Synodic month
The month that is used to determine festivals etc (including most Indian festivals) is called the synodic month or the month of phases of the moon. A synod is a gathering of priests or religious groups where the important day would be declared by e.g. sighting of the moon. However, this is a misnomer in India as Indians knew how to calculate the phases of the moon. First thing to understand is that the sun shines by its own light, whereas the moon and planets shine by reflected light. And half of the moon and each planet (except sun) is always dark.
Therefore, it is a new moon (or perhaps no moon) when the sun and moon are exactly on the same side of the earth and from earth we only see the side of the moon in shadow.
The full moon, when the sun and moon are on the opposite side of the earth and we see the bright side of the moon.
Some of the children asked how we are able to see the moon when earth is in between and he explained that there is a difference in the planes of the revolution of the moon around the earth and the earth around the moon (around 5’) and occasionally the two planes meet which causes eclipses.
Tithi
Tithi is simple and elegant system which Indians worked out to moon’s phases. A tithi is the time in which the moon moves ahead of the sun by 12°. More precisely, it is the time in which the celestial longitude of the moon increases by 12° over the longitude of the sun.
[Inter day the moon moves around 13° and sun around 1° in one day, so the relative movement of 12° as a measure of ‘day’ is sensible.]
A full rotation of 360° with a relative speed of 12° would give us 30 titis for the sun and the moon come back the same relative position separated by 0° or 360°. That is, 30 tithi’s is the time from full moon(purnima) to full moon or from new moon to new moon. This period of 30 tithi’s (not days) is called a synodic month. Tithis is not a day!
The tithi’s are divided into two groups of 15 tithi’s:
- शुक्ल पक्ष (shukl paksh), waxing phase of the moon.
- कृष्ण पक्ष (krshn paksh), waning phase of the moon.
[To remember this we can think of Krishna – dark sot he krish paksh makes the moon from bright to dark.]
In each phase, the tithi’s are counted in sanskrit number 1 to 14 and then the amavasya or purnima for the 15th tithi. This simple scientific system can be used because there are always 30 tithi’s in a month.
Names of tithi’s,
In terms of days, a synodic month is 29.53 days. Why is the synodic longer than the sidereal month of 27.3 days?
In 27.3 days or 1 sidereal month, the moon has orbited the earth once. But in this time the sun has moved by about 27° relative to earth (or the earth has moved by about 27° round the sun). So the moon must move by another 27° round the earth. Since the moon moves by about 13.33° a day round the earth, this would take it a little over 2 days, plus a fraction for the 2° earth/sun movement in the extra 2 days in between. That is why the synodic month is about 2.2 days longer than the sidereal month.
How to calculate tithi?
Stated by Aryabhata
Why 720 minutes? As 12° = 12×60’ = 720’
Two Complications
There are complications in this scheme of things. The first is to link the “synodic” month of phases of the moon to the year or solar cycle. Not doing this would make a purely lunar calendar which will slip with respect to the solar calendar. The second is to link the relative motion of the moon and sun to the civil day which is based solely on the rotational motion of the sun.
The story of the colonized mind is that the Indian calendar is a lunar calendar. The Indian calendar is a luni-solar calendar.
There is a simple rule for syncing the lunar cycle with the solar cycle. Whenever there would be no sankranti in a chandramasa, an extra chandramasa is added. This is called adhik (more) masa. This keeps the solar and lunar month in sync. This happens once within 3 years.
In the rare cases when there is more than one sankranti in a chandramasa, it is treated as a kshaya (reduce) masa and dropped. However, in this case in that year there will always be a different adhik masa, so the number of lunar/solar months/sankrantu is at least 12. For example, if the sun transits into both mesa and vrsabha rashi in a chandramas, then it will be called chaitra-vaisakha ksaya-masa. There will be no separate months labeled chaitra and vaisakha.
Likewise to keep tithi synchronized to civil days, there can be added or removed tithi. Thus, a true tithi is always the time for the moon to get ahead of the sun by 12°. However, to decide when to celebrate festivals and map it to a ‘civil tithi’, the tithi prevailing at sunrise is assigned to the civil day.
