The fact that neither months nor years occupied a whole number of days was recognized quite early in all the great civilizations. Some observers also realized that the difference between calendar dates and the celestial phenomena due to occur on them would first increase and then diminish until the two were once more in coincidence. The succession of differences and coincidences would be cyclic, recurring time and again as the years passed. An early recognition of this phenomenon was the Egyptian Sothic cycle, based on the star Sirius (called Sothis by the ancient Egyptians). The error with respect to the 365-day year and the heliacal risings of Sirius amounted to one day every four tropical years, or one whole Egyptian calendar year every 1,460 tropical years (4 × 365), which was equivalent to 1,461 Egyptian calendar years. After this period the heliacal rising and setting of Sothis would again coincide with the calendar dates ( see below The Egyptian calendar).

The Earth spins three hundred and sixty five times in one year. That’s why we have three hundred and sixty five days in a year.After summer it starts tilting away from the Sun again. The days get shorter and colder as we move into Autumn. The top half of the Earth we call the northern hemisphere, and the bottom half we call the southern hemisphere. The year is the period taken by the Earth to complete an orbit around the Sun and, again, there are a number of ways in which this can be measured. But for calculating a calendar that is to remain in step with the seasons, it is most convenient to use the tropical year, since this refers directly to the Sun’s apparent annual motion. The tropical year is defined as the interval between successive passages of the Sun through the vernal equinox (i.e., when it crosses the celestial equator late in March) and amounts to 365.242199 mean solar days. Determining the Moon’s rising and setting points along with the rising and setting points of the fixed stars allows the Moon to be used to give direction during the night. The line separating light and dark in the Moon points approximately north and south since the Moon is positioned east or west of the Sun as it arcs through the night sky. The planets

Hipparchus, who flourished in Rhodes about 150 bce and was probably the greatest observational astronomer of antiquity, discovered from his own observations and those of others made over the previous 150 years that the equinoxes, where the ecliptic (the Sun’s apparent path) crosses the celestial equator (the celestial equivalent of the terrestrial Equator), were not fixed in space but moved slowly in a westerly direction. The movement is small, amounting to no more than 2° in 150 years, and it is known now as the precession of the equinoxes. Calendrically, it was an important discovery because the tropical year is measured with reference to the equinoxes, and precession reduced the value accepted by Callippus. Hipparchus calculated the tropical year to have a length of 365.242 days, which was very close to the present calculation of 365.242199 days; he also computed the precise length of a lunation, using a “great year” of four Callippic cycles. He arrived at the value of 29.53058 days for a lunation, which, again, is comparable with the present-day figure, 29.53059 days. The month is determined by the Moon’s passage around the Earth, and, as in the case of the day, there are several ways in which it can be defined. In essence, these are of two kinds: first, the period taken by the Moon to complete an orbit of the Earth and, second, the time taken by the Moon to complete a cycle of phases. Among primitive societies, the month was determined from the phases; this interval, the synodic month, is now known to be 29.53059 days. The synodic month grew to be the basis of the calendar month. Another early and important cycle was the saros, essentially an eclipse cycle. There has been some confusion over its precise nature because the name is derived from the Babylonian word shār or shāru, which could mean either “universe” or the number 3,600 (i.e., 60 × 60). In the latter sense it was used by Berosus ( c. 290 bce) and a few later authors to refer to a period of 3,600 years. What is now known as the saros and appears as such in astronomical textbooks (still usually credited to the Babylonians) is a period of 18 years 11 1/ 3 days (or with one day more or less, depending on how many leap years are involved), after which a series of eclipses is repeated.

The Sun’s rising and setting points change through the year

Venus – Kōpū – also known as Meremere-tū-ahiahi (evening star) and Tawera-i-te-atatū (morning star) The Metonic cycle was improved by both Callippus and Hipparchus. Callippus of Cyzicus ( c. 370–300 bce) was perhaps the foremost astronomer of his day. He formed what has been called the Callippic period, essentially a cycle of four Metonic periods. It was more accurate than the original Metonic cycle and made use of the fact that 365.25 days is a more precise value for the tropical year than 365 days. The Callippic period consisted of 4 × 235, or 940 lunar months, but its distribution of hollow and full months was different from Meton’s. Instead of having totals of 440 hollow and 500 full months, Callippus adopted 441 hollow and 499 full, thus reducing the length of four Metonic cycles by one day. The total days involved therefore became (441 × 29) + (499 × 30), or 27,759, and 27,759 ÷ (19 × 4) gives 365.25 days exactly. Thus the Callippic cycle fitted 940 lunar months precisely to 76 tropical years of 365.25 days.

The calendar dating of historical events and the determination of how many days have elapsed since some astronomical or other occurrence are difficult for a number of reasons. Leap years have to be inserted, but, not always regularly, months have changed their lengths and new ones have been added from time to time and years have commenced on varying dates and their lengths have been computed in various ways. Since historical dating must take all these factors into account, it occurred to the 16th-century French classicist and literary scholar Joseph Justus Scaliger (1540–1609) that a consecutive numbering system could be of inestimable help. This he thought should be arranged as a cyclic period of great length, and he worked out the system that is known as the Julian period. He published his proposals in Paris in 1583 under the title Opus de emendatione temporum.The northern hemisphere continues to tilt more and more towards the Sun, until the longest summer days in June. The Earth’s tilt means we experience four seasons as we orbit the Sun. So, starting with winter in the northern hemisphere, the Earth moves round and the days get longer and warmer until it becomes spring. Up here on the International Space Station I don’t get affected by the seasons but on Earth the seasons are always changing: Spring, Summer, Autumn and Winter. The Julian period is a cycle of 7,980 years. It is based on the Metonic cycle of 19 years, a “solar cycle” of 28 years, and the Indiction cycle of 15 years. The so-called solar cycle was a period after which the days of the seven-day week repeated on the same dates. Since one year contains 52 weeks of seven days, plus one day, the days of the week would repeat every seven years were no leap year to intervene. A Julian calendar leap year cycle is four years, therefore the days of the week repeat on the same dates every 4 × 7 = 28 years. The cycle of the Indiction was a fiscal, not astronomical, period. It first appears in tax receipts for Egypt in 303 ce and probably took its origin in a periodic 15-year taxation census that followed Diocletian’s reconquest of Egypt in 297 ce. By multiplying the Metonic, solar, and Indiction cycles together, Scaliger obtained his cycle of 7,980 years (19 × 28 × 15 = 7,980), a period of sufficient length to cover most previous and future historical dates required at any one time. At this point in the orbit, the Earth’s tilt means that the southern hemisphere is facing more towards the Sun. This means that the light and heat from the Sun is more direct and stronger. The days are the longest in the year and the nights, the shortest. This is summer in the southern hemisphere.