front of you. Mentally stretch the disk of the chart so that it forms a dome over your position. The positions of stars on this imaginary dome now correspond to their positions in the sky.

 Fig. 1. The sky over Honolulu on 01/14/05, 21:00 (01/15/04, 07:00 UT), produced using Your Sky. Stars are shown as dots, with larger dots for brighter stars; the lines between stars outline constellations. The blue cross near the top of the chart is the north celestial pole, and the blue curve is the celestial equator; blue numbers are celestial coordinates in right ascension (see below). The red curve is the ecliptic. From left to right, the five round symbols show the positions of Jupiter, Saturn, the Moon, Mars and Venus respectively; notice that all these objects are near to the ecliptic. Compass points are shown around the edge of the chart.

You can get a pretty good idea of how the sky will look on 01/14/05, 21:00 by using the chart shown in Fig. 1. For example, the constellation of Taurus appears near the center of the chart, so it will be nearly overhead. The Moon appears on the right side of the chart, about one-third the distance from the center to the edge, so you can expect to see it in the west-south-west, about 30° above the horizon.

If you are used to reading maps of the Earth, the east and west compass points in Fig. 1 may seem to be reversed. On a terrestrial map with north at the top, you would expect to find west to the left and east to the right. However, a celestial map with north at the top has west at the right and east at the left. The reason for this reversal is that a terrestrial map shows a view looking down at the Earth, while a celestial map shows a view looking up at the sky. Astronomical charts usually have north at the top and west to the right. When using a telescope, you'll notice that stars drift toward the west as a result of the Earth's rotation; this is a convenient way to determine the correct way to view a star chart.

### ALTITUDE AND AZIMUTH

There are several coordinate systems that can be used to describe the positions of objects in the sky. The one that is the most useful to us is called 'altitude-azimuth'. The altitude coordinate is just the distance above the horizon in degrees; it goes from zero to 90°. The azimuth is the direction you're facing: You can use compass directions, or the angle in degrees. The azimuth angle starts at north, increases toward the east and runs from zero to 360°. So east is 90°, southwest is 225° and so on. Our telescopes work in this kind of coordinate system: the base swivels around in azimuth, and the tube can be moved up and down in altitude. With these two adjustments, the telescope can be pointed at any part of the sky.

In describing positions in the sky, it's sometimes hard to estimate the angles. Fortunately, we have some built-in scales. With your arm outstretched and your fingers spread, your thumb and little finger cover an angle of about 20° on the sky. Your closed fist covers about 10°, and one finger covers about two degrees--all with outstretched arm, of course. These approximations work pretty well for people of very different sizes.

### CELESTIAL COORDINATES

While alt-az coordinates are fixed to an observer on earth's surface, celestial coordinates are fixed to the sky. To a good approximation, each star has a constant location in celestial coordinates.

Just as latitude and longitude can be used to specify any point on the Earth's surface, two celestial coordinates can be used to specify any point on the celestial sphere. Imagine starting from the point on the sky the point where the Sun, moving north, crosses the celestial equator (this is the point labeled '0 h' in the chart above). To reach any given point on the celestial sphere, you could first travel east along the celestial equator, and then towards one of the celestial poles, until you reach your destination. The angle you've traveled along the equator is called the right ascension; it's measured in units of hours, where 1 hour = 15°. The angle you've traveled towards one of the poles is called the declination; it's measured in degrees, with positive declinations towards the north celestial pole, and negative declinations towards the south celestial pole.

Celestial coordinates are often useful for locating objects. Stars & Planets, for example, often gives celestial coordinates when discussing stars If you look at the description of alpha Orionis on p. 194, you'll see '5h 55m +7°.4' just after the star's name. This means that alpha Orionis has a right ascension of 5h 55m (just slightly less than 6 hours) and a declination of +7°.4 (a little north of the celestial equator). Celestial coordinates also appear on the constellation charts; for example, see the chart of Orion on p. 195, which shows that Orion lies across the celestial equator at about 5h 30m right ascension.

### WEB RESOURCES

An interactive planetarium, set up to show the sky now above Honolulu. You can chose other dates and times, select other viewing sites, and zoom in on selected areas; for these and other options, see http://www.fourmilab.to/yoursky. Created by John Walker.

• One Day: high res. (5.1 Mbyte mpeg); low res. (1.4 Mbyte mpeg).

Shows how the sky above Honolulu changes during one day, from 01/01/04, 20:00 to 01/02/04, 20:00. This animation illustrates the effect of the Earth's rotation. The various symbols you see moving along with the stars represent the Sun, Moon, and planets. On this particular day, the Moon appeared very close to the Sun, though it was not actually close enough to cause an eclipse.

• One Year: high res. (5.7 Mbyte mpeg); low res. (1.6 Mbyte mpeg).

Shows how the sky above Honolulu changes during one year, from 01/01/04, 20:00 to 12/31/04, 20:00. This animation illustrates the effect of the Earth's revolution around the Sun. Note how the constellations visible in the night sky change as the Earth revolves around the Sun. Also, note the Moon's monthly passages across the sky along the ecliptic and the fairly gradual motion of other planets, especially red Mars.

### REVIEW QUESTIONS

• If you face north, which way does the celestial sphere appear to rotate - clockwise or counter-clockwise?

• If you see the full Moon rising in the east in the evening, where would you expect to see it very early next morning?

• What is 01/20/04, 7:35 UT in local 24-hour time? What day of the week? Is it morning or evening?

• Using the all-sky chart above, which direction should you face to find Saturn? How far above the horizon should you look?

• Why is one hour in right ascension equivalent to 15 degrees along the celestial equator?

Donald L. Mickey (mickey@ifa.hawaii.edu)