Staying with a short count (using normal human years) also results in very interesting results. Consider the representation below:

This is similar to the chart I have depicted in the post defining the idea of Yugas, except this shows the cyclic nature of this phenomenon. It also adds a few calender pointers. Sri. Yuktheshwara defined (in his book The Holy Science) the beginning of the first Satya Yuga as being the time when the autumnal equinox is at the First Point of Aries (i.e. the start of the Aries constellation). He then computes (I do not know how) that the last time this happened was in 11,501 BC. The rest of the Yugas follow (I depict all BC years as negative numbers for convenience of calculation):

If we attempt to correlate this table to various known (and speculative) data points, some mixed messages emerge:

The current inter-glacial period that we are in (known as the Holocene) started around 11,400 years ago. Sri. Yukteshwara places his descending Satya Yuga as starting immediately after the ice sheets started receding. This also implies that he places his ascending Satya Yuga (and pretty much the entire previous Maha Yuga) firmly in the last glacial age when ice covered the earth!

The Indus Valley civilization is attributed to the period between 7000 BC – 1300 BC (click here to see the chronology of the Indus Valley Civilization). As per the table above, this covers the descending (i.e. when humankind was waning) Treta and Dwapara Yugas. Specifically:

• the Mehrgarh civilization (neolithic stone age, early food producing era) is attributed to 7000 BC, which is at the start of Treta Yuga
• the Early Harappan civilization (bronze age, regionalization era) is attributed to 3300 BC which is the start of Dwapara Yuga

I am startled by the striking co-incidence of these dates. Also, what we consider as advancement from stone age to iron age, the ancient Indians considered as descending from Treta Yuga to Dwapara Yuga, which I presume indicates a loss of spiritual capacity.

It is widely accepted by Indians that the events of the Mahabharatha took place around 3100 BC and kick-started Kali Yuga. There is another opinion that the Mahabharatha events took place around 5500 BC. Yet the table above places these date at the beginning of Dwapara Yuga and Treta Yuga respectively. Hence the tradition that Mahabharatha ended a Dwapara Yuga and kick-started Kali Yuga invalidates the Yuktheshwara model. The Yukteshwara model places Mahabharata as occurring circa 700 BC. This roughly corresponds with the European Indologists who placed Mahabharatha (and the entire Vedic civilization) as being post-Harappan circa 1000 BC! Which in turn supports the Aryan Invasion Theory, which has been thoroughly discredited by Talegeri!

If we switch attention to the Ramayana, there is very little consensus of when those events occurred. As per some analysis, the events of the Ramayana occured circa 7300 BC. If we accept this, we are face with Ramayana occuring towards the end of Satya Yuga and not Treta Yuga as tradition holds.

As per this model, we are no longer in Kali Yuga. We are in an ascending Dwapara Yuga since 1700, which coincides with the beginning of the industrial revolution in Europe!

All speculative, and all highly intriguing!

1 Maha Yuga = 12,000 * 360 = 4,320,000, i.e. 4.32 Million solar years

Beyond a Maha Yuga comes a Kalpa which is made-up of 1,000 Maha Yugas.

1 Kalpa = 4,320,000,000, i.e. 4.32 Billion solar years

One Kalpa is considered half a day of Brahma the creator. Thus a full day of Brahma is made of two Kalpas, one representing Brahma’s daylight hours, and the other Brahma’s night. During Brahma’s night, while Brahma sleeps, the entire universe is destroyed and Brahma starts creation afresh at the start of his next day.

Thus the entire universe is re-created from scratch once every 8.64 Billion solar years (2 kalpas). Modern science estimates the age of our Universe as 13.75 ± 0.11 billion years. Seems like the ancient Indians significantly under-estimated the lasting power of the Universe (or Brahma is badly behind schedule). Yet the very fact that the ancient Indians realized the age of the universe to be in the billions of solar years is extremely impressive.

