Shabad Kirtan: Maagh Majan Sangh Sadhuaa (Barah Maha Manjh) – by Bhai Harjinder Singh Ji. Thank you Ji for the soulful Kirtan. (Source: Shabad Gurbani on You Tube) 

By Harnaak Singh

We will now continue with the study of calendars.  We will be discussing planetary concepts a little at a time as necessary to explain the discussion.  These concepts are important in understanding the calendar systems.  Note that the orbits are elliptical but for our discussion we will consider them to be a circle unless it is necessary to explain some concept or observation.  

Note that we will continue with the figure number from Part 1.

Before we continue with the calendar, it is important to understand how the lengths of months and years are determined.  

There are three main methods of determining the length of the month and two for the year.  These are the 

• sidereal, synodic and tropical for the moon and 
• sidereal and tropical for the earth.

We will discuss this below.

Types of Lunar months

There are three common methods of defining lunar months.  The sidereal, the synodic and the tropical lunar months.

Sidereal lunar month

This is the time it takes the moon to return to the same position in its orbit around the earth in relation to the stars (i.e. looking from the stars).  This gives the lunar month to be 27.32 days.  See Figure 6.

Figure 6: Sidereal and Synodic month (picture source Durham University UK)

Synodic lunar month

The synodical month is the average lunar month over one year taking into consideration of the movement of the earth around the sun.  It is the time it takes for the moon to return to the same position in its orbit around the earth in relation to the earth along the sun-earth axis (i.e. looking from the earth to the sun).  Over one year this averages out to a synodic lunar month of 29.53 days.  

Note that this (synodic lunar month) is what we see as the lunar month, because we are looking at the moon from the earth’s surface practically along the sun-earth axis.  

The lunar phases (dark moon massia, full moon puranmasi) are based on the synodical lunar month.

Tropical lunar month

The tropical lunar month is the time it takes for the moon to return to its elliptic longitude of 0 deg which is a little shorter than the sidereal month (which is 27.321661 days).  The tropical lunar month is 27.321582 days.  Note that there is a difference although very small.  This is due to precession (see below).

Precession

We saw that the tropical lunar month is a little shorter than the sidereal lunar month.  The reason for this is that the constellation cylinder itself is rotating backwards at the rate of one cycle i.e. 360 degrees in about 25,800 years (this is about 1 degree every 72 years).  Figure 7 shows this rotation which is called “precession” 

Figure 7: Movement of the constellation cylinder – precession (note the “1 day” at the top of the picture should read “1 cycle i.e. 360 degrees”)

 

It is important to understand precession as we will be referring to this in our discussions.

Types of Years

In the following discussion on types of years two references are considered to aid understanding.  Reference to Figure 7 will help in understanding this.  

• One is the fixed stars with Aries in the constellation as the reference.  This means we look at the earth from reference point Aries.  The sun moves with the constellation.  
• The other is the earth as the reference which means we view the sun/constellation from the earth.

We will discuss this below.

Sidereal year

The sidereal year is the time it takes for the earth to return to the same position in its orbit around the sun with Aries as reference.  This is shown in Figure 8 and explained as follows.  

At the summer or vernal Equinox 0, the earth is at position 0 and the earth-sun axis points towards 0-Aries/Chet.  The sun is directly overhead the earth’s equator.  One sidereal year later the earth returns to position 1A.  The earth-sun axis does not point to Aries/Chet because the Aries constellation has move to 1-Aries/Chet due to “precession”.  However the precession has no impact on the location of the Aries with respect to the earth, because we are looking from the reference stars constellation towards the earth.  So the position is “1A Aries/Chet” (the same as 1-Aries/Chet) but at this point in time the sun will not be directly overhead the earth’s equator.

The mean sidereal year is 365.25636 days.  

The sidereal year does not keep in line with the seasons (see section on seasons below).

Figure 8: Sidereal and Tropical year (note that the precession is actually very small but shown exaggerated so we can see what is happening)

Tropical year

The tropical year is the time it takes for the earth to return to the same position with the earth as reference when seen from the earth.  This can be from summer equinox back to summer equinox.  

See Figure 8 for the position of the earth after 1 tropical year.  At the summer or vernal Equinox 1, the earth is at position 1 and the earth-sun axis points towards 1-Aries/Chet after 1 tropical year.   Equinox 1 occurs earlier since the constellation Aries has moved to position 1-Aries/Chet due to precession.  At this time, i.e. Equinox 1, the sun is directly overhead the earth equator unlike the sidereal case where the sun is not overhead the equator.     

Notice that the tropical year occurs earlier and hence is shorter than the sidereal year because of precession.  The mean tropical year is 365.24219 days.

