You Need to Know

Much of our initial discussion on sundials will concern the motion of objects in the sky. Therefore, we shall introduce some terminology and a coordinate system that allow us to specify succinctly the location of particular objects in the heavens.

The Celestial Sphere

The celestial sphere
Figure 1

It is useful in discussing objects in the sky to imagine them to be attached to a sphere surrounding the Earth. This fictitious construction is called the celestial sphere. At any one time we see no more than half of this sphere, but we will refer loosely to the imaginary half-sphere over our heads as just the celestial sphere. (See Figure 1).

The north celestial pole (NCP) and the south celestial pole (SCP) are the imaginary points in the sky directly above the geographic north and south pole, respectively. (See Figures 3 and 5 below.)

The point on the celestial sphere that is directly over our heads at a given time is termed the zenith. The imaginary circle passing through the north and south points on our horizon and through the zenith is termed the meridian.

The meridian separates the morning and afternoon positions of the Sun. In the morning, the Sun is east of the meridian. At local noon, the Sun is right on the meridian. In the afternoon, the Sun is west of the meridian.

We will introduce additional terminology associated with the celestial sphere later.

Motion in the Sky

It is clear after only minimal observation that objects change their positions in the sky over a period of time. This motion is conveniently separated into two parts:

  1. The entire sky appears to turn around the NCP and the SCP once in 24 hours. This is termed the daily or diurnal motion of the celestial sphere, and is in reality a consequence of the daily rotation of the Earth on its axis. The diurnal motion affects all objects in the sky and does not change their relative positions: the diurnal motion causes the sky to rotate as a whole once every 24 hours.
  2. Superposed on the overall diurnal motion of the sky is "intrinsic" motion that causes certain objects on the celestial sphere to change their positions with respect to the other objects on the celestial sphere. These are the "wanderers" of the ancient astronomers: the planets, the Sun, and the Moon.

In our discussion, we will imagine the Sun rotating around a stationary Earth, although the Sun's apparent motion around us is actually due to the Earth's rotation about its axis.

Diurnal Motion at Different Latitudes

Actually, all objects are slowly changing their relative positions on the celestial sphere, but for most, the motion is so slow that it cannot be detected over time spans comparable to a human lifetime; only the "wanderers" have sufficiently fast motion for this change to be easily visible.

The "Path of the Sun" on the Celestial Sphere

Path of the Sun
Figure 2

Another important imaginary object on the celestial sphere is the ecliptic or "path of the Sun", which is the imaginary path that the Sun follows on the celestial sphere over the course of a year. As Figure 2 indicates, the apparent position of the Sun with respect to the background stars (as viewed from Earth) changes continuously as the Earth moves around its orbit, and will return to its starting point when the Earth has made one revolution in its orbit.

Ecliptic path
Figure 3

Because the rotation axis of the Earth is tilted by 23.5 with respect to the plane of its orbital motion (which is also called the ecliptic), the path of the Sun on the celestial sphere is a circle tilted by 23.5 with respect to the celestial equator, which is the imaginary circle around the sky directly above the Earth's equator. It intercepts the horizon at the points directly east and west anywhere on Earth. (See Figure 3).

East and West on the Celestial Sphere

It is useful to define east and west directions on the celestial sphere, as illustrated in Figure 4.

celestial east west
Figure 4

Objects to the west of the Sun on the celestial sphere precede the Sun in the diurnal motion of the celestial sphere (they "rise" before the Sun and "set" before the Sun). Likewise, objects to the east of the Sun trail the Sun in the diurnal motion (they "rise" after the Sun and "set" after the Sun). Generally, one object is west of another object if it "rises" before the other object over the eastern horizon as the sky appears to turn, and east of the object if it "rises" after the other object.

Motion of the Sun

Celestial sphere
Figure 5

The ecliptic and the celestial equator intersect at two points: the vernal (spring) equinox and autumnal (fall) equinox. The Sun crosses the celestial equator moving northward at the vernal equinox around 21st March and crosses the celestial equator moving southward at the autumnal equinox around 22nd September. When the Sun is on the celestial equator at the equinoxes, everybody on the Earth experiences 12 hours of daylight and 12 hours of night for those two days (hence, the name ``equinox'' for ``equal night''). The day of the vernal equinox marks the beginning of the three-month season of spring on our calendar and the day of the autumnal equinox marks the beginning of the season of autumn on our calendar. On those two days of the year, the Sun will rise in the exact east direction, follow an arc right along the celestial equator and set in the exact west direction.

path of the Sun
Figure 6

When the Sun is above the celestial equator during the seasons of spring and summer, you will have more than 12 hours of daylight. The Sun will rise in the northeast, follow a long, high arc north of the celestial equator, and set in the northwest. Where exactly it rises or sets and how long the Sun is above the horizon depends on the day of the year and the latitude of the observer. When the Sun is below the celestial equator during the seasons of autumn and winter, you will have less than 12 hours of daylight. The Sun will rise in the southeast, follow a short, low arc south of the celestial equator, and set in the southwest. The exact path it follows depends on the date and the observer's latitude.

