a Elongation from the Sun or relative separation between planets.

a Elongation from the Sun or relative separation between planets.

2.4.3. Planetary Phenomena

Morning and evening stars are only aspects of a more general class of observed events collectively known as planetary phenomena. The configurations that the planets achieve with the Sun, stars, or with each other, enabled early observers to keep track of the planets' motions and, from these, to discover periodicities. The phenomena were summarized in terms of elongations or differences in celestial longitude (see Table 2.8). Astrologers make use of all the configurations, but the sextile and trine configurations are not often referenced in modern astronomy. Among other astrological terms that are used to refer to the positions of planets in the sky are ascendancy (rising), descendancy (setting), medium caelum or mid-heaven (where the object traverses the celestial meridian),34 and imum caelum or anti-heaven (where the object traverses the portion of the celestial meridian below the horizon). Figure 2.21 demonstrates the geocentric planetary configurations, viewed from the north ecliptic pole.

34 For a circumpolar object, the "mid-heaven" refers to the upper of the two meridian transits, namely, the upper culmination.

Equatorial site_Northern mid-latitude site

Figure 2.20. The orientations of the ecliptic and celestial equator to the horizon near the east and west points of the horizon as seen from the equator and from mid-latitude sites for the important turning points of the seasons: the solstices and the equinoxes. These are views from inside the celestial sphere. Drawn by E.F. Milone.

Figure 2.21. The geocentric planetary configurations—and cosmology—of antiquity. Drawing by E.F. Milone.

Note that an object at a conjunction will rise at the same time as the Sun,35 whereas an object at opposition will be opposite the Sun in the sky and so will set as the Sun rises, and rise as the Sun sets. Planetary phenomena may involve another planet, the Moon, or a star, but in such cases, the other object is always named. The Sun is intended implicitly when no other object is stipulated. Several other terms that depend on sky location are the sextile (separation of 60°), quadrature (90°), and trine (120°). At quadrature, a planet will rise ~6 hours before (if at eastern quadrature) or after (if at western quadrature) the Sun. The sextile and trine are little used in astronomy, but are frequently used by modern astrologers and, more important for us, were extensively used by ancient astrologers.

Several terms are used to describe the visibility of the an object. When a star or planet formerly invisible due to proximity to the Sun first becomes visible in the morning sky, it is said to be at heliacal rising. When the object is last seen to set in the west after the Sun in the evening sky, it is said to be at heliacal setting. Two other pairs of terms are often confused with heliacal risings and settings. Either the rising or setting of a star in the evening, i.e., at or just after sunset, is referred to as acronychal36 and either the rising or setting of a star at sunrise is said to be cosmical. Thus, a star that is first seen to rise as the Sun sets is said to be at acronychal rising, and if it sets with the Sun, acronychal setting; one that sets as the Sun rises is at its cosmical setting, and if it rises as the Sun rises, it is at cosmical rising. Astronomers do not always follow these definitions strictly, however; so the context must be used to understand what the terms are

35 Or nearly so: Conjunction is sometimes taken to mean identical celestial longitude, and sometimes, right ascension;in either case, if the declination of the two objects is not the same, they will almost certainly rise at slightly different instants of time.

36 Or acronycal. Additional spellings that have been used for this word include acronical, achronical, and achronichal!

intended to mean. Parker and Neugebauer (1960, pp. 55, 57, 72) unambiguously identify the term "acronychal setting" to mean setting right after the Sun, i.e., seen in the west just after sunset, in accord with the definitions. In Sky Watchers of Ancient Mexico, Aveni (1980, p. 325, n. 16) correctly uses the term "cosmic rising" to indicate rising at the same instant as the Sun (and "cosmic setting" to indicate setting at the instant that the Sun sets). However, he also defines "achronic" to indicate rising when the Sun sets (in agreement with the standard definition of "acronychal") but also a setting as the Sun rises (which disagrees). Elsewhere in Sky Watchers, the applications of "heliacal rising" and "heliacal setting" are consistent with both our and Aveni's definitions (e.g., pp. 87, 99, 109ff), except for one discussion in which "heliacal setting" is used to describe a setting at sunrise in a discussion of the behavior of the Pleiades at Teotihuacan (Aveni 1980, p. 112). Indeed, many authors use this broader usage of "heliacal" to encompass both the restricted sense of the word and the acronychal definition (because they are both, in a sense, heliacal phenomena). However, in the current work, we try to be consistent with the stricter definitions.

As we note in §3.1.5, the hour angle difference from the Sun and the altitude of the object at first and last visibility depend on its brightness and on sky conditions; it is more difficult to see the light of most celestial objects when they near the horizon because the light-scattering path through the atmosphere is the longest at such times. The relationship between the first and last visible phenomena and the true instants when the star/planet and the Sun rise/set together was the topic of a book in the ancient world written by Autolycus of Pitane: On the Risings and Settings.

Because the Moon, Mercury, and Venus were considered to be below the orbit of the Sun, they were called inferior planets; those beyond the Sun were superior planets. Heliocentrically, they are interior and exterior, respectively, to Earth's orbit. There are important differences between the apparent motions of these two types of planets.

