Read an Excerpt
A Field Guide to the Heavens
By Mark R. Chartrand, Helmut K. Wimmer
St. Martin's PressCopyright © 1982 St. Martin's Press
All rights reserved.
How you see the sky depends upon where you are on Earth. Even the way the sky seems to move overhead depends upon your terrestrial location. To specify a location on Earth precisely, two coordinates are used — two because Earth's surface is two-dimensional.
Latitude is the north-south coordinate, measured in degrees north and south of the equator, which is the imaginary line around our planet midway between the poles. The poles are the ends of the planet's axis of rotation, and for our purposes can be considered fixed. The equator is at latitude 0°. Northern latitudes are positive, southern ones negative. The north geographic pole is at latitude +90°, the south geographic pole at – 90°. Locations having the same latitude are said to be on the same parallel of latitude.
Longitude is the east-west coordinate. A line from one pole to the other is called a meridian of longitude. (Such a line is an example of a great circle: a line on the surface of a sphere which is part of a circle whose center coincides with the center of the sphere.) A prime meridian is needed from which to start measurements eastward or westward. A century ago, different prime meridians were in use by different countries, each wanting the prime meridian to go through its capital. Since that situation was confusing to navigators and astronomers, all nations finally adopted the present prime meridian, which runs through Greenwich, England. Sometimes called the Greenwich meridian, it is marked at the Greenwich Observatory by a brass line in the pavement, so that you can stand with your feet in different hemispheres.
Longitude, like latitude, can be measured in degrees — from the prime meridian east and west up to 180°. At 180°, opposite the Greenwich meridian, is the international date line, which divides the Pacific Ocean. (For political and practical reasons, the line zigs and zags near the 180° meridian.) Along this line each new day begins and the previous day ends, so that, for example, when the time is 12:01 a.m. Wednesday just east of the line it is 12:01 a.m. Thursday just west of the line. Since the time of day when we see astronomical objects depends on Earth's rotation, longitude is often measured in hours, one hour equaling 15°. (See here.)
Although Earth's surface is two-dimensional, the planet is three-dimensional. Latitude and longitude are not just lines on the surface, but refer to angles measured at Earth's center. Latitude is the angle between the equator and the location referred to, and longitude is the angle between the prime meridian and the meridian of the location referred to. Each degree of latitude or longitude can be divided into 60 minutes (abbreviated '), and each minute into 60 seconds ("). But navigators and astronomers commonly use degrees with decimal fractions, rather than minutes and seconds, because they make computations easier.
Looking up at the sky from a plain, we seem to be at the center of the universe, with a flat Earth stretching off to infinity in all directions. We are at the center of the celestial sphere, an imaginary globe of indefinitely large size, on the inner surface of which all heavenly bodies and their motions appear as if projected onto a screen. This concept allows us to ignore distances of celestial objects except when relevant, heeding only their directions.
Often an observer wants to specify the direction of a celestial object with respect to his location. One convenient way is by means of horizon coordinates, sometimes called topocentric coordinates.
First, imagine a flat plane tangent to Earth's surface at your location. This is your horizon plane. The line along which it intersects the celestial sphere is your horizon. This divides the universe into the part you see above the horizon, and the invisible part below it. North is the point on the horizon in the direction of the geographic north pole; south is opposite. Facing south, east is on your left, west on your right.
Your celestial sphere has a spot unique for you: the point directly overhead, the zenith. If you move, your zenith moves. No other location on Earth has the same zenith as yours. The point opposite the zenith on the celestial sphere is the nadir.
The location of a celestial object with respect to the observer's location is described by the two angles called altitude and azimuth.
Altitude is the angle between the horizon and the object. This angle is measured from the horizon and perpendicular to it. Altitude is not height above the ground, as of an aircraft. It is an angle centered on you; or, an arc along the celestial sphere. Altitude ranges from 0° at the horizon to +90° at the zenith. Objects below the horizon have negative altitudes. Objects at the same altitude are said to be on a parallel of altitude. A line of constant altitude around the sky is called an almucantar.
Azimuth is the compass direction toward an object. More precisely, it is the angle measured around the horizon, beginning at north (0°) through east (90°) and so on until you reach a line drawn perpendicular from the object to the horizon. Thus east is azimuth 90°, south 180°, west 270°, and north 360° — the same as 0°.
You can estimate altitude or azimuth simply by extending your fist to arm's length. At this distance your fist will appear to be about 10° wide. If you align the bottom of your fist with the horizon, the top is at about 10° altitude. Stacking fist on fist, you can estimate wider angles. This method of approximately measuring distances across the sky is convenient when you are attempting to locate a star or other object that is a known number of degrees from an object you have already identified. A navigator uses a sextant to determine altitude and azimuth accurately.