The tropical year keeps in line with the seasons (see section on seasons below).  This is because the tropical year by definition is in line with the Spring Equinox.

Difference between sidereal and tropical year

The sidereal year is 20 min 24.5 seconds longer then the tropical year.  The reason for this is, as shown above, the rotation of the constellation, “precession”, in the opposite direction to the rotation of the earth around the sun.  This is reflected clearly in Figure 8.

The sidereal year does not keep in line with the seasons while the tropical year keeps in line with the seasons.

Seasons

On earth we experience seasons, spring, summer, autumn and winter.  Generally spring is considered the beginning of the seasonal cycle and this ends with winter.  Spring begins with the summer equinox (northern hemisphere) which is generally 21^st March. 

The tropical solar year is only one that keeps in line with the seasons by ITS DEFINITION. 

Figure 9: Sidereal and Tropical year and Seasons

Figure 9 shows the start of SPRING in the solar year.  It is very important to understand the impact of the precession on the shifting of seasons.

Referring to Figure 9, at the start of Year 0 both Sidereal and the Tropical year experience the start of spring SPRING 0 (at Equinox 0) at the same time. 

At the end of 1 Tropical year, the Earth at position 1 is at the equinox Equinox 1.  At this time the earth experiences the start of spring SPRING 1 since the sun is overhead the equator.  This is also the start of spring SPRING 1A for the sidereal year which has not completed 1 sidereal year as yet.

At the completion of 1 sidereal year the earth is at position 1A, but spring SPRING 1A has already started earlier at earth position 1.  Therefore for the sidereal year we see a shifting of the start of spring and therefore the seasons experience a shift for the sidereal year and this shift becomes greater as the years go by.

CALENDARS

Even though we have already discussed the Georgian and Julian calendar, we shall backtrack a little to discuss some basics about calendars.

There are three distinct type of calendars,

• Solar Calendar
• Lunar Calendar
• Lunisolar Calendar.

Solar calendar

Solar calendars approximate earth’s complete revolution around the sun using days.  Because the days in a complete revolution is not an integer (e.g. 365 is integer and 365.24219 is not an integer), days are added to a particular year, termed leap year, to get an average number of days as close as possible to the actual.  A solar calendar is divided into months and these months do not follow the moon phases.

The solar months are marked by the entrance of the sun into the zodiac signs.  There are 12 zodiac signs each 30 deg apart and accordingly there are 12 solar months.  This applies both for the sidereal and tropical year.

The solar calendar may or may not keep in line with the seasons depending on the type.  The 

• sidereal solar calendar does not keep in line with seasons and 
• the tropical solar calendar keeps in line with the seasons

as we have seen above under the discussion on types of years.

Lunar calendar

Lunar calendars consist of lunar months.  There are basically two types of lunar months with each month covering the

• period between new moons or 
• period between full moons.

This period is in days and uses the synodic lunar month.  The average length of a lunar month is 29.5 days.  There are 12 lunar months which gives 354 days (29.5 x 12).  This is 11 days shorter than the 365 day year.

Hence the lunar calendar does 

• not keep in line with the year AND does
• not keep in line with the seasons.

Lunisolar calendar

Lunisolar calendars use solar year but use lunar months.  Due to the difference in the days in a lunar year and lunar months, occasionally a lunar month is added every few years to help keep the calendar aligned with the solar year.  This additional month is known as the leap or intercalary month.

Generally the lunisolar calendar inherently does not keep in line with the seasons unless adjustments are made to the dates (see metonic cycle below).

Metonic cycle of the lunisolar calendar

The Metonic cycle is a mathematical rule to determine when a leap month should be added to keep the lunisolar calendar in pace with the tropical or sidereal year.

Calculations show that the lunisolar calendar catches up with 19 tropical or 19 sidereal years by adding 7 leap months every 19 lunar years interval.

Therefore the metonic cycle provides a way of determining occurrence of leap months in the lunar year to catch up with the sidereal or tropical year.  

However not all lunisolar calendars follow this cycle. 

The Indian lunisolar calendars rely on the positions of the Sun and the Moon to determine the occurrence of leap months. 

Please do not hesitate to ask for clarification if you would like to understand further any of the concepts presented above.

We will stop here and continue next with discussion on Indian calendars in the next post.

Thank you for reading.  Hope you enjoyed the discussion.  

ਵਾਹਿਗੁਰੂ ਜੀ ਕਾ ਖਾਲਸਾ ਵਾਹਿਗੁਰੂ ਜੀ ਕੀ ਫਤਹਿ

To be continued