A brief introduction to concepts found in astronomy. It can be used as a reference, or read as a whole. To aid in the understanding of Sørnes' clocks, the Norwegian names are added in paranthesis when applicable.


Calendars are about organizing the days. Traditionally, the Moon has been used as a calendar as it is reliable and easy to use. The word 'month' stems from moon and its orbit time around the Earth. Another period of time that are of interest for us humans is the year and the seasons, i e the Earth's orbit time around the Sun.

As we will see, the problem with constructing a calendar is that neither of these two periods contains a full number of days.

Solar calendar

This type of calendar is based on the seasonal cycle, that is, the mean time it takes the Sun to return to the same position in the cycle of seasons. Common seasonal markers used for measuring the length of the year are vernal equinox to vernal equinox. This period of time is called a tropical year, and is very close to the Earth's orbit time around the Sun, called a solar year (the tropical year is about 20 minutes shorter than the solar year, see further section precession of the equinoxes).

While the Earth rotates around the Sun and gives us the seasons, it also rotates around its axis, which gives us the days and nights. It would have been nice if the Earth performed an even number of rotations around its axis during the year, then the year would consist of a whole number of days. But the average tropical year has 365.2422 days.

To make each year contain a full number of days, we can take advantage of that 0.24 day adds upp to (nearly) a whole day in four years. This is what the Julian Calendar does, it has 365 days per year, except every 4th year which has 366 days and is called a leap year.

The solar calendar is divided in twelve months that varies between 28 and 31 days. The months in the solar calender has no correlation with the position of the Moon.

Lunar calendar

Another way of keeping track of days is to measure the time between two new moons, the so-called synodic month. The appearance of the Moon depends on its position with respect to an imaginary line between the Sun and the Earth. When the Moon has completed a full revolution around the Earth, which takes 27.32158 days, the Earth has also moved in its orbit around the Sun. To reach the same position relative the imaginary line, the Moon needs to move a little further.

Photo of the synodic month

The average of this longer period is the synodic month (also called a lunation), which has 29.53059 days. Months in lunar calendars consists of 29 or 30 days to maintain this average. The most common example of a lunar calender is the Islamic Calendar, which defines the calendar year as 12 lunations, equal to 354.36 days. As this is about 11 days shorter than the tropical year, seasonal markers such as vernal equinox will occur about 11 days later each year.

Another example of when a lunar calender is used, is the calculation of the date of the Easter.

Lunisolar calendar

Like the lunar calendar, this calendar is also based on the synodic month, but in order to stay in sync with both the Sun and the Moon, the calendar year varies between 12 and 13 lunations. By inserting an extra month, called an embolismic month, every two or three years, the average length of the year matches the seasonal cycle.

Examples of lunisolar calendars are the Hebrew Calendar and the Buddhist Calendar.

Julian Calendar

The Julian Calendar was introduced by Julius Caesar in 46 BC, and used in most of Europe until 1582, when it was superseded by the Gregorian Calender. It has a regular year of 365 days and a leap year in February every four years. The Julian year is, therefore, 365.25 days long. But as seen above, the average length of the tropical year is 365.24 days, a difference of about 11 minutes. This means that the calendar will gain one day in 128 years.

Gregorian calendar

The drift addressed in the Julian Calendar was greatly reduced in the Gregorian reform 1582 by modifying the regular cycle of leap years:

Every year that is divisible by four is a leap year, except for years that are divisible by 100, unless also divisible by 400. For example, the year 1900 is not a leap year; the year 2000 is a leap year.

In C code, this is calculated as follows:

if (year mod 400 == 0)
  leap_year = true;
else if (year mod 100 == 0)
  leap_year = false;
else if (year mod 4 == 0)
  leap_year = true;
  leap_year = false;

This modification improves the accuracy to an error of about one day in 3,300 years with respect to the mean tropical year. However, because of the the precession of the equinoxes, the error with respect to vernal equinox is 1 day in 7,700 years.

The Metonic cycle (Månesykel)

The greek astronomer Meton of Athens discovered in the 5th century BC, that a period of 19 years is almost exactly equal to 235 synodic months. The difference is only a few hours. This means that every 19 years, the Moon will have virtually the same position and phase.

Knowledge of the Metonic cycle is useful when constructing a lunisolar calendar (which needs to have an extra month added some years) as it allows for making a scheme that repeats every 19 year. The Hebrew Calendar follows a scheme where the years 3, 6, 8, 11, 14, 17 and 19 are the long, 13 month years.

Solar cycle (Solsykel)

The solar cycle is a 28-year cycle that occurs in the Julian calendar. After this period of time, the calendar can be re-used. As the Julian calendar can begin on any day of the week, and as it has leap years every 4th year, it is possible to create 14 different calendar configurations. It will however take 28 years before the cycle repeats, as 4 and 7 has a smallest common factor of 28. This means that if, for example February 29, is on a Friday, it will take 28 years before the same date is on a Friday again.

To see all 28 years of the solar cycle as calendars, check this out.

The Solar Number of a year identifies the position of the year within the solar cycle and is calculated accordingly:

Solar Number = (year + 8) mod 28 + 1

The Gregorian Calendar has a solar cycle of 400 years, but can use the solar cycle of the Julian Calendar if skipping 16 years of the solar cycle between February 28 and March 1.