A tithi or the time in which the moon gets ahead of the sun by 12°, can be longer or shorter than a civil day. It is possible for a tithi to continue across two civil days as well.
Seasons
An important function of the calendar is to tell the seasons, this was very important for India which was for thousands of years and agricultural society.
For example, when is the right time to sow? When is the right time to reap?
In the west there are only two seasons, hot and cold, though the intermediate periods go from summer to winter and from winter to summer. However, rains can occur throughout the year. However, on the Indian calendar every two months there is a different season so there are six seasons.
Vedic names for months
The earliest vedic names for months are from before the vedanga jyotisha. They named month according to season, not nakshatra or lunar phase.
Reference in Taittiriya samhita
Many of us think that the summer and winter are due to the distance of the sun from earth. Actually, the hot and cold seasons are because the axis of rotation of the earth is tilted to the ecliptic or the plane of the observed orbit of the sun (suryavrtta).
When the Northern hemisphere faces the sun it is summer in the north and winter in the south. When it faces away it is winter in the north and summer in the south.
Geocentric vs Tychonic vs Heliocentric vs Barycentric
He explained the various models of the solar system that were thought of and followed to model what was seen in the sky.
Geocentric model
Geo(earth)centric model is what you actually observe, the sun, moon, planets, going round the earth in the sky.
Tychonic model
All other planets go around the sun and the sun with all the planets goes round the earth.
Barycentric model
Moon and earth or sun and earth rotate about a common center of mass because earth is massive compared to the moon, and sun is massive compared to planets. This barycentric often (but not always) lies inside the more massive body.
Rainy season
A season unique in the calendar and not found in the western calendar is the rainy season. It’s not found in the western calendar since there is no specific rainy season in Europe. But in India the major season is the rainy season because the entire economy and reproductive cycles of animals depend on it across India.
Whereas the heat balance decides hot and cold seasons, the rainy season is decided by the moisture balance and the wind regime. There is no direct one-one relationship between solar motion and rain.
Going by the western calendar often leads to the phenomenon of delayed monsoons. He believes there is a causal relationship between the motion of the moon and the wind regime for monsoons. He showed a few newspaper images as an example of delayed monsoons.
Rainy season and culture
Rainy season is when all life on the subcontinent reproduces. Easy availability of food.
He showed a few bollywood songs to children about how the rainy season played an important role.
Festivals
There are broadly two calendar systems
- The amanta ends with amavasya, beginning with sukla paksa pratipad.
- Purnimant ending with purnima, beginning with krishna paksha pratipada.
The festival which falls in the shukla paksha belongs to the same month in both calendars. A festival which falls in the krishna paksha will be a month earlier in the amanta system.
Example: Diwali is on amavasya in the krishna paksh. As per amanta calendar, five days of Diwali festivity span over two months.
- Diwali begins – Krishna Paksha Trayodashi(28th tithi) of Ashwin(7th month)
- Diwali ends – Shukla Paksha Dwitiya(2nd tithi) of Kartik (8th month)
As per Purnimanta Calendar
- Diwali begins – Krishna Paksha Trayodashi (13th tithi) of Kartik(8th month)
- Diwali ends – Shukla Paksha Dwitiya(17th tithi) of kartik(8th month)
The civil days are the same in both cases, but the names of the months are different. Festival based on the Sankaranti is Makar Sankranti or Pongal transit of sun 15 jan 2024
Festivals based on christian calendar are Republic day 26 Jan 2024 and Independence day 15 Aug. He asked children whether it is good or bad to have the most important Indian festival based on the christian calendar.
Weekdays
Apart from the vast majority of stars, which move in an orderly fashion, there are seven celestial bodies which move in a more erratic fashion. These bodies are called planets. In ancient usage, the seven planets or wanderers in the sky, including sun and moon. The vara or 7 days of the week, are named after the planets.
The 7-day week is common across several cultures. Sunday, Monday and Saturday are clearly named after the sun, moon, and saturn(shani).