THE CELESTIAL SPHERE
Imagine Earth as surrounded by a very large sphere on the surface of which all stars, planets, and other celestial objects are placed. This is similar to the observer's celestial sphere mentioned here, but not exactly the same. Now we are imagining the astronomer's celestial sphere, with the center of Earth as the center of the sphere.
Next, imagine Earth's equator expanding outward until it intersects the sphere. The intersection will be a great circle on the sphere called the celestial equator. It is halfway between the north celestial pole (NCP) and the south celestial pole (SCP), which are the locations on the celestial sphere directly above the north and south geographic poles on Earth's surface.
In the sky there are counterparts to meridians of longitude, but for reasons explained more fully here, they are usually called hour circles. You should keep in mind that as Earth turns, the meridian of longitude under a given hour circle changes continuously.
Another fundamental plane in the sky is the plane of Earth's orbit, called the ecliptic plane, or ecliptic. As seen by us on Earth, the ecliptic is an imaginary line in the sky along which the Sun moves during a year's journey around the sky against the background of stars. As seen by an observer sitting "on the NCP," the Sun would move counterclockwise. Perpendicular to the plane of the ecliptic are the north and south ecliptic poles.
When Earth formed from a cloud of gas and dust about five thousand million years ago, its axis of rotation did not coincide with the axis of the ecliptic poles. The two axes, and hence the plane of the equator and the plane of the ecliptic, are inclined to one another at an angle of about 231/2°. This angle is called the obliquity of the ecliptic. Thus the north ecliptic pole is at R.A. 18h, Dec. + 661/2°, while the south ecliptic pole is located opposite at R.A. 6h, Dec. – 661/2°.
The two points on the celestial sphere where the equatorial and ecliptic planes meet are termed the equinoxes. The point at which the Sun crosses the celestial equator when going north in spring is called the vernal equinox. The point where the Sun crosses when going south in autumn is the autumnal equinox. (See here for the relationship of the equinoxes to the seasons.)
Keep in mind that the celestial sphere is indefinitely large. All that concerns us are the directions of celestial objects from us. For most purposes, it makes no difference whether the center of the celestial sphere is assumed to be at the center of Earth or at our location. Remember also that the illustration here and on other pages shows the celestial sphere as seen from the "outside," while we on Earth are looking out from inside. The celestial sphere is the "screen" on which the drama of the sky is played.
To specify an object's location on the celestial sphere, equatorial coordinates are used. These refer to the celestial equator.
The north-south coordinate (similar to latitude) is called declination (Dec, or δ, the lower-case Greek letter "delta"), measured in degrees north ( + ) and south ( – ) of the celestial equator, which is at declination 0°. The celestial poles are at + 90° and – 90°.
The east-west coordinate is called right ascension (R.A., or a, the lower-case Greek letter "alpha"). Its zero-point is the vernal equinox. Right ascension is expressed sometimes in degrees, but more commonly and usefully in hours, minutes, and seconds. Since Earth turns 360° in about 24 hours, one hour (1h) of right ascension (or time) is 15° of arc, one minute of time (1m) is 15 minutes of arc (written 15'), and one second of time (1s) is 15 seconds of arc (15").
A degree of declination always represents the same distance on the celestial sphere, but an hour of right ascension represents a shorter distance on the celestial sphere as we move farther away from the celestial equator. In other terms, 1° of arc in R.A. always equals 4m of time, but represents a shorter distance on the celestial sphere as declination increases. Thus an object at Dec. 0° (that is, on the celestial equator) seen in a fixed telescope with a field of 1° will cross the field in 4 minutes, but at Dec. 45° the object would be in the field about 6 minutes.
The vernal equinox is right ascension Oh, and the opposite point, the autumnal equinox, is 12h, from which we go on to 24h, which is the same as Oh. Right ascension increases counterclockwise — that is, toward the east — around the north celestial pole. As observers we are inside the sphere; hence the sky pattern is reversed compared to the illustration, which shows the pattern from outside.
In the illustration are two stars: #1 and #2. Their positions can be specified thus:
Star #1: α = 2h45m00s, δ = + 62°26'56".
Star #2: α = 22h40m55s, δ = – 36°44'05".
Celestial longitude is similar to right ascension, except that it is measured along the ecliptic rather than along the celestial equator. Celestial latitude is the angular distance of an object from the ecliptic. These coordinates are useful for specifying the positions of planets, since planets are always close to the ecliptic.