The name comes from Sunday, the traditional first day of the week.

The Indiction

The Indiction specifies the position of the year in a 15 year taxation cycle. The system was introduced by the Roman emperor Constantine the Great in 312, and used until 1806.

Indiction = (year + 2) mod 15 + 1

The Indiction has no astronomical significance, but it is part of forming the Julian Period, used by astronomers to assign a unique number to every day, which is probably the reason why Rasmus Sørnes implemented a dial for it in his third and fourth clock.

Julian Period (and Julian day number)

Under construction.

The seasons

Illustration of the axis tilt The Earth's rotational axis through the poles is tilted 23.4° with respect to the orbital plane around the Sun. This, in combination with the yearly orbit, is what gives us the seasons.

When the northern pole is tilted away from the Sun, the northern hemisphere receives less direct sunlight than average and has its winter. At the same time, the southern hemisphere receives more direct sunlight than average, and has its summer. Six months later, the seasons are the opposite.

The axis tilt is also the reason why the areas above the Arctic Circle and below the Antarctic Circle experiences midnight sun in the summer and polar night in the winter.

Illustration of the elliptic orbit

Depending on the latitude, the number of seasons varies. Closer to the poles, spring and autumn is noticable in between summer and winter, while the seasons around the equator primarily consists of rainy season and dry season.

Also, the distance between the Earth and the Sun varies throughout the year as the orbit is elliptic. Note that when it is summer on the northern hemisphere, the distance to the Sun is at its maximum.

The ecliptic

Illustration of the ecliptic As we see above, the rotational axis of the Earth is tilted 23.4° with respect to the orbital plane. If we for a while pretends that the Sun rotates around the Earth, then its apparent motion against the background stars throughout the course of a year will be along a path that has this angle against the equator.

This apparent path is called the ecliptic and the angle is knows as the obliquity of the ecliptic. The crossings between the ecliptic and the equator are are known as the equinoxes. The crossing from south to north is called the vernal equinox, and the crossing from north to south is called autumnal equinox.

As we will see in the precession of the equinoxes, the locations of the crossing are not fixed, but slowly moves clockwise along the equator with a period of about 26,000 years (0.014° per year).

The apparent path of the Sun reaches its highest and lowest latitude at the summer and winter solstice.

If you draw a circle, parallel to the equator, through this highest latitude, you will get the Tropic of Cancer. This is the most northerly position at which the Sun may appear directly overhead. The same circle through the lowest latitude is called the Tropic of Capricorn.

The zodiac

The word is derived from latin and means "circle of animals". It is an imaginary belt around the solar system, 16° wide and centered upon the ecliptic. It has twelve divisions, each roughly containing a major stellar constellation (sign). With the exception of Libra (the Scales), all twelve signs of the zodiac are animals or mythological creatures.

Over the course of the year, the Sun seems to move over the backdrop of the zodiac. The traditional zodiac originates from Babylonian astronomers in the 7th century BC. They assigned a sign to each month, starting with March (the month of the vernal equinox), which is associated with Aries (the Ram).

Because of the precession of the equinoxes, the Sun is today located over Pisces (the Fish) during vernal equinox, but the traditional assignments are still being used.

Sidereal time

Illustration of sidereal time If you leave a telescope pointing to a certain star, and return the next evening at the same time, you will find that the star is not found in the exact same location. This is illustrated by the picture to the right [1], and explained below. For this reason, astronomers uses a time-keeping system called sidereal time.

In our daily life, the time measurement we use is based on the apparent motion of the Sun. The average time it takes for the Sun to return to its highest point is 24 hours. The earth makes a rotation around its axis in a sidereal day, and during that time it moves a short distance along its orbit around the Sun.

This means that the Earth needs to rotate a bit more before the Sun again reaches its highest point. This rotation takes 3:56 minutes and hence a sidereal day is this much shorter than a solar day.

The number of sidereal days in a year is one more than the number of solar days.

Precession of the equinoxes

Illustration of axial precession As you know, Earth rotates around its axis. This axis, in turn, rotates around a second axis, orthogonal to the Earth's orbit [2]. It takes 25,772 years to perform a complete rotation (a Platonic year). One effect of this is that the stars assigned the roles of the polar stars needs to be updated in between.

Another consequence is similar to what is described in section sidereal time; the sidereal year is 20 minutes shorter than the tropical year (which measures the cycle of seasons, e g solstice to solstice).

This causes the apparent position of the Sun relative the firmament at some seasonally fixed time, e g the vernal equinox, to slowly change. In 25,772 years it regresses a full 360° through all twelve constellations of the zodiac.

Combining precession and sidereal time yields that the true sidereal day, called a stellar day, is 8.4 ms shorter than the sidereal day.

Source reference

  1. Illustration by Francisco Javier Blanco González, May 29, 2009. Licensed under Attribution-ShareAlike 3.0
  2. Illustration by NASA.
  4. Illustration from Wikipedia. Wikimedia Commons
  5. Illustration from Wikipedia. Wikimedia Commons
  6. Illustration from Wikipedia. Wikimedia Commons
  7. Illustration from Wikipedia. Wikimedia Commons