Celestial sphere: The apparent motions of the Sun, Moon, planets, and stars

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Celestial sphere: The apparent motions of the Sun, Moon, planets, and stars

The celestial sphere is an imaginary projection of the Sun, Moon, planets, stars, and all astronomical bodies upon an imaginary sphere surrounding Earth. Although originally developed as part of the ancient Greek concept of an Earth-centered (geocentric) universe, the hypothetical celestial sphere gives astronomers an important tool for fixing the location and plotting movements of celestial objects.

Ancient Greek astronomers envisioned concentric crystalline spheres centered around Earth, upon which the Sun, Moon, planets, and stars moved. Although heliocentric (Sun-centered) models of the universe were also proposed by the Greeks, they were disregarded as counterintuitive to the apparent motions of celestial bodies across the sky.

Early in the sixteenth century, Polish astronomer Nicolaus Copernicus (1473–1543) reasserted the heliocentric theory. Although sparking a revolution in astronomy, this system was deeply flawed by the fact the sun is certainly not the center of the universe, and Copernicus’s insistence that planetary orbits were circular. Even so, the heliocentric model developed by Copernicus fit observed data better than the ancient Greek geocentric concept. For example, the periodic backward or retrograde motion of Mars, Jupiter, and Saturn, and the lack of such motion for Mercury and Venus was more readily explained by the fact that the former planets’ orbits were outside of Earth’s. Thus, Earth “overtook” them as it circled the Sun.

Planetary positions could also be predicted much more accurately using the Copernican model. Danish astronomer Tycho Brahe’s (1546–1601) precise observations of movements across the celestial sphere allowed German astronomer and mathematician Johannes Kepler (1571–1630) to formulate his laws of planetary motion that correctly described the planet’s elliptical orbits.

The modern celestial sphere is an extension of the latitude and longitude coordinate system used to fix terrestrial location, a grid system that can plot any location on Earth’s surface. Latitudes—also known as parallels—mark and measure distance north or south from the equator. Earth’s equator is designated 0° latitude. The north and south geographic poles respectively measure 90° north (N) and 90° south (S) from the equator. The angle of latitude is determined as the angle between a transverse plane cutting through Earth’s equator and the right angle (90°) of the polar axis. Longitudes—also known as meridians—are great circles that run north and south, and converge at the north and south geographic poles.

On the celestial sphere, projections of latitude and longitude are transformed into declination and right ascension. A direct extension of Earth’s equator at 0° latitude is the celestial equator at 0° declination. Corresponding to Earth’s rotation, right ascension is

measured from zero to 24 hours around the celestial sphere. Accordingly, one hour represents 15 angular degrees of travel around the 360° celestial sphere.

Declination is subdivided into arcminutes and arcseconds. In 1° of declination, there are 60 arcminutes (60^”) and in one arcminute there are 60 arcseconds (60). Right ascension hours are subdivided into minutes and seconds of time.

The designation of 0° longitude is an arbitrary international convention held since the days of British naval superiority. This established the 0° line of longitude—or Prime Meridian—as the great circle that passes through the Royal Observatory in Greenwich, England. On the celestial sphere, zero hours (0 h) right ascension is also arbitrarily defined by international convention as the line of right ascension where the ecliptic—the apparent movement of the Sun across the celestial sphere established by the plane of Earth’s orbit around the Sun—intersects the celestial equator at the vernal equinox.

Just as every point on Earth can be expressed with a unique set of latitude and longitude coordinates, every object on the celestial sphere can be specified by declination and right ascension coordinates. For any latitude on Earth’s surface, the extended declination line crosses the observer’s zenith—the highest point on the celestial sphere directly above the observer. By international agreement and customary usage, declinations north of the celestial equator are designated as positive (+) and declinations south of the celestial equator are designated as negative (–).

The polar axis is an imaginary line that extends through the north and south geographic poles. The earth rotates on its axis as it revolves around the Sun, tilted approximately 23.5 degrees to the plane of the ecliptic. The changing tilt of Earth’s polar axis is principally responsible for the cyclic progressions of the seasons. The polar axis also establishes the principal axis about which the celestial sphere rotates, creating north and south celestial poles. In the Northern Hemisphere, the star Polaris (also known as the North Star)is currently within approximately one degree (1°) of the north celestial pole. This means that all stars and other celestial objects appear to rotate about Polaris; depending on the latitude of observation, stars located near Polaris (circumpolar stars) may never “set.”

For any observer, the angle between the north celestial pole and the terrestrial horizon equals and varies directly with latitude north of the equator. For example, at 30° N latitude an observer views Polaris at + 30° declination; at the terrestrial North Pole (90° N), Polaris would be directly overhead (at the zenith) at + 90° declination.

The celestial meridian is an imaginary arc from the north point on the terrestrial horizon through the north celestial pole and zenith that terminates on the south point of the terrestrial horizon. Regardless of location on Earth, an observer’s celestial equator passes through the east and west points of the terrestrial horizon. In the Northern Hemisphere, the celestial equator is displaced southward from the zenith (the point directly over the observer’s head) by the number of degrees equal to the observer’s latitude.

