to Zenith A


Figure 2.8. The effects of solar altitude on ground warming. Note that a given cross-section of sunlit area is spread out on the ground by a factor that increases with solar zenith distance. Drawing by E.F. Milone.

Figure 2.8. The effects of solar altitude on ground warming. Note that a given cross-section of sunlit area is spread out on the ground by a factor that increases with solar zenith distance. Drawing by E.F. Milone.

would have been ~01h45m, which is ~2 hours smaller than today, and its declination would have placed it further south, at 8 ~ 15° compared with about 24° today. Thus, the Sun would need to be east of the vernal equinox and just west of the Pleiades for the Pleiades to be seen setting just after the Sun. As a rule of thumb, stars as faint as the Pleiades are required to be ~5° or more above the horizon to be seen clearly by the naked eye in an otherwise dark sky because of the dimming of star light by the long sightline through the atmosphere of an object near the horizon. The Sun must be sufficiently below the horizon (~10°) for these relatively faint naked eye stars to be seen above the twilight. See §3.1 for discussions of the visibility of astronomical objects and particularly § on atmospheric extinction and § on sky brightness and visibility. A simulation of the sky (Figure 2.9) shows that these conditions would last apply in early-to-mid-April, and thus early spring, as indicated by Whiston, but not in February!

From Hesiod's Works and Days, (8th century b.c.), we find the use of seasonal signs among the stars:

When first the Pleiades, Children of Atlas, arise, begin your harvest; plough, when they quit the skies,

In West's (1978) translation. We can see that these verses provide calendrical references: the visibility of well-known asterisms at important times of day, typically sunup or sundown. Two and a half millennia ago, the Pleiades had a right ascension, a ~ 1h 15m, nearly two and a half hours less than it has today. However, we must ask what Hesiod meant by the first rising of the Pleiades. If they were seen to rise as the Sun set, an "acronychal rising" as we call this phenomenon,17 the Sun must have been almost opposite in the sky or at a ~ 13-14 h, and this implies the time of year—about a month past the Autumnal equinox, a suitable enough time for harvesting, one might think. Then when the Sun approached the Pleiades so closely that they were no longer visible, and they disappeared before the end of evening twilight ("heliacal" or "acronychal setting"), the Sun's RA must have been ~1-2 hours; so the time of year must have been early spring, not an unsuitable time for planting. If a heliacal rising is intended, then the Sun must be least 10-20 minutes further east than the Pleiades, and so at a ~ 2h; this places the time of year a month after vernal equinox, in late April or early May. However, a contrary reading of the "begin your harvest" passage is possible and turns out to be more likely (see Pannekoek 1961/1989, p. 95; and Evans 1998, pp. 4-5), viz, that the heliacal rising of the Pleiades signifies the season for harvesting a winter wheat crop. Moreover, if "plough when they quit the skies" implies that the Pleiades set as the Sun rises, the autumn planting of a winter wheat crop would have been implied. It is well known that

17 See §2.4.3 for a full discussion of the terms "heliacal" (referring to a rise/set close to the Sun), "acronychal" (associated with the setting sun), and "cosmic" (connected with the rising Sun).

Figure 2.9. The heliacal setting of the Pleiades in Jerusalem in 132 b.c. would have occurred no later than -April 10, according to the Red Shift planetarium software package (Maris,

London). The simulation sky map of that date shows the Pleiades to be 4° to 5° above and the Sun -9° below the western horizon at -6:40 p.m., Local Time.

winter wheat was grown in the ancient world, even though at some point summer wheat was also (see, e.g., Pareti, Brezzi, and Petech 1965, p. 385). Hesiod instructs his brother, "Plough also in the Spring," and in a later passage, he cautions against waiting until the Sun reaches its "winter turning point," thus resolving the issue for the main planting time.

Another passage from the same work,18 indicates an important late-winter/early-spring activity:

When from the Tropic, or the winter's sun, Thrice twenty days and nights their course have run;

And when Arcturus leaves the main, to rise A star shining bright in the evening skies;

Then prune the vine.

Here, the season and time are delineated, and we can interpret the comment directly. The Sun has now and had then a

18 Translation by T. Cooke, cited in R.H. Allen 1963 ed., p. 95.

right ascension of -18h at winter solstice, and moves ~2h east each month; thus, 60 days after the solstice, a© ~ 22 h. As the Sun sets, Arcturus (currently a = 14h 16m, 5 = +19°2; 2500 years ago, a <= ~12h 18m, 5 <= ~+31°3) rose in the east; in the Mediterranean region, it could well have arisen from the sea. Here, Arcturus's higher declination in the past would have caused it to rise earlier than it does today at a site with the same latitude.

A late-night talk-show host in the 1990s garnered a number of laughs by showing through interviews how few students understood the astronomical cause of the seasons (hopefully they were not astronomy students!). Most thought that the varying distance of the Earth from the Sun was the primary cause. Had they lived in the Southern hemisphere, they could have been forgiven for this incorrect view, because the Earth is closest to the Sun in January, but they still would have been wrong. The varying distance does have an effect on the seasons, but it is a secondary one (it would have a greater effect if the Earth's orbit were more eccen-

Figure 2.10. The off-center circle Hipparchos model for the eccentric solar orbit.

tric than it is). The main cause is that the Sun does not travel along the celestial equator but along the ecliptic. Its declination changes with season and, consequently, so do the mid-day altitude and the length of time spent above the horizon and so does the insolation, as we have shown. The distance of the Sun from the Earth does indeed vary around the year, but at the present time the Earth's passage through perihelion, or nearest point to the Sun, occurs during the Northern Hemisphere winter.

The primary and secondary causes for seasonal effects were understood in antiquity. Ptolemy correctly defines the equinoxes and solstices with respect to the relations between the ecliptic and the celestial equator. He also states (Almagest, Toomer tr., 1984, p. 258) that both Sun and Moon vary in distance, and he proceeds to calculate their parallaxes (shift in position as viewed, for example, by observers at different places on Earth). That the Sun's motion on the ecliptic is not uniform throughout the year was also known, and this was modeled in terms of the varying distance of the Sun from Earth. Hipparchos detected the inequality of the seasons and deduced that the Sun moves slower in some parts of its path than it does in others. Because in keeping with all ancient Greek astronomers he believed that planetary bodies moved on circular paths, he had to devise a way to explain why the rate should be different from season to season. His explanation was that the Earth did not lie at the center of the Sun's orbit. As viewed from the Earth, therefore, the Sun's orbit, although circular, appeared eccentric. Such an orbit was referred to as an eccentre (or sometimes by the adjective form, eccentric). The model is illustrated in Figure 2.10. Hipparchos's observation was correct, and his explanation was a reasonable approximation for his time.

The lengths of the seasons vary slightly from year to year as the Earth's orbit slowly rotates. Meeus (1983b) has tabulated the lengths of the seasons for each millennium year beginning with -3000 (3001 b.c.), when autumn was the shortest season, and notes that winter has been the shortest only since the year 1245. The lengths of the (Northern Hemi-

Table 2.3. Changes in lengths of the seasons over millennia.






Year length8

2001 b.c





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