A calendar

The question of creating a calendar relates to the longer-term units of time and the search for their relationships and relations. The basic factors for creating the calendar are the mean solar day (24 h), the synodic month, describing the changes of the shape of the lunar disk from the Earth-bound observer’s point of view. Its length is 29.530 588 853 days, the synodic month is described in more detail in the previous chapter. The third basic unit of time for calendar needs is the tropical year defined as the time between two passages of the Sun through the vernal point (the vernal point is the intersection of the ecliptic, that is, the imaginary trajectory of the Sun in the celestial sphere, with the celestial equator, in which the Sun is at the beginning of spring). It equals 365.242 192 129 days (365 d 5 h 48 min 45 s). The seasons change in the temperate geographical zones in a period.

The three basic time units mentioned above correspond to the most important astronomical periods affecting people‘s lives. One day is the time of Earth‘s revolution in relation to the Sun (to be precise we should use a true solar day here instead of a medium solar day but from a practical point of view it would not be very useful as it is described in more detail in chapter 6.3.1), the synodic month is a period of Moon phases (described in detail in section 6.3.2) and the tropical year is a period in which the seasons change in the temperate geographical zones. All specified time periods are the content of the curriculum for children of younger school age.

Making of the calendar

People have been engaged in the issue of calendar creation since antiquity. Because the times mentioned above are not commensurable numbers, any calendar is filled with recalculations that bring a lot of irregularities to the issue of the calendar, and hence the complications of its use by the general public. Moreover, everything is even more complicated due to the long-term changes of the mean solar day, the synodic month and the tropical year, i.e. the basic time scales for the calendar. These long-term changes are related to the astronomical character of all these quantities, and although the long-term changes are small, they cannot be neglected in the long term. Moreover, these changes are not regular and thus they are not predictable.

It would seem, for example, that the synodic month with the duration of 29.530 588 853 days can be replaced without much difficulty in the calendar with alternating „large“ and „small“ months with lengths of 30 and 29 days. However, the calendar designed this way would have to be adjusted after less than three years as the difference between the reality and the calendar, for example between the true and calendar new moon, would grow by 1 day in just 33 months. Similarly, for the length of the tropical year of 365.242 192 129 days with the choice of 360 days in a calendar year, the calendar deviates by 5 or 6 days, and its length has to be adjusted. This way it worked in ancient Egypt, for example, where every 360-day year was supplemented by 5 or 6 additional days of holidays and feasts according to the calculations of priests. When choosing a calendar year of 365 days, it will deviate from the real length in 4 years and with the choice of 365.25 (every fourth year is leap with 366 days) in 128 years. In these cases, we keep comparing only one time unit with the length of the day, i.e. the length of the month or year. Given the fact that we are looking for a connection between the three quantities at the same time, the whole situation is much, much more complex. From the above stated, it is therefore clear that the simpler the calendar we choose, the sooner we will need to modify it, so that it does not differ from the real lengths of astronomical periods of the day length, the period of Moon phases, or the period of alternating seasons. Conversely, the more complicated the calendar we choose, the later we will need to modify it to match it with the real astronomical periods.

Types of calendar

As mentioned above, it is difficult to set basic parameters in calendar creation so that the calendar is not only simple and understandable for the wide folk classes that will use it, but also for the conversion of the base time units typical for the calendar stable in the long term with regard to the astronomical basis that these units are based on.

Three basic types of calendars are based on that:

The lunar or monthly calendar derives from the idea that the most important of the long-term time units is the synodic month, representing the period of alternating phases of the Moon. The significance of the phases of the Moon for the longer-term perception of time was typical of ancient civilizations, especially for people living around the equator where the Moon’s cycle was more important than the solar cycle lasting one year, which is not as significant in these areas because the seasons do not change here. All months in the lunar calendar begin with the same phase of the Moon, usually with New Moon. In the lunar calendar the months alternate after 29 and 30 days; the length of the year is then 354 days and is not bound to the period of alternating seasons. Because alternating months after 29 and 30 days deviates from the real length of the month, a leap month is entered in the calendar after about 3 years (irregularly) and the year has then 355 days. Currently, the most significant of the lunar calendars is the Islamic calendar which has been counted since the beginning of the journey of the Prophet Mohammed from Mecca to Medina (in the Gregorian calendar it corresponds to the date of July 14, 622). It is called AH (from the Latin Anno Hegirae: „in the year of the Hijra“), now from 3. 10. 2016 to 21. 9. 2017 it is the year 1438 AH.

Solar calendar is based on the notion that the base calendar unit is not a month, but a year, the tropical year, related to the passage of the Sun through the vernal point. The length of the month is irrelevant from the solar calendar’s point of view, so the lengths of the months are not bound to the synodic month but divide the year only into smaller portions. As this calendar is used in our countries, it will be given exclusive attention with the regard to its use in formal and informal education of children of younger school age. It is called AD (from Latin Anno Domini: „The Years of the Lord“), it has been counted since the birth of Christ (precisely from his circumcising, because the birth would correspond to the 25th of December), but the identification of the beginning of the era with the birth of Christ failed to be executed properly, and so today we know, from historical data, that if Christ was a real figure, he was born a few years before the beginning of the calendar. From 1. 1. 2017 to 31. 13. 2017 it is the year 2017 AD.