This creation myth is postulated in Srimad Bhagavatham - Canto 3. This text further refines the definition of Kalpa into one more unit called Manvantaras as follows:

Brahma’s day begins with a preparatory period called Adhi-Sandhya which is 4 charans in duration. This is followed by 71 Maha Yugas (called a Manvantara) and then another yuga sandhya of 4 charanas duration. Each manvantara is presided over by a Manu (a very wise and very long lived being):

1 Manvantara = 71 Maha Yugas = 71 * 4,320,000  = 306,720,000, i.e. 306.72 Million solar years

This Manvantara-Yuga Sandya pair repeats 14 times in one Kalpa. This entire scheme is depicted below:

Be sure to check out Srimad Bhagavatham. It makes for very interesting reading.

We have seen a solar year, and a lunar year. What happens beyond a year? Is there the concept of century and millenium in the Indian system?

Beyond the year, the Indian system proposes longer timeframes called yugas as follows:

Thus, instead of centuries, the Indian system moves in a near-millennial scale of 1200 years (referred to as charana) with one Maha Yuga extending to 10 charanas (12,000 years). This figure is approximately half a precession of the equinox. And two Maha Yugas is within 7% of one complete precession of the equinox (25,772 years). This provides the correlation to some planetary phenomena that I have come to expect from the ancients.

Is this scheme used for actual calender dating? Yes but with little accuracy and reliability.

There is a general acceptance that we live in Kali Yuga now, but there is no agreement on when Kali Yuga began. The Surya Siddhantha puts the start of Kali Yuga at 3102 BC.  An alternate interpretation by Sri. Yuktheshwara says that Kali Yuga started in 499 AD and goes on to say we are no longer in Kali Yuga. There is a general belief that the Ramayana played-out in a Treta Yuga and the Mahabharatha very close to the end of a Dwapara Yuga (it got the subsequent Kali Yuga rolling by means of the great, destructive Kurukshetra war), yet historians have not been able to place these epics on a calendar with any degree of accuracy.

One interesting speculative meaning assigned to a pair of Maha Yugas is that humankind starts at a peak of perfection in Satya Yuga and wanes through the next nine charanas to reach its nadir at the end of Kali YugaThen the Yugas progress in reverse order (Kali to Satya) as humankind starts ascending again and gradually regains its virtues and regains its peak of perfection at the end of the next Satya Yuga:

The above approach (proposed by Sri Yuktheshwara) is not widely accepted though. And in two respects:

• While the idea of humankind descending from Satya Yuga to Kali Yuga is widely know, the converse of humankind ascending from Kali Yuga to Satya Yuga is little known. Most Indians believe that Kali Yuga is ended by Kalki (an avatara of Vishnu) who destroys all the bad elements and restores humankind back to Satya Yuga.
• The widely accepted approach defines “year” as a year of the gods, i.e. “deva year” which is then defined to equal 360 “human” years (i.e. solar years). This results in each charana becoming 432,000 years! While this blows any relation to the precession of the equinox completely out of the ballpark, this does shift the time frames to a geological scale (1 Maha Yuga  = 12,000 * 360 = 4,320,000 Solar Years), which is more suitable for a creation mythology. More about that in my next post.

This hot period is often referred to as Agni Nakshatra in south India. We have already seen what the Nakshatras are (they are 27 equal-width segments of the ecliptic). None of them is called Agni Nakshatra. So where did this Agni Nakshatra come from?

I saw a clear definition of Agni Nakshatra in Jayashree Saranathan’s blog:

As per astrology, Agni nakshatra is the time when the sun moves through the 7 paadas (paada = ¼ of the star) starting from Bharani 3rd paada to Rohini 1st paada..
These are Bharani 3rd & 4^th paadas, all the 4 paadas of Kritthika and Rohini 1st paada.

In other words, Agni Nakshatra is a composite of Bharani, Kritthika and Rohini Nakshatras. She also adds that “The Agni nakshathra starts on 4^th May this year and ends on 28^th May.”

I successfully verified these dates using the same astronomical techniques I have illustrated so far.

I used the Swiss Ephimeris to see where the sun is positioned at midnight GMT which begins each day of May (since I am scanning the positional variance of sun over a period of time, using an Ephimeris is a more suitable technique than using Stellarium). Since the Swiss Ephimeris measures ecliptic longitudes based on the Vernal Equinox as the zero point, I had to apply ayanamsas to bring this to the Indian measurements.

