Seasons from the Sun
Kamal Lodaya, Bengaluru
This is the seventh of a series about calendar makers from history.
Earlier articles talked about {lunar} calendars based on {phases} of the Moon, {seasonal} calendars based on seasonal happenings (such as rains or river flooding which were important for farmers) and {intercalary} calendars whose years were seasonal but whose months were based on the Moon's phases. 
There are several calendars in India, using different Eras. Today we know that the rotation of Earth {precesses}, like a top whose axis keeps shifting slightly as it spins. This makes the solstices (longest and shortest days) shift to an earlier date every year, which becomes noticeable over centuries. To fix this, a {leap day} was introduced to the seasonal year every four years by the Egyptians, and later by Julius Caesar of Italy helped by an astronomer called Sosigenes.
Seasonal calendar, 6th century CE
In earlier articles, we mentioned the Indian National calendar of 1957 CE, following the Shalivahana Shaka Era which began in the year 78 CE. It uses a leap day every four years, when the month of Chaitra has 31 rather than 30 days. This follows the idea of Sosigenes, in which the month of February has 29 rather than 28 days.
A related Indian Nirayana calendar is ahead by three weeks, beginning on 14 April rather than 22 March. In this, it is the month of Phalguna which has a leap day.
The Tamil seasonal calendar, based on the Sun, was described by the Sangam poet Nakkirar around the 3rd century CE. In 499 CE, the Indian astronomer Aryabhata, an Ashmaka (likely from the Godavari valley) who lived in Kusumapura (Patna in Bihar), introduced the {Kaliyuga Era}. He declared the Tamil calendar beginning with Chaitra (Chittirai) that year to be 3600 KE. His seasonal calendar is used in Kerala and Tamil Nadu.
Aryabhata was a mathematician. He wanted to {calculate} the seasonal months, {without} using a leap day. If the Sun moves by 360 degrees during a year (actually it is Earth going around the Sun, but keep Earth fixed), then moving by 30 degrees is a seasonal month. This can be roughly determined by which of 27 {nakshatras} is highest in the sky at midnight, hence opposite to the Sun. The Sun will move by 2 1/4 nakshatras every seasonal month, if we think of nakshatras as covering parts of the Sun's path, rather than as just stars.
Here is how these ideas work, roughly speaking. When the Sun travels in the sky from Revati nakshatra (star) in Meena rashi (constellation) to Ashwini nakshatra in Mesha rashi, this is called Mesha {sankranti}, and the Chitra nakshatra (star) in Kanya rashi (constellation) is exactly opposite and highest in the sky at midnight. 
The seasonal month is called Chaitra or Chittirai after the opposite nakshatra. Thirty degrees after Mesha comes Vrishabha rashi and one can find out when the Vrishabha sankranti takes place.
Duration of seasons
It turns out that the Sun's speed through the sky is not the same. Here are observations of the lengths of months from earlier years, which were compiled in texts like the {Surya Siddhanta}, attributed by 6th century polymath Varahamihira of Ujjain to Laatadeva, which suggests a person from the Narmada valley. It was updated to the {Vakya} version several centuries later. The second last column of the table is written in units of days, hours, minutes and seconds for our convenience. The last column gives festivals determined by this calendar.
Now if you know what time Mesha sankranti was (about 3 am on 14th April) this year, you can just add up from the table and calculate the other sankrantis. So, in the Tamil calendar this year, Karthikai seasonal month will begin {on 17 November} and not on 16 November, since the sankranti time is at night. You can see that Aani seasonal month this year had 32 days! If you know how the festivals at the end of the table are connected to the calendar, you can find out their dates yourself. If you add all the durations in the third column of the table, you will find that one year lasts 365:06:12:36.56 (days:hours:mins:seconds) and so the next Sankranti is on 14 Apr at 9am the next year.
Isn't this all wrong? If you ask any one, they will tell you that this year Deepavali, falling on the {amavasya} (New Moon) of Karthikai {lunar} month, is on 4th November. This is nowhere near the seasonal month of Karthikai shown in the table! This is because we also have months determined by the Moon.
Box: Numbers and calculation
Do you find Aryabhata's calendar easier or Julius Caesar's? As seen in the last issue of {JM}, the Indians had developed arithmetic calculations that we learn in school, by the time of Aryabhata. They were delighted to use their new knowledge at every possible opportunity.
Aryabhata knew the Roman calendar, because one of Varahamihira's five texts was the {Romaka Siddhanta}, known in India since 2nd century CE. One can imagine Aryabhata thinking: 31,28,31,30,..., why do days in months have to be in this arbitrary fashion? Why have months like July and August, arbitrarily named after emperors, when they can be named after stars for a sensible reason? Why not just calculate the days in every month?
Little is known about him, yet Aryabhata's work appears scientifically minded. Some historians think he taught at the university in Nalanda, Bihar. Arithmetic calculations were not then taught in primary schools like they are today. Keeping track of the exact time of sankrantis from year to year and sunrises or sunsets from month to month was not easy.
This goes back to 575 CE, when Varahamihira compiled all the calendars known to him in his {Panchasiddhanta} (five texts). He combined earlier Hindu and Jain calendars based on the Moon with Aryabhata's calculations of the Kaliyuga calendar. Aryabhata's and Varahamihira's calendars were taken up by {jyotishis} who made {panchangs} (publicly available calendars).
Varahamihira's grandfather, father and son, as well as he himself, were jyotishis. The story continues in the next issue of {JM}.