The lunisolar calendar considers both basic units of time, the synodic month and the tropical year, to be significant and tries to maintain the same phase of the Moon at the beginning of each month, while preserving the length of the year as far as possible. This causes disproportionate complexity and complications because the approximate matches with the length of the tropical year are achieved by the inclusion of leap months (leap months are included seven times in 19 years in a total, which is a kind of „over period“ during which the whole number of months and years is achieved; in the nineteenth-year cycle leap years are always years 3, 6, 8, 11, 14, 17, and 19), and it cannot do without leap days as well. The lunisolar year can thus have 353, 354, 355, 383, 384 or 385 days. Nowadays, the most famous representative of this type of a calendar is the Jewish calendar. This calendar has been counted since the biblical creation of the world (in the Gregorian calendar it would correspond to the date 6. 10. 3761 BC; at 23 h 11 min 20 s), the days start with the set of the solar disk. It is called AM (from the Latin Anno Mundi: „in the year of the world“), now from 2. 10. 2016 to 20. 9. 2017 it is the year 5 777 AM.


As mentioned above, a solar calendar is used in Europe. The initial origins of it can be sought in the Egyptian solar calendar, which was based on the annual floods of the Nile. The Roman commander and politician Gaius Julius Caesar noticed the calendar during his victorious campaign into Egypt, and in comparison to then-used Roman calendar, he rated it as of much higher quality. Therefore, he commissioned Sosigenes of Alexandria,a Greek astronomer, with the preparation of the Roman calendar reform and introduced this reform from 1St January 45 BC (at the time, of course, years were counted differently than today, since the founding of Rome, without the knowledge of the future conversion based on the birth of Christ). The established calendar already had a length of 365 days and included leap years, even though the leap years were introduced somewhat differently from Sosigenes’ suggestion. This calendar is called Julian in honour of Caesar. Likewise, the naming of July in many European countries is remembrance of Caesar (the name of this month, previously called Quintilis-“fifth“, was approved in honour of Caesar by the Roman senate). After the modification of the Julian calendar (especially the correct inclusion of leap years) by Emperor Augustus (his birth name was Gaius Octavius) in the year 8 AD, the Senate named the month of August after the Emperor (the name of this month, previously called Sextilis-“sixth“, was approved in honour of Augustus again by the Senate) and at the same time it was decided that August will be just as “large” month as July i.e. it will have 31 days (the day was already removed from the shortest month, February).

The Julian year has 365.25 days and with the tropical year with the duration of 365.242 192 129 days deviated by one day every 128 years. Therefore, on 24th February 1582 Pope Gregory XIII instituted the reform of the Julian calendar by papal bull Inter gravissimas. The reform was prepared by an Italian astronomer, physician and philosopher Aloysius Lilius (Luigi Lilio) at the pope’s impulse. The adjustment lay in the deletion of 10 days and the adjustment of the rule for leap years. According to the new rule, the years ending in 00 are leap years only if the year designation is divisible by 400. Thus, the year 2000 was leap, while 2 100, 2 200, and 2 300 will not be. The reform, named after the pope, is called Gregorian and has been implemented in different countries gradually, in some countries as late as in the last century. However, this calendar is currently valid in the vast majority of countries that use the solar calendar.

Gregorian calendar

For activities related to the Gregorian calendar based on the length of the tropical year, it is possible to implement, for example, the following three activities for children of younger school age:

Length of the months: according to the knuckles on the hands, months that are „large“ and „small“ can be named, i.e. which months have 31 days and which fewer. As mentioned above, for the fact that July and August follow consecutively after each other and both have 31 days, the Roman senate’s decision from over 2 000 years ago is responsible.

Beginnings and lengths of the seasons: The beginnings of the seasons are determined by the astronomical position of the solar disk in the sky. Spring begins when the solar disk passes through the vernal point. After passing an angle of 90°, the summer begins, after another 90° (when passing through the autumnal point), the autumn begins and after another 90°, the winter begins. Typically, the dates of the seasons’ beginnings are 21st March, 21st June, 23rd September and 21st December. However, in the view of the complexity of the current (Gregorian) calendar, the beginnings of the seasons are not firmly fixed. Since the year 2 000 was a leap year, the beginnings of the seasons in this century are a little sooner, its influence also has the fact whether the given year is leap, the first year after the leap year, the second after the leap year, or the third after the leap year. The most common beginning of spring will be the 20th March in the next few years and similarly the other seasons will start earlier. The exact dates of the seasons can be found on the Internet or, for example, in the Astronomic almanac. In addition to finding these dates, pupils that are more talented can try to calculate the length of each season. They will surprisingly find that the longest is summer (almost 94 days), then spring (93 days), autumn (almost 90 days) and the shortest is winter (89 days). The values for each year may vary by 1 day. The fact that the lengths of the seasons are different is due to the elliptical rotation of the Earth round the Sun. It is true, of course that the seasons in the southern hemisphere are opposite to the northern hemisphere ones.

Simulation of the Earth‘s revolution around the Sun: on the pitch you can model the Earth’s revolution around the Sun (it can also be accompanied by the Moon), either by the movement of one (or two) children, or by the movement of a child with a globe as a model of the Earth. When moving with the globe, it is important to maintain the direction of the Earth’s axis in space; the Earth’s axis does not bend during the Earth‘s revolution!