The Swiss Ephimeris specifies relative positions, i.e degrees relative to a zodiac position. For instance, on May 1 the sun is 11° 1′ 41” into Taurus. Since Taurus starts after 30° (the first 30° are occupied by Aries), the absolute coordinate of the sun on May 1st are 41° 1′ 41”. Applying an ayanamsa of 24° 1′ 54”, the adjusted coordinates fall in Mesha-Bharani-Pada 2. Similarly for the other days.

From my post on Nakshatras earlier, Bharani Pada 3 starts at > 20°. From the above table, on May 5th 0:00 Universal Time (i.e. 5:30 AM IST) the sun is at 20° 52′ 28”. Hence the sun moved into Bharani-Pada 3 sometime on May 4th. Same way, it can be seen that the sun moved out of Rohini-Pada 1 (ends at 43° 20′) sometime on May 28th. QED.

That said, it is still not clear to me why Agni Nakshtra stops with May 28th. The northern hemisphere continues to tilt toward the sun until the summer solstice which falls on Jun 20th. This means that until Jun 20th there should be no respite from heat in the northern tropical regions of India, but by then south Indians (being around 13° N latitude), receive the sun’s rays in an oblique angle and hence it looses some of its bite. Also, all of us in south India do observe that May is indeed the hottest month of the year. This is why Agni Nakshatra is a south Indian concept.

I also guess north Indian would prefer to stretch Agni Nakshatra beyond Rohini into Mrigashira-Pada 4 (which ends on June 21st).

1. Surya (Sun)
2. Chandra (Moon)
3. Kuja / Mangala (Mars)
4. Budha (Mercury)
5. Guru / Brihaspathi (Jupiter)
6. Shukra (Venus)
7. Shani (Saturn)
8. Rahu (Ascending [south to north] orbital node of the moon)
9. Ketu (Descending [north to south] orbital node of the moon)

Contrary to popular perception, these are not all plants as defined today. Sun is a star. The moon is a satellite of planet Earth. Rahu and Ketu are orbital nodes where the moon’s orbit intersects the ecliptic., i.e. these are not even heavenly “bodies” but are simply points on the celestial sphere!

The entire body of Indian astrology depends on tracking the movement of these navagrahas across the rashis and nashatras. These movements are correlated with the janma nakshatras (nakshatra where the moon resides at the time of birth) of individuals (or couples) with a view towards making life predictions. While the position and movements of these navagrahas across rashis and nakshatras are computed in an entirely scientific fashion, the predictions that derived from these movements are faith-based.

For instance, an Indian horoscope plots the position of the navagrahas (with respect to the rashi, nakshatras and padas as explained in earlier posts) at the time of birth of a baby. These positions can be verified using any modern-day astronomical software (Stellarium is my favorite though it depicts the positions  visually and not in term of degrees and minutes along the ecliptic) but there is no mechanism for verifying the predictions made based on these horoscopes!

To see how this works, consider the position of Mercury on my birthday, as viewed from my place of birth, as per Stellarium:

The constellation art looks really nice and places Mercury in Gemini, i.e. Mithuna rashi. This is not entirely reliable since:

• the boundaries of IAU constellations are irregular while those of the rashis are very regular (30° each).
• the zero ecliptic longitudinal point (vernal equinox) that Stellarium uses has drifted away significantly from that used by ancient Hindu astronomers (due to the precession of the equinoxes. This is a very gradual shift (approx 25772 years to complete a 360° shift around the earth). This video explain the idea nicely (consider the point marked as γ as the equinox;. ignore the position of the sun since that misleading. This video is not about the annual movement of the sun. This is about the 25772 year movement of the equinox).

Hence,

• we have to pay attention to the ecliptical longitude of Mercury as computed and displayed by Stellatium (116° 17′ 11”); the ecliptical latitude is irrelevant – it always stays with a few degrees of the ecliptic, north or south.
• adjust it to account for the drift as of my birth date (23° 20′ 24”) to arrive at the vedic coordinate (92° 56′ 47”). This adjustment is called ayanamsa and there is a formula for doing this (refer this link)
• walk through the ecliptic in steps of 30° (the span of each rashi) to reach Cancer (Karkataka) and not Gemini!

If we walk through the ecliptic in steps of 13° 20′ (the span of each nakshatra) we can locate the nakshatra and pada as Punarvasu – Pada 4.