For Mercury and Venus, the elongation reaches maximum values both east and west: the greatest eastern elongation (GEE) and greatest western elongation (GWE), respectively. When at eastern elongation, the planet is visible east of the Sun, therefore, after sunset and in the western part of the sky. At western elongation, the object is west of the Sun, and there visible before sunrise, and in the eastern part of the sky.

The geometry of the planetary configurations can be understood from Figure 2.22, which, although presented in a heliocentric framework, shows how the planetary configurations are generated relative to the earth.

It will be noticed that only interior planets go through an inferior conjunction and only exterior planets can achieve quadrature and opposition. Both types of planets can go through superior conjunction, although in current usage, superior planets are merely said to be at "conjunction" at such times, because this is the only type of conjunction (with the Sun) that they can achieve; i.e., they can never be at inferior conjunction. Exterior planets move eastward through the configurations: superior conjunction, eastern quadrature, opposition, western quadrature, and superior conjunc-

Figure 2.22. Successive positions of exterior and interior heliocentric planetary orbits, relative to an arbitrary position of the Earth, and showing how they give rise to the planetary configurations. Drawn by E.F. Milone.

tion. Their motion is eastward all the time except during an interval around opposition when they briefly appear to show retrograde (westward) motion.37 Interior planets may be in conjunction with the Sun, but most of the time, they are at some elongation less than GEE or GWE. Interior planets move from superior conjunction through increasing eastern elongations to GEE to decreasing elongations to inferior conjunction to increasing westward elongations to GWE to decreasing western elongations to superior conjunction. Following maxiumum eastern elongation (when they are evening stars), Venus and Mercury seem to fall toward the Sun at an increasing rate, and then move rapidly into the morning sky, where they continue westward at a decreasing rate until maximum western elongation is reached. Figure 2.23 illustrates their motions in the western and eastern skies and associated locations in a heliocentric sketch.

The order of the configurations over a synodic cycle, arbitrarily beginning at its heliacal rising, is as follows (with associated phenomena shown below each configuration). For an interior planet,

(1) First visibility in the morning sky (retrograde motion continuing) (heliacal rising, morning star)

(2) Greatest western elongation (onset of prograde motion) (morning star)

(3) Last visibility in the morning sky (prograde motion continuing) (morning star)

(4) Superior conjunction (prograde motion continuing) (rises and sets with the Sun)

(5) First visibility in the evening sky (prograde motion continuing) (heliacal/achronical setting, evening star)

Figure 2.23. The motions of an interior planet in the (a) eastern and western skies and (b) in a heliocentric frame of reference. Note the ready explanation in the heliocentric system for the apparent limitation in the motion of an inferior planet. Drawn by E.F. Milone.

37 It is important to note that in the ancient world, our "direct" or "prograde" (eastward) and "retrograde" (westward) terms for these motions were not in use. Ptolemy uses the term "eiZ ta £PO|ieva," "toward the rear," to mean eastward motion. He uses the term "eiZ t a ppOhgoi)|ieva," "toward the front," to mean westward. To Ptolemy, the "forward" direction was that of the diurnal motion. See Toomer (1984).

Figure 2.23. The motions of an interior planet in the (a) eastern and western skies and (b) in a heliocentric frame of reference. Note the ready explanation in the heliocentric system for the apparent limitation in the motion of an inferior planet. Drawn by E.F. Milone.

(6) Greatest eastern elongation (onset of retrograde motion) (evening star)

(7) Last visibility in the evening sky (retrograde motion continuing) (evening star)

(8) Inferior conjunction (retrograde motion continuing) (rises and sets with the Sun)

(9) First visibility in the morning sky (retrograde motion continuing) (heliacal rising, morning star)

so that the interior planet moves westward from its GEE evening star appearance (through inferior conjunction) to its GWE morning star appearance; and it moves eastward from GWE (through superior conjunction) to GEE. For an exterior planet, again from heliacal rising:

(1) First visibility in the morning sky (prograde motion continuing) (heliacal rising, morning star)

(2) Western quadrature (prograde motion continuing) (morning star)

(3) First stationary point (beginning of retrograde motion)

(4) Opposition (acronychal rising)

(5) Second stationary point (end of retrograde motion)

(6) Eastern quadrature (prograde motion continuing) (evening star)

(7) Last visibility in the evening sky (prograde motion continuing) (evening star, heliacal/acronychal setting)

(8) Superior conjunction (prograde motion continuing) (rises and sets with the Sun)

(9) First visibility in the morning sky (prograde motion continuing) (heliacal rising, morning star)

Note that the average ecliptic motion of exterior planets is less than that of the Sun and, consequently, get passed by the Sun. The only retrograde motion that these planets undergo is around opposition, when the Earth, in a faster, interior orbit, passes these planets.

The observations of specific configurations, especially of first and last visibility in ancient Mesopotamia, will be elaborated in § See Aveni (1980, pp. 109-117) for a similar treatment of configuration visibility in Mesoamerica. The apparent path of a planet in the sky varies from cycle to cycle because of the relative changes in ecliptic latitude as well as in longitude due to orbital inclinations. Thus, for example, the retrograde motion of an exterior planet may be a loop of various degrees of flattening or a zigzag. The looping pattern of an interior planet also varies during its pass through inferior conjunction. The relative periods of motion may be used to determine repetitions of these motion patterns.

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