Eclipse.
Ecliptic. The mean apparent annual path of the Sun in the Earth's sky, so called because it is where eclipses occur. Each day the Sun appears to move approximately 0.986° (=360°/365.2425) eastwards along the ecliptic relative to the stars. Because of the complexity of the motion of the Earth-Moon system, the centre of the Sun is sometimes a little above, sometimes a little below the true ecliptic.
Ecliptic Coordinate System.
Egyptian Calendar. The main calendar used in ancient Egypt was a solar calendar and paid no attention to the phases of the Moon. Given the struggles that other ancient societies experienced in trying to reconcile the apparent movements of the Sun and the Moon, the simple Egyptian calendar has been called "the only intelligent calendar which ever existed in human history" (Neugebauer 1957: 81). In fact, our modern Gregorian calendar (implemented in 1582 CE), by way of the Julian calendar (implemented wrongly in 45 BCE and correctly in 8 CE), is a derivative of it.
In origin, the Egyptian Calendar consisted of three seasons of four months each. In the earliest phase, probably before c. 3000 BCE, each month consisted of 30 days, to give a total of 360 days for the year. But in the early Old Kingdom, probably by about 2700 BCE when it was realised that the existing calandar was too short, five epagomenal days were added to bring the total to 365 days. The months did not have names and were divided into three decans of ten days each, known later as first, middle and last. The seasons were called Akhet (Flood), Peret (Emergence or Winter) and Shemu (Low Water or Summer). By the New Kingdom period, dates could be expressed as, for example, II Akhet 15, meaning the fifteenth day in second month of Akhet.
The whole Egyptian year was structured around the annual flooding of the Nile. From earliest times, the Egyptians realised that the beginning of the flooding coincided approximately with the heliacal rising of the Sirius, the brightest star in the night sky and which they called Sothis. This event, a little after the middle of July each year, was deemed to be the start of the ancient Egyptian year. Because Sirius is so bright (magnitude –1.45) it can in theory be seen (with extincted magnitude of 6.00) when it is just 1° above the horizon, providing that the Sun is sufficiently far below the latter (typically, at least 10°). But in practice we also need to take into account the fact that Sirius is only about 50° from the Sun in azimuth, meaning that due to skyglow the altitude typically needs to be at least 1.5° (with extincted magnitude of 4.8) above the horizon for the star be visible. In the early third millennium BCE at Memphis this state of affairs existed on 19th July.
However, since the Egyptian year throughout the Old, Middle and New Kingdoms consisted of only 365 days (and was not modified successfully until the Roman period), and the actual year is closer to 365.25 days, the heliacal rising of Sirius appeared to rise one day later every four years. In effect the Egyptian year slipped by one day every four years, making it an example of a wandering year. Thus, if the start of the original calendar was fixed at I Akhet 1 with the rising of Sirius, four years later Sirius would rise on I Akhet 2, and four years later it would be on I Akhet 3 and so on. Eventually, the rising would return to the original date after a period of 1460 years, an event known as an apocatastasis 'restoration'. The C3rd CE Roman writer Censorinus reports (On the Day of Birth 21.33) that an apocatastasis occurred on 21st July 139 CE. Therefore we can work back from this to the equivalent years 1322 BCE and 2782 BCE when the rising of Sirius would also be on I Akhet 1, the latter being the most plausible start date for the calendar during the second dynasty and on the eve of the Old Kingdom period.
The table below shows the dates of the heliacal risings of Sirius (with altitude and magnitude) at Memphis (latitude +29°50') tabulated every 365 years since the presumed inception of the calendar. This is reconstructed from Censorinus' report of the apocatastasis occurring in 139 CE on 21st July. The altitude of Sun has been fixed at –10° whilst the altitude and extincted magnitude of Sirius has been limited to the range 1°38' to 2°16'. A typical value for atmospheric refraction (39' at 2° apparent altitude) has been incorporated.