This rashi, nakshatra and pada agrees perfectly with a horoscope I got from the Internet for my place, date and time of birth (http://www.astrobix.com/kundli/):

In short, it possible to determine the ecliptical longitude of each of the navagrahas (except Rahu and Ketu) as observed from a particular place at a particular date and time off of Stellarium and generate an a Indian horoscope using Excel:

Why are Rahu and Kethu left blank? As mentioned above, these are lunar orbital nodes and Stellatium does not “show” their position (since they are not real, visible entities).

I tried this with a few more birth dates. Except for one instance when the ayanamsa looped back below zero (which I handled by adding 360 but it does not tally with the horoscope), in all other cases Stellarium tallies perfectly with the horoscopes.

This is the astronomy part of a horoscope. The horoscope I got from Astrobix goes on to say:

You will have an aggressive spirit and will have an interest in social work and political activities. You are disposed to injury in the head and face ( left side if male, right side if female. You may join military service or acquire success through pioneer work. Your life will be changeful and remarkable in many ways. You will have a proud and haughty nature, will be aspiring and ambitious. You will have interest in practical arts, and will be generous and extravagant. Although impulsive and critical, you will be courteous. You may be in government service and will secure favours from big shots. You will be a bright person, highly passionate, pleasure-loving and fairly adept in art and poetry. Your nature will be kind and generous, but very impulsive and over-ardent. With your warm and sparkling disposition. You will have many friends.

All this is apparently “written in the stars”. This is where astronomy ends and astrology begins. The astronomy is impressive. As for astrology, well, it indeed tells me lots of things I never knew about myself!

Bottom line is:

• The Navagraha’s you go around nine times in the temple are really out there in the sky (well, at least seven of them are)
• Your horoscope does indeed record the position in the celestial sphere where each of these grahas was positioned at the time of your birth. Stellarium can show them to you any time you want with just a few deft clicks of the mouse, and they are indeed where your horoscope says they should be.
• These horoscopes were in all likelihood being charted for over one thousand five hundred years (since the time of Aryabhata [476 - 550 AD]  during the Gupta era).

Impressive, to say the least.

In addition to the 12 division of the ecliptic (rashis), Indian astrologers have created another set of 27 subdivision of the ecliptic that they called nakshatras (the popular perception of a nakshatra as a single star is wrong by definition), each having a span of 13° 20′ (360 divided by 27) along the ecliptic. These nakshatras are further divided into four padas each resulting in a total of 108 padas. Thus each pada has a span of 3° 20′ along the ecliptic and nine padas fit in a rashi.

The nakshatra of any moment in time is the nakshatra where the moon is at that point in time. The nakshatra of a day is the nakshatra in which the moon is at sunrise.

Nakshatras are used solely for astrological purposes and have no relevance for time keeping. Thus, though nakshatra of a day and janma nakshatra (the nakshatra at birth of a baby) are determined using astronomical principles, their application is entirely astrological.

The following tables maps rashis, nakshatras and padas to degrees and minutes along the ecliptic:

To see a mapping of these nakshatras to the actual constellations as defined today by International Astronomical Union, refer this link.

The entire celestial sphere is divided into eighty eight irregular sections by the International Astronomical Union (IAU). Each of these sections is a constellation containing a set of planets, stars, galaxies and nebulae and is labeled with a unique name. Think of the celestial sphere as a 3D jigsaw puzzle with eighty eight pieces. Every piece of this jigsaw is a constellation. Here is a complete list of the eighty eight constellations. It is easy to see that this is nothing but a very detailed map of the celestial sphere.

A detailed study of these constellations and their position on the celestial sphere shows that thirteen of these eighty eight constellations span the ecliptic, i.e. the sun “moves” through thirteen of them. The names of these thirteen, in the order in which the sun traverses them, are:

1. Aeris
2. Taurus
3. Gemini
4. Cancer
5. Leo
6. Virgo
7. Libra
8. Scorpius
9. Ophiuchus
10. Sagittarius
11. Capricornus
12. Aquarius
13. Pisces

It is easy to see that this list is nothing but the familiar western zodiac defined by ancient Greeks which is used by astrologers around the world (with the exception of Ophiuchus which the Greeks completely omitted).