Tuesday is derived from “Tiv’s day” which is named after the Norse god of single combat. Among the norse gods and goddesses, Tyr is identified with Mars. Tyr[Mars = Mangal, and Managalvara].
Wednesday is derived from “Wooden’s day”. Wooden is identified with Mercury [Mercury = budh and budhvara].
Thursday from “Thor’s day”. Thor is identified with Jupiter [Jupiter = Guru and Guruvara].
Friday from “Freya’s day”. Freya is identified with Venus [venus = shukra and shukravara].
He asked is there any reason for the order of the weekdays? Which is original? If it is an Indian one. Why?
The logical explanation for this order of the week day is available only in the Indian tradition. This explanation relates to the seven planets that wanderers visible to the naked eye are as follows.
Aryabhata orders the planets according to the observed speed of movement.
The day is named after the lord of the day = the lord of the hour prevailing at sunrise. “The fourth in order of speed are the lords of the successive days reckoned from sunrise(at lanka)”
The chart for the lords of the first hour of each day. That tells us why the weekdays are in the given order.
Time and angle measurement
Most of us must have heard of popular terms like muhurta. He asked what does the term muhurta mean?
Vedic timekeeping (before the use of hours) was successively sexagesimal. Instead of 24 hours of 60 mins in a day, a day had 60 ghatis (of 24 mins), each ghati had 60 pala (of 24 seconds), each pala has 60 vipala (of 0.4 seconds).
Two Ghatis is a muhurta.
Converting hours, min, sec to ghati, pala, vipal
E.g. Convert 10 h 30 m 12 s to ghati, pala, and vipala.
Divisions of time
There were finer divisions of time such as (1/33750) which were not used in everyday life called murta.
1 prana = time for 1 breath = 4 sec (15 breaths per min)
A common unit was the yama (pahar) consisting of ⅛ of a day and night or 3 hours measured from sunrise. Thus, do pahar = six hours from sunrise = noon.
Yuga System
There were also very large measures of time in the yuga system found in the Surya siddhanta and in the vishnu purana etc.
These large measures of time puzzled the early British colonizers who had never encountered such large numbers before.
One reason for these large numbers is clear. They represent higher precision, which needs precise fractions.
There is also a difference between Aryabhata and Surya Siddhanta. Aryabhata has all four yuga’s of equal duration.
Year and 60 year Jupiter cycle (samvat and samvatsar)
There are 3 popular systems of naming years, Kali samvat, year count starts at -3101 CE (=3102 BC), Shaka samvat +78 CE and Vikram samvat its start date is -57 CE.
In the Hindu version of the preamble of the constitution of India, the date of its adoption (26 November 1949) is presented in Vikram samvat as Mrgsheersh shukla saptami samvat 2006. In this case 57 years are added in November.
Complication 1
The Indian calendar uses sidereal years not the tropical years used by the Gregorian calendar. Thus the number of years to add or subtract from the Gregorian calendar will depend on the month.
Complication 2
A calendar has to be recalibrated for the place since the times of sunrise varies from place to place and the civil day and civil tithi are decided by the time of sunrise.
The change in time of sunrise depended on the longitude was known as shown above. yavakoti must be east of Lanka by 6 hours, Siddhapura must be east of yavakoti by 6 hours and Romaka must be west of Lanka by 6 hours (or east of siddhapura by 6 hours).
Note that like Lanka, these are not actual places, but four points on the equator 90° apart. All four points are in the midst of the Ocean.
Because of variations of time and sunrise with longitude, the panachang calculations are done for the prime meridian (yamyottari) passing through Ujjain and Lanka.
The word Yaama, as already explained, is a vedic term for a period of 3 hours. The time difference is 1 hour per 15 degrees of longitude per 360 degrees in 24 hours i.e, it has latitude 0 and the same longitude as Ujjain which was earlier treated as longitude 0 degree. Later this system was copied by the British who made the meridian through Greenwich as longitude 0 degree and also GMT clock time 0.