No matter where you are on the Earth, you will see 1/2 of the celestial equator's arc. Since the sky appears to rotate around you in 24 hours, anything on the celestial equator takes 12 hours to go from exact east to exact west. Every celestial object's diurnal (daily) motion is parallel to the celestial equator. So for northern observers, anything south of the celestial equator takes less than 12 hours between rise and set, because most of its rotation arc around you is hidden below the horizon. Anything north of the celestial equator takes more than 12 hours between rising and setting because most of its rotation arc is above the horizon. For observers in the southern hemisphere, the situation is reversed. However, remember, that everybody anywhere on the Earth sees 1/2 of the celestial equator so at the equinox, when the Sun is on the equator, you see 1/2 of its rotation arc around you, and therefore you have 12 hours of daylight and 12 hours of nightime every place on the Earth.

The geographic poles and equator are special cases. At the geographic poles, the celestial equator is right along the horizon and the full circle of the celestial equator is visible. Since a celestial object's diurnal path is parallel to the celestial equator, stars do not rise or set at the geographic poles. On the equinoxes the Sun moves along the horizon. At the north pole the Sun ``rises'' on 21st March and ``sets'' on 22nd September. The situation is reversed for the south pole. On the equator observers see one half of every object's full 24-hour path around them, so the Sun is above the horizon for exactly 12 hours for every day of the year.

Tilt of the Sun
Figure 7

Since the ecliptic is tilted 23.5 with respect to the celestial equator, the Sun's maximum angular distance from the celestial equator is 23.5. This happens at the solstices. For observers in the northern hemisphere, the farthest northern point above the celestial equator is the summer solstice, and the farthest southern point is the winter solstice. The word ``solstice'' means ``sun standing still'' because the Sun stops moving northward or southward at those points on the ecliptic. The Sun reaches winter solstice around 21st December and you see the least part of its diurnal path all year---this is the day of the least amount of daylight and marks the beginning of the season of winter for the northern hemisphere. On that day the Sun rises at its furthest south position in the southeast, follows its lowest arc south of the celestial equator, and sets at its furthest south position in the southwest. The Sun reaches the summer solstice around 21st June and you see the greatest part of its diurnal path above the horizon all year---this is the day of the most amount of daylight and marks the beginning of the season of summer for the northern hemisphere. On that day the Sun rises at its furthest north position in the northeast, follows its highest arc north of the celestial equator, and sets at its furthest north position in the northwest. The seasons are opposite for the southern hemisphere (eg., it is summer in the southern hemisphere when it is winter in the northern hemisphere). The Sun does not get high up above the horizon on the winter solstice. The Sun's rays hit the ground at a shallow angle at mid-day so the shadows are long. On the summer solstice the mid-day shadows are much shorter because the Sun is much higher above the horizon.

Celestial Coordinate Systems

There are a couple of popular ways of specifying the location of a celestial object. The first is what you would probably use to point out a star to your friend: the altitude-azimuth system. The altitude of a star is how many degrees above the horizon it is (anywhere from 0 to 90 degrees). The azimuth of a star is how many degrees along the horizon it is and corresponds to the compass direction.

altitude - azimuth system
Figure 8: A star's position in the altitude-azimuth coordinate system. The azimuth = 120 and the altitude = 50. The azimuth is measured in degrees clockwise along the horizon from due north. The azimuths for the compass directions are shown in the figure. The altitude is measured in degrees above the horizon. The star's altitude and azimuth changes throughout the night and depends on the observer's postion (here at the intersection of the north-south and east-west line.) The star's position does not depend on the location of the NCP or celestial equator in this system.

Azimuth starts from exactly north = 0 and increases clockwise: exactly east = 90, exactly south = 180, exactly west = 27, and exactly north = 360 = 0.

The second way of specifying star positions is the equatorial coordinate system. This system is very similar to the longitude-latitude system used to specify positions on the Earth's surface. This system is fixed with respect to the stars so, unlike the altitude-azimuth system, a star's position does not depend on the observer's location or time.

The lines on a map of the Earth that run east-west parallel to the equator are lines of latitude and when projected onto the sky, they become lines of declination. Like the latitude lines on Earth, declination (dec) is measured in degrees away from the celestial equator, positive degrees for objects north of the celestial equator and negative degrees for objects south of the celestial equator. Objects on the celestial equator are at 0 dec, objects half-way to the NCP are +45, objects at the NCP are +90, and objects at the SCP are -90.

equatorial coordinate system
Figure 9

Parts of a Sundial

parts of a sundial
Figure 10

The gnomon is usually a rod or a triangular piece of metal or wood on a sundial. The style is the sloping edge of the gnomon. The style is usually used to cast the shadow on the dial plate to show the hour of the day. In a horizontal dial, the angle Ø is equal to the latitude of the location.

The hour lines are the numbered time lines that the shadow falls along.

The nodus is a "marker" along the gnomon to get an exact point on the shadow.

Dial furniture are the markers other than the hour lines on the dial plate. It is there to provide other information, such as the date and declination of the Sun.