Our interest is in astronomy and not in astrology. Hence, we are interested in these constellations (and not in the remaining seventy five) because they lie on the path traced by the sun around the celestial sphere over the course of a year. Click on any constellation above to see its exact shape and equatorial coordinates.

Indian astronomers too defined twelve constellation as lying on the ecliptic but they called them rashis instead of constellations and they named them very differently:

1. Mesha
2. Vrishabha
3. Mithuna
4. Karkataka
5. Simha
6. Kanya
7. Thula
8. Vrishchika
9. Dhanus
10. Makara
11. Kumbha
12. Meena

The rashi names correspond to the animal signs of the western zodia (for instance mesha is goat, vrishabha is bull, simha is indeed lion, meena is fish etc.). The ancient Indians (circa 500 AD) did indeed borrow these names from the ancient greeks (circa 400 BC) indicating that globalization is not a modern phenomena.

What does all this have to do with a solar calendar? Indian astronomers defined each of these rashis as having equal span along the ecliptic, i.e. 30° (360 divided by 12). They further defined the point in time when the sun “enters” a constellation (a sankramana or sankaranthi) as the being the beginning of a solar month. Hey presto! You now have a solar calendar with twelve solar months (soura masas) making up a solar year, with the names of the rashis becoming the names of the solar months!

Days within a solar month are numbered (starting from 1) similar to the Gregorian calendar. Sunrise marks the start of a new day.

Since the earth’s orbit around the sun is not circular but elliptical, the time taken by the sun to traverse successive 30° arcs is not uniform, i.e. the time taken by the sun to traverse successive rashis is not uniform, i.e. the duration of saura masas are not equal. Ancient Indian astronomers had multiple systems of calculations to compute the duration of a solar month. The most accurate of these is the Drigganitha system used to construct the Indian almanacs (Panchangas). Surya Sidhantha and Vakya are two other coarse grained, less accurate systems.

In addition to the above-mentioned 12 division of the ecliptic, Indian astrologers have created another set of 27 subdivision of the ecliptic that they called nakshatras (the popular perception of a nakshatra as a single star is wrong by definition), each having a span of 13° 20′ (360 divided by 27). More about that in my next post.

The Indian solar calendar (Souramana calendar) also splits a solar year into 12 months but the rationale behind the months is based on the apparent movement of the sun vis-a-vis the fixed stars. Understanding this requires a good understanding of the concept of the celestial sphere.

When astronomers and stargazers look up at the night sky they perceive a giant dome littered with stars. This dome is one half of a celestial sphere that envelopes the earth, with the earth at its center. Using a couple of different coordinate systems (Alt-Azimuth, Declination-RA), astronomers can uniquely address any point on this celestial sphere. We are no much concerned with the coordinate system in this discussion.

As the earth orbits the sun, the sun appears to move around the earth, i.e. the sun’s position on the celestial sphere keeps changing continuously. Putting it differently the sun appears in a different portion of the celestial sphere day after day, week after week, month after month. This implies that the backdrop of stars behind the sun keeps changing day after day, week after week, month after month.

This is not to be confused with the sun’s apparent movement due to the rotation of the earth on its polar axis, resulting in day and night. In this case, as the sun moves east to west, its entire backdrop of start too moves with it, east to west.

To observe the orbital movement, it is necessary to observe the backdrop of the sun over time, at a specified hour, i.e. the backdrop of the sun at 10AM on April 15 will be significantly different from the backdrop of the sun at 10AM on September 15 due the orbital movement of the earth around  the sun.

This zodiac simulator is a great help in understanding this orbital motion of the sun (and many of the ideas that are to follow). Play abound with it and see how the backdrop of stars behind the sun changes month to month (for our purpose now just think of each zodiac as a unique distinguishing pattern of stars – more about the zodiac in my next post).

The apparent orbit of the sun around the earth is known as the ecliptic. To a observer on  the earth the ecliptic is oriented east-west. If the earth’s axis was perpendicular to its orbital plane (which it is not), the ecliptic will simply be a projection of the terrestrial equator out on to the celestial sphere.

It is also interesting to note that all planets in the solar system orbit the sun pretty much in the same plane as the earth does, i.e. to an observer from the earth, all planets will appear somewhere near the east-west ecliptic on the celestial sphere. So, if you are trying to planet in the night sky, look above your head along an east-west arc and look for bright unblinking stars.