Rotation about the polar axis results in the diurnal cycle of night and day, causing the apparent motion of the Sun across the imaginary celestial sphere. The Earth rotates about the polar axis at approximately 15 angular degrees per hour and makes a complete rotation in 23.9 hours. This corresponds to the apparent rotation of the celestial sphere. Because Earth rotates eastward (from west to east), objects on the celestial sphere usually move along paths from east to west (i.e., the Sun “rises” in the east and “sets” in the west). One complete rotation of the celestial sphere comprises a diurnal cycle.

As Earth rotates on its polar axis, it makes a slightly elliptical orbital revolution about the Sun in 365.26 days. Earth’s revolution about the Sun also corresponds to the cyclic and seasonal changes of observable stars and constellations on the celestial sphere. Although stars grouped in traditional constellations have no proximate spatial relationship to one another (i.e., they may be billions of light years apart) that do have an apparent relationship as a two-dimensional pattern of stars on the celestial sphere. Accordingly, in the modern sense, constellations establish regional location of stars on the celestial sphere.

A tropical year (i.e., a year of cyclic seasonal change), equals approximately 365.24 mean solar days. During this time, the Sun appears to travel completely around the celestial sphere on the ecliptic and return to the vernal equinox. In contrast, one orbital revolution of Earth about the Sun returns the Sun to the same backdrop of stars—and is measured as a sidereal year. On the celestial sphere, a sidereal day is defined as the time it takes for the vernal equinox— starting from an observer’s celestial median—to rotate around with the celestial sphere and recross that same celestial median. The sidereal day is due to Earth’s rotational period. Because of precession, a sidereal year is approximately 20 minutes and 24 seconds longer than a tropical year. Although the sidereal year more accurately measures the time it takes Earth to completely orbit the Sun, the use of the sidereal year would eventually cause large errors in calendars with regard to seasonal changes. For this reason the tropical year is the basis for modern Western calendar systems.

Seasons are tied to the apparent movements of the Sun and stars across the celestial sphere. In the Northern Hemisphere, summer begins at the summer solstice (approximately June 21) when the Sun is reaches its apparent maximum declination. Winter begins at the winter solstice (approximately December 21) when the Sun’s highest point during the day is its minimum maximum daily declination. The changing orientation of Earth’s polar axis to the Sun alters the Sun’s apparent declination. The vernal and autumnal equinox are denoted as the points where the celestial equator intersects the ecliptic.

The location of sunrise on the eastern horizon, and sunset on the western horizon also varies between a northernmost maximum at the summer solstice to a southernmost maximum at the winter solstice. Only at the vernal and autumnal equinox does the Sun rise at a point due east or set at a point due west on the terrestrial horizon.

During the year, the moon and planets appear to move in a restricted region of the celestial sphere termed the zodiac—a region extending outward approximately 8° from each side of the ecliptic. The modern celestial sphere is divided into twelve traditional zodiacal constellation patterns (corresponding to the pseudoscientific astrological zodiacal signs) through which the Sun appears to travel by successive eastward displacements throughout the year.

During its revolution about the Sun, Earth’s polar axis exhibits parallelism to Polaris. Although observing parallelism, the orientation of Earth’s polar axis exhibits precession—a circular wobbling exhibited by gyroscopes—that results in a 28, 000-year-long precessional cycle. Currently, Earth’s polar axis points roughly in the direction of Polaris. As a result, over the next 11, 00 years Earth’s axis will precess or wobble so that it assumes an orientation toward the star Vega. Precession causes an object’s celestial coordinates to change. As a result, celestial coordinates are usually accompanied by a date for which the coordinates are valid.

Corresponding to Earth’s rotation, the celestial sphere rotates through 1° in about four minutes. Because of this, sunrise, sunset, moonrise, and moon-set, all take approximately two minutes because both the Sun and Moon have the same apparent size on the celestial sphere (about 0.5°). The Sun is, of course, much larger, but the Moon is much closer. If measured at the same time of day, the Sun appears to be displaced eastward on the star field of the celestial sphere by approximately 1° per day. Because of this apparent displacement, the stars appear to rise approximately four minutes earlier each evening and set four minutes later each morning. Alternatively, the Sun appears to rise four minutes earlier each day and set four minutes earlier each day. A change of approximately four minutes a day corresponds to a 24-hour cycle of rising and setting times that comprise an annual cycle. In contrast, if measured at the same time each day, the Moon appears to be displaced approximately 13° eastward on the celestial sphere per day and therefore rises and sets almost one hour earlier each day.

Because the Earth revolves about the Sun, its displacement along its orbital path causes the time it takes to complete a cycle of lunar phases—a synodic month— and return the Sun, Earth, and Moon to the same starting alignment to be slightly longer than the sidereal month. The synodic month is approximately 29.5 days.

Earth rotates about its axis at approximately 15 angular degrees per hour. Rotation dictates the length of the diurnal (day/night) cycle, creating time zones with differing local noons. Local noon occurs when the Sun is at the highest point during its daily skyward arch from east to west (i.e., when the Sun is at its zenith on the celestial meridian). The Sun’s location (and reference to local noon) is described as ante meridian (A.M.—east of the celestial meridian—or post meridian P.M.)—west of the celestial meridian.See also Astrolabe; Celestial mechanics; Cosmology; Geographic and magnetic poles; Precession of the equinoxes; Solar illumination: Seasonal and diurnal patterns; Zodiacal light.