Because it is curved, when the celestial sphere is represented on a flat page, distortions occur — areas get squeezed or stretched out of shape. The bottom illustration shows a flat map with the celestial equator and the ecliptic marked, along with one or two stars. Study carefully the two methods of showing the same thing. Both methods are useful in depicting the sky and will be used later in this book.
TIME AND THE SKY
Most timekeeping and calendrical schemes depend on celestial motions. A day is the time it takes for one complete rotation of Earth, a month for a complete cycle of Moon phases, a year for one circuit of Earth's orbit.
Unlike common clocks, the "face" of the celestial clock moves while the "hand" stands still. For observers in the northern hemisphere, the center of the clock face is the NCP (north celestial pole), marked approximately by the star Polaris. Since the plane of an observer's horizon is tangent to Earth's surface at his location, the altitude of the NCP from his location is the same angle as his latitude. At latitude + 40°, the NCP is 40° above the north point on the horizon. All stars within that many degrees of the NCP will always be above the horizon. Similarly, all stars within that many degrees of the SCP will never rise. Since the celestial equator is perpendicular to the axis between the celestial poles, for any observer anywhere it will cross the sky and intersect the horizon at the due-east and due-west points, and its angle with the horizon will be 90° minus the observer's latitude.
For any observer, the "hand" on the clock is an imaginary line in the sky called the celestial meridian, or just meridian. It is the observer's meridian of longitude extended out to the celestial sphere. It runs from the due-north point, through his zenith, to the due-south point, and underneath Earth back to north. The meridian for one location is different from the meridian for any other location to the east or west. An observer due north or south of you shares the same meridian, but for that observer the NCP is at a different altitude.
An imaginary circle drawn on the celestial sphere through the celestial poles and a celestial object is the hour circle of that object. The angle, or arc, between the celestial meridian and the hour circle of the object is the hour angle. Since the sky moves westward, the hour angle increases westward, from Oh on the meridian through 24h. It decreases eastward. Thus an object in the eastern sky has an eastern, or negative, hour angle. The hour angle is the measure of how long ago (or before) the object was (or will be) on the meridian.
In the illustration, the Sun's hour angle is about 2h, since it is about 30° west of the meridian. Our time of day is defined by the hour angle of the Sun, but since we want a new day to begin at midnight, when the Sun is crossing the invisible lower meridian, we use this definition: Local Apparent Time = Hour Angle of the Sun + 12h. The time is apparent because it is according to where the Sun appears, and local because it depends on the observer's location. A person east of you has a later local apparent time (a later time shown on a sundial), because the Sun crosses his meridian before it crosses yours. A person west of you has an earlier local apparent time because the Sun will cross his meridian after it crosses yours.
Before the days of fast communication and travel, differences in local apparent time between places a few tens of miles east or west of one another did not matter. Today it is necessary to standardize local times so that a person will not encounter different times in each different town he visits.
Standardization has been done by establishing 24 time zones around the world, each 15° wide. Within a zone, every location has the same standard time. Zones are centered on standard meridians at longitudes 0°, ± 15°, ± 30°, and soon, thus differing by Oh, ± 1h, ± 2h, and soon, from the time at Greenwich, England, on the prime meridian (see here).
For political and practical reasons, some boundaries between zones are irregular; there are also areas where the time in the zone is a half hour more or less than in the adjoining zones. Time-zone boundaries generally appear in atlases, almanacs, and road maps, but may change.
Some areas adopt a standard time one hour later on the clock than the geographic zone they are in. At certain times of the year, some other regions, including most of the United States, adopt daylight time, which sets the local time one hour later on the clock than standard time, thus making daylight last farther into the evening. In the United States, daylight time is usually in effect from the first Sunday in April until the last Sunday in October. The mnemonic for adjusting the clock is "Spring ahead, Fall back."
Time zones covering the contiguous United States are: Eastern, at 75° or + 5h; Central, at 90° or + 6h; Mountain, at 105° or + 7h; and Pacific, at 120° or + 8h. Alaska, Hawaii, and United States possessions have different times. The number of hours tells you how many hours your clock is earlier than Greenwich Mean Time, or GMT. Astronomical almanacs often give times of events in GMT, which is also the same as Universal Time, or U.T., and is sometimes called Zulu or Z-time. You can find the time difference between two zones by subtracting the lower number from the higher. Thus, Philadelphia (Zone + 5h) and Fresno (Zone + 8h) are three hours apart, and at any given moment Fresno's clock shows an earlier time.
Excerpted from Night Sky by Mark R. Chartrand, Helmut K. Wimmer. Copyright © 1982 St. Martin's Press. Excerpted by permission of St. Martin's Press.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.