What exactly are these lunar and solar calendars? Thanks to Wikipedia it is easy to do research now a days. I also got hold of a soft copy of an excellent text “Basics of Panchangam” by Mr. S. Narasimha Rao published by the Shree Pejavara Mutt. Combining these two with other resources available on the Internet and some actual observations of the movements of the moon and stars over a couple of weeks made it relatively easy to understand these calendars. Keeping aside the astrological part (which has nothing to do with logic) and focusing on only the astronomical aspects, here is what I discovered.

The Lunar Calendar is easier to understand so let me cover that first.

The moon goes around the earth in 30 days, waxing for 15 days until Full Moon and then waning for 15 days until New Moon. Hence, a chandramana masa consists of two fortnights Shukla Paksha (waxing phase) and Krishna Paksha (waning phase). No weeks; only fortnights.

Each days of the fortnight has a name, i.e. no Sunday, Monday but the following:

1. Prathama
2. Dwitheeya
3. Thrutheeya
4. Chathurthi
5. Panchami
6. Shashti
7. Sapthami
8. Ashtami
9. Navami
10. Dashami
11. Ekadashi
12. Dwadashi
13. Trayodhashi
14. Chathurdashi
15. Pournami / Amaavasya

Clearly there are now two possibilities to mark the beginning of a lunar month (all graphics from The Basics of Panchangam):

• The day after an Amavasya (Amantha Masa)

• The day after a Pournami (Pournamantha Masa)

In Gujarath, Maharashtra, Karnataka, Kerala, Tamil Nadu and Bengal follow the former (Amantha Masa) tradition. The rest of India follows the latter (Pournamantha Masa) tradition.

Each days is referred to as a thithi (i.e. the day names listed above are the names of thithis). The duration of a day is neither 24 hours nor sunrise to the next sunrise (here is where it gets complicated). The duration of a day is defined by Mr. Narasimha Rao as follows:

A thithi is the time occupied by the moon in
increasing its distance from the sun by 12 degrees. In other words, at the exact point of time when the moon moving eastwards from the sun after the Amavasya, leaves the sun behind by 120 degrees, the first thithi, Pratipath (Prathama) ends, 240 for the end of Dwitheeya, 360 for Thrutheeya, . . 1800 for Pournami, 1920 for Krishna Prathama, 2040 for Dwitheeya, . . 3600 for Amavasya. One complete synodic revolution of the moon occupies 30 thithis for the 360 degrees.

To understand this, I had to observe the moon in its waxing phase (starting with the waxing crescent two days after new moon) for a fortnight. Then I got it.

What I observed was that the waxing crescent moon was setting in the west practically with the sun (say a hour or so after sunset), but as it waxed it also started “falling behind”, i.e. it was setting progressively later than the sun. So much so that seven days after new moon I saw the waxing quarter moon right over my head at sunset. And after 15 days, the full moon was rising in the east when the sun was setting in the west!

Now I went back to Mr. Narasimha Rao’s definition and noted that 12 degrees = 360 degrees / 30 days and the definition made sense.

If you are too lazy to observe, check out this simulation of lunar phases.

It turns out that given the relative movements of the sun, earth and the moon, the time required for the moon to “increase its distance from the sun by 12 degrees” is not constant and varies for every subsequent 12 degrees. The following table give you some idea of this variation (60 Ghatis make a 24 Hour day):

Thus you can see that some days have a duration of less than 24 hours and some have more than 24 hours. Specific duration of any given day is documented in a Panchangam.

One final addition to the definition a day in the lunar calendar: In all Hindu calendars, sunrise defines the start of a day. The thithi prevailing at sunrise (determined by the moons position at that point in time) is considered the thithi for that day. This, combined with the variation in thithi duration mentioned above, often leads to the interesting situations of:

• two days having the same thithi (i.e. a thithi with duration greater than 24 hours spanning two consecutive sunrises)
• one thithi being entirely skipped when moving from one day to another (i.e. a thithi with duration less than 24 hours starting and ending between two consecutive sunrises)

The twelve months of the Chandramana calendar are named as follows:

1. Chaithra
2. Vaishaka
3. Jyeshta
4. Aashada
5. Shravana
6. Bhadrapada
7. Aashwayuja
8. Karthika
9. Marghashira
10. Pushya
11. Magha
12. Phalguna
13. Adhika Masa

What is this Adhika Masa at the end? It is a link to the Souramana calendar and occurs once in about two and a half years. Mr. Narasimha Rao defines this as follows:

A period of 12 lunar months ( Chandramana Masa) falls short of the solar year by eleven days. To bring the lunar year as near as possible to the solar year, a lunar month is added to the lunar month at certain intervals. Such a month is called a adhika or intercalated month. This addition of a masa follows the rule of a masa without sankramana.