| Year | Egyptian Date | Julian Date | Sirius Alt / Mag |
|---|---|---|---|
| 2782 BCE | I Akhet 1 | 19th July | 1°38' / 4.68 |
| 2417 BCE | IV Akhet 2 | 19th July | 2°05' / 3.89 |
| 2052 BCE | III Peret 3 | 19th July | 1°45' / 4.39 |
| 1687 BCE | II Shemu 4 | 20th July | 2°13' / 3.68 |
| 1322 BCE | I Akhet 1 | 20th July | 1°50' / 4.24 |
| 957 BCE | IV Akhet 2 | 20th July | 2°16' / 3.61 |
| 592 BCE | III Peret 3 | 20th July | 1°49' / 4.28 |
| 227 BCE | II Shemu 4 | 21st July | 2°11' / 3.74 |
| 139 CE | I Akhet 1 | 21st July | 1°39' / 4.57 |
It can be seen that, whilst it cycles through the whole Egyptian calendar twice, the date of the heliacal rising of Sirius (owing to precession) drifts forward in the Julian calendar only by a couple of days in nearly three millennia. During the New Kingdom each month acquired an individual name based on the festival that was to be held at the start of the next month. Later, in the Hellenistic period these month names were rendered into Greek and were subsequently used by Ptolemy for his dating system.
An attempt was made in 238 BCE by king Ptolemy III Euergetes (not Ptolemy the later astronomer) to correct the discrepancy arising from the 365 day year by inserting a sixth epagomenal day every four years. Possibly this was at the of suggestion of Eratosthenes, since it had been known since the time of Kallipos in the previous century that 365¼ days was a good approximation for the length of the year, but the scheme was never implemented. Probably it was rejected by the Egyptian priesthood with whom Ptolemy III was in dialogue at the time. However, under Roman rule, and in line with the Julian calendar reforms, the emperor Augustus imposed the sixth epagomenal day in 22 BCE.
In the Almagest, Ptolemy derived his epoch from the reign of the Babylonian king Nabonassar (747 – 734 BCE) and set the start of it on Thoth 1 which was equated to 26th February 747 BCE. After four years Thoth 1 would have fallen on 25th February 743 BCE. After 725 years of accumulated discrepancies, this had slipped in 22 BCE by 181.25 days, and Thoth 1 fell on 29th August. However, for the sake of consistency, Ptolemy did not incorporate the Julian reform into his astronomical dating scheme, and so by the time of his own observations (c. 140 CE) the calendar had slipped by a total of 221 days since the era of Nabonassar. (Of course, as a Roman citizen in Egypt, Ptolemy would have used the actual Julian calendar for non-astronomical, everyday purposes). Therefore, the Egyptian calendar as used by Ptolemy can be given below (the double days are due to the fact that the Egyptian day starts at midday whereas the day in the Julian calendar starts at midnight):
| Egyptological | Season / Month | Julian Date |
|---|---|---|
| I | Akhet / Thoth | 19/20th July – 18/19th August |
| II | Akhet / Phaophi | 18/19th August – 17/18th September |
| III | Akhet / Athyr | 17/18th September – 17/18th October |
| IV | Akhet / Choiak | 17/18th October – 16/17th November |
| V | Peret / Tybi | 16/17th November – 16/17th December |
| VI | Peret / Mechir | 16/17th December – 15/16th January |
| VII | Peret / Phamenoth | 15/16th January – 14/15th February |
| VIII | Peret / Pharmouthi | 14/15th February – 16/17th March |
| IX | Shemu / Pachon | 16/17th March – 15/16th April |
| X | Shemu / Payni | 15/16th April – 15/16th May |
| XI | Shemu / Epiphi | 15/16th May – 14/15th June |
| XII | Shemu / Mesore | 14/15th June – 14/15th July |
| XIII | 5 or 6 epagomenal days | 14/15th July – 19/20th July |
It is also worth noting that by this time (c. 138 CE) the heliacal rising of Sirius at Memphis was on 21st July, a shift of only two days since the origination of the Egyptian calendar.
Equation of Time.
Equatorial Coordinate System.
Equinoctial Hour.
Equinox.
Exeligmos.
