Today a solar calendar is kept in step with the seasons by a fixed rule of intercalation. But although the Egyptians, who used the heliacal rising of Sirius to determine the annual inundation of the Nile, knew that the tropical year was about 365.25 days in length, they still used a 365-day year without intercalation. This meant that the calendar date of Sirius’ rising became increasingly out of step with the original dates as the years progressed. In consequence, while the agricultural seasons were regulated by the heliacal rising of Sirius, the civil calendar ran its own separate course. It was not until well into Roman times that an intercalary day once every four years was instituted to retain coincidence. Complex cycles The planets (initially known as wandering stars) appear to move among the fixed stars – at too fast a pace to be really useful in navigation. Also, they don’t follow consistent orbits, so they aren’t reliable for finding direction. However, they can be helpful in holding a direction because we know they rise broadly in the east and set broadly in the west and are easy to recognise. Venus is particularly bright and recognisable. Observation of the Sun is done at sunrise and sunset. When the Sun is low on the horizon, its path is narrow and obvious, but as it rises, it gets wider and wider. When it’s too high, you can’t tell where it has risen from and have to use other clues for navigation, such as the shape and direction of the waves. Phases of the Moon 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. 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

Venus – Kōpū – also known as Meremere-tū-ahiahi (evening star) and Tawera-i-te-atatū (morning star) 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.From March to September, the Sun’s path appears to be north of the celestial equator. From September to March, it appears to be south of the celestial equator. The Sun crosses the celestial equator at spring and autumn. The Sun’s rising and setting points change through the year 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 tropical year and the synodic month are incommensurable, 12 synodic months amounting to 354.36706 days, almost 11 days shorter than the tropical year. Moreover, neither is composed of a complete number of days, so that to compile any calendar that keeps in step with the Moon’s phases or with the seasons it is necessary to insert days at appropriate intervals; such additions are known as intercalations.

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 northern hemisphere continues to tilt more and more towards the Sun, until the longest summer days in June. Meanwhile, the northern hemisphere is tilted away from the Sun. The light and heat from the Sun is less direct, and it is spread over a wider area so it brings less warmth. The tilt means that nights are longer, days are shorter. This is winter in the northern hemisphere.

In Scotland we experience winter at the beginning of the year. Six months later the Earth hastravelled halfway around its orbit. The southern hemisphere is now tilted away from the Sun so it is winter.At the same time it is summer in the northern hemisphere because it is now tilted more towards the Sun. 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 most famous of these is Stonehenge in Wiltshire, Eng., where the original structure appears to have been built about 2000 bce and additions made at intervals several centuries later. It is composed of a series of holes, stones, and archways arranged mostly in circles, the outermost ring of holes having 56 marked positions, the inner ones 30 and 29, respectively. In addition, there is a large stone—the heel stone—set to the northeast, as well as some smaller stone markers. Observations were made by lining up holes or stones with the heel stone or one of the other markers and watching for the appearance of the Sun or Moon against that point on the horizon that lay in the same straight line. The extreme north and south positions on the horizon of the Sun—the summer and winter solstices—were particularly noted, while the inner circles, with their 29 and 30 marked positions, allowed “hollow” and “full” (29- or 30-day) lunar months to be counted off. More than 600 contemporaneous structures of an analogous but simpler kind have been discovered in Britain, in Brittany, and elsewhere in Europe and the Americas. It appears, then, that astronomical observation for calendrical purposes was a widespread practice in some temperate countries three to four millennia ago.