What is a sankramana? More on that in my upcoming post on the Souramana calendar.

So, that is a Chandramana calendar. Twelve months; each with two Pakshas; each with 15 thithis; each with average length of 23 hours, 37 minutes and 28.092 seconds. A month can start at the end of Amavasya (Gujarath, Maharashtra, Karnataka, Kerala, Tamil Nadu, Bengal) or Pournami (rest of India).

Relatively easier to understand than the Solar calendar (Sauramana calendar) which I will attempt to explain in a subsequent post.

Some practical notes on the Moon’s movements:

I have been dabbling with stargazing using an amateur telescope.

Since the balcony in my house faces west, I am restricted to a western quadrant of the celestial sphere. Also, the best time to observe the moon is when it is a crescent (the contrast on the surface of the moon is excellent). Hence, I get brilliant sightings in thrutheeya to shashti thithis of Shukla Paksha of any chandramana masa.

I have a problem catching a “full” moon since the moon comes over into the western sky well after midnight in the Ekadashi – Pournami of Shukla Paksha of any lunar month. I hate to stay up so late! It gets even worse once Krishna Paksha starts (post Pournami).  If I had a east facing balcony this would have been easy.

The Krishna Paksha of any month gets progressively bad for moon gazing (i.e. fewer hours of nighttime visibility), since the moon is progressively straying into the daylight hours until it is synchronous with the sun in rising and setting on Amavasya thithi (New Moon day). Not only is the side facing earth unlit by the sun, it is also there in the sky only during daylight  hours!

Statistics offers a wonderful tool for measuring relative consistency of batsmen’s performances – the Standard Deviation of their scores. Standard Deviation is a measure of  the variance of their scores around their average. The lower the standard Deviation the less the variance and hence the higher the consistency.

Consider the following chart which plots the Fab Four’s Standard Deviation over their entire career vs. their Standard Deviation over the eight matches they played in the recent England and Australia away tours (Sehwag sat out two of them in England because he was too tired):

Sehwag displayed the most dramatic improvement in consistency with his Standard Deviation dropping from from 60 to a jaw dropping 23! He caught up with Tendulkar and the ever dependable Laxman in terms of consistency! Strangely, the ever studious Dravid shows precious little improvement in consistency. Further investigation revealed that the three centuries he scored in England marred his consistency figures badly. “If only I had not scored those centuries” rued Dravid, “not only my consistency figures would have improved, I would also have got lots more time for shopping”.

“We are very happy to see  that such outstanding consistency from our seniors. The improvement of Standard Deviation from 40s and 50s down to 20s is simply fantastic Di. They have fully justified our faith in them Di. Except for Dravid. We surely have to drop him to make way for a deserving youngster Di” said the Chairman of the Selection Committee Krishnamachari Srikant from Chennai.

When queried about the other statistical measure that is often used to measure a batsman’s performance, Srikant enigmatically replied ‘Baalu kalaru redu redu; redu kalaru blacku”.

Ravi Shastri, on the other hand, had the following to say “It is not correct to measure great batsmen like Tendulkar, Dravid, Sehwag and Laxman on the basis of a single statistics such as batting average. One has to take a wholistic view which is provided by their superior Standard Deviation. Only when the younger players display such consistency can the seniors’ position in the team be challenged”.

Sunil Gavaskat reportedly fell off his chair when he saw the consistency  figures  until he saw the averages chart. He then remarked “Hell, I have to stop talking about the Glorious Uncertainties of Cricket from now onwards”.

To which Srikanth replied “Dingu Dongu Dongu Dingu; Dongu Dingu Bongu”. At which point Ganguly slapped him.