9. Worthen has also given us a description of the role of Arcturus:

"Sixty days after the winter solstice corresponds by astronomical definition to February 20. On that date in 1250 B.C. Arcturus rose before sunset, was two and one-half degrees above the horizon at sunset, and seven degrees above the horizon by thirty-tree minutes after sunset, when it could shine through the fading glow of the day.

On the same date in 700 B.C., Arcturus did not rise until after sunset and did not attain a seven-degree elevation above the horizon until one hour and twelve minutes after sunset. By then it was totally dark; the facts of 700 B.C. simply do not seem to fit the circumstances of acronychal rising as defined in the passage of Hesiod ... Curiously enough ... [the] phenomena Hesiod mentions are ... more appropriate to a date of 1250 than to Hesiod's date of 700 B.C. There is a rather technical temporal formula given at Works and Days 564-566:

'When Zeus, after the turn of the (winter) solstice, has completed sixty wintry days, that's when the sign-star Arcturus leaves the cold stream of Ocean and first rises acronychally in splendor'.

The occurrence of the solstices was not determinable by any exact stellar apparition but was to be found roughly by the use of a gnomon. The apparition of Arcturus confirms that the solstice was sixty days past. Its rising is one of the few sure signposts of the year. Arcturus is the fifth brightest star (zero magnitude) visible in the northern latitudes. If it is not obscured by haze or a high horizon, it will become visible within a half-hour after sunset."

Around 1250 B.C. Arcturus rose in the early evening to announce that winter solstice (north of the equator) now was 2 months in the past. South of the equator the star would have been harder to observe because it was summer solstice.

Anyhow, Arcturus could by ancient tradition have been connected with a cardinal point 2 months beyond the solstice. South of the equator observers on Easter Island (had there been any at that early date) could have known where Arcturus was in the summer sky without looking - it was just to close your eyes and turn the time-space map of the sky roof in your mind to the proper position.

Significantly Arcturus was one of the Tahitian star-pillars ('sign stars'). I have tried to guess where it could be in the year when the G text was composed, and the day numbers in my table below are counted from winter solstice (south of the equator) and equal to those of today minus 10 days (due to a guess as to the effects of the precession):

Arcturus is not located in the summer half of the year (185 days from Ana-mua to Ana-muri), but rising about a month earlier. 141 - 108 = 33 must be added to the position of Arcturus to reach Antares, and 60 + 33 = day 93 would be around spring equinox north of the equator in the era of Hesiod.

The precession must have moved Arcuturs to a later position since the days of Hesiod. From 1250 B.C. to 2100 A.D. the change in day number should be an additional 3350 / 72 = ca 45 days, i.e. Arcturus ought at present to rise in the early evening around day number 105 instead of in day number 60.

I have calculated my day number for Arcturus above (108 = 118 - 10) by using its right ascension and then translating hours and minutes in a cycle with 24 hours to days in a cycle of 365 days:

"Right ascension is the celestial equivalent of terrestrial longitude. Both right ascension and longitude measure an angle that increases toward the east as measured from a zero point on an equator. For longitude, the zero point is the Prime Meridian on the geographic equator; for right ascension, the zero point is known as the first point of Aries, which is the place in the sky where the Sun crosses the celestial equator at the March equinox." (Wikipedia)

14h 13m is the current value for Arcturus. 14 * 60 + 13 = 853 and 853 / (24 * 60) = 59.236 % of the cycle, which results in 59.236 % * 365 = day 216. If the cycle should be 360 days, then Arcturus would be at day number 213. These day numbers are counted from autumn equinox (the first point of Aries) south of the equator. Arcturus has a rectascension value which indicates it will be close to Sun ca 7 months after autumn equinox, i.e. ca 1 month after spring equinox.

266 + 216 - 365 = day number 117 (= 87 + 30), which we can compare with my guessed day number 108  (a lower day number because of the precession). The date for my table could be around (117 - 108) * 72 = ca 650 years before today.

The time for observation of Arcturus passing straight above (crossing the meridian) is around 6 hours later than when it can be observed to rise and around 6 hours earlier than when it can be observed to sink in the west. When Hesiod described the rise of Arcturus in the early evening the star had not yet crossed the meridian, this event would come around 6 hours later.

To reach the rectascention day number a quarter (= 6 hours / 24 hours) of the cycle should be added, and increase it from day 60 beyond winter solstice to day 60 + 91 = 151, which happens to be my current day number for Antares south of the equator.

Day 151 for Antares is counted from winter solstice south of the equator, a quarter of the year earlier than equinox. This difference corresponds to the difference between observing a star rising in the east compared to observe it passing straight above.

When Antares was seen rising in the evening it was 60 days after winter solstice north of the equator = 60 days after summer solstice south of the equator. If Sun was going down in the west at the same time as Arcturus was going up in the east it means Arcuturus was at the opposite end of the cycle compared to Sun, Arcturus was 'antipodal' to Sun. The antipodal position of full Moon can be used to locate Sun:

... The astronomers would have known, however, that the equinoctial point was at Aldebaran by observing the full moon falling near the expected date or near a point in the sky exactly opposite Aldebaran (since the full moon is 180º from the sun), that is, near the star Antares ...

To get Arcturus into the same position as Sun we must turn the sky roof half a cycle around, and then Arcturus will rise in the early morning (together with Sun) instead of in the early evening (in the antipodal position). With Sun positioned close to Arcturus it would have been 60 days after summer solstice north of the equator = 60 days after winter solstice south of the equator.

Anyhow, 60 days from the beginning of the front side of G we possibly could find the end of darkest time of the year (in which case the front side maybe could begin 30 after winter solstice):