It's the traditional new year time here again in Sri Lanka. I find this new year celebration fascinating because it is celebrated at a particular time of the day (which changes every year) as opposed to midnight. The tradition is celebrated among Budhhists as well as Hindus in Sri Lanka. You can read more about how the timings are calculated in two of my old posts:
http://galileoscamera.blogspot.com/2013/04/math-of-astrology-1.html
http://galileoscamera.blogspot.com/2013/04/math-of-astrology-2-sinhalahindu-new.html
One of the first things to note about calendars and periodic astronomical events is that you need to account for the precession of equinoxes. Each year, Sun's apparent position relative to the backdrop of stars move about 50.3 arc seconds backwards. This partially gets corrected with the leap years, but not completely. Therefore what happens is that starting from a leap year, the position recedes every year at the given time and on the next leap year, jumps a little bit forward, but not completely to catch up.
2020 is a good year to analyse this as we are in a leap year and are after the leap day (February 29th). According to the tradition, the new year dawned at 20:23:00 UTC+05:30. Since we are tracking the lateral movement of the Sun, we only need to look at the 'longitude' of the celestial sphere. In astronomy, we call this Right Ascension. To track the location of the Sun, I used Stellarium, a software that is used by a large number of observers for accurate positioning.
On 13th April, 20:23:00 UTC+05:30, the Sun was at 1h 28m 19.99s. Where would the Sun be at subsequent years at the exact same day at the exact same time? Here's a tabulated result:
We can see that through the three non-leap years, the error accumulates quite dramatically, reaching almost 3 arc minutes. Then it kind of compensates with the error with the leap year correction, but never quite catches up to the exact amount.
But before we go any further, we need to inspect one more thing. In my explanation above, I said that the Sun's apparent position moves back about 50.3 arc seconds every year. However the observations above show that it is around 57 arc seconds and varies each year. What's going on here?
The reason for that is that the amount by which the position recedes is not a fixed rate of 50.3 arc seconds per year. The latest formula adopted by the IAU stands as follows:
Cumulative precession (arc seconds) = 5028.796195t+1.1054348t2+0.00007964t3−0.000023857t4−0.0000000383t5
Here, the term t refers to Julian Centuries. But explaining that is going to be another series of posts, so I am going to leave it at that ;) But at this point it is sufficient to note that as time passes, smaller parts add up to that 50.3 arc seconds.
Now let's get back to the problem at hand. Was Knox's observation simply explainable by the precession? As the formula for calculating precession is quite complex, I decided to use the aid of a simulator for this. As before, my tool of choice was Stellarium.
To find out what the New Year could've been "back then", I started going in reverse from 2020 New Year time and tried to simulate at which date and time on each of the years the Sun would be at the same position.
As you can seem the New Year date recedes back to 11th by around early 19th century and goes to 8th and 9th of April during the time Robert Knox was a prisoner in Sri Lanka. This is still far from the end-March dates that are mentioned by Knox on his publication though.
This is where a calendar change comes in. Up until 1582, Europeans were largely using the Julian calendar. From 1582 on wards the new calendar introduced as the Gregorian calendar (named after Pope Grogory XIII who was behind its development) became gaining popularity. However, Britain did not switch to this calendar till 1752, and when it did, there was a loss of 11 days from the Julian calendar to the Gregorian calendar. Brits went to sleep on 2nd September 1752 on the Julian calendar and woke up on 14th September on Gregorian calendar.
Given that Knox's book was published in 1681, his dates invariably refer to the Julian calendar. When you adjust for that calendar change, we get the dates of 08th and 09th April on the Gregorian calendar as 28th and 29th on the Julian calendar. It appears that his observations and the calculations Sri Lankans used at the time were pretty perfect.
But, all mystery is not solved yet. One of Knox's passages where he mentions about the New Year reads as follows:
They reckon their Time from one Saccawarsi an ancient King. Their year consists of 365 days, They begin their year upon our Eight and twentieth day of March, and sometimes the Seven and twentieth, and sometimes, but very seldom, on the Nine and twentieth. The reason of which I conceive to be, to keep it equal to the course of the Sun, as our Leap year doth.
But based on the simulations during the time when he was a prisoner, the New Year has fallen almost all the time on 28th and 29th of March and never on 27th. So what happened? Was he off by a day? Was he simply mistaken? Or are the simulations off by some amount?
I would be very glad if I knew the exact answer, but for the moment, I am content in knowing that the approximation works :)
http://galileoscamera.blogspot.com/2013/04/math-of-astrology-1.html
http://galileoscamera.blogspot.com/2013/04/math-of-astrology-2-sinhalahindu-new.html
Few years ago, one of my friends pointed out that a text written in 17th century by a English prisoner in Sri Lanka, refers to the new year being celebrated by late March as opposed to April. Robert Knox, i.e. the prisoner, published the book An Historical Relation Of The Island Ceylon In The East Indies in 1681, detailing his observances of Sri Lanka during his time of capture between 1660 to possibly 1680. In this, he makes several references to the New Year being celebrated between 27th-29th of March. Was he simply mistaken about the time? Did he miss a month when counting? This time around I decided to find more details about this.
One of the first things to note about calendars and periodic astronomical events is that you need to account for the precession of equinoxes. Each year, Sun's apparent position relative to the backdrop of stars move about 50.3 arc seconds backwards. This partially gets corrected with the leap years, but not completely. Therefore what happens is that starting from a leap year, the position recedes every year at the given time and on the next leap year, jumps a little bit forward, but not completely to catch up.
2020 is a good year to analyse this as we are in a leap year and are after the leap day (February 29th). According to the tradition, the new year dawned at 20:23:00 UTC+05:30. Since we are tracking the lateral movement of the Sun, we only need to look at the 'longitude' of the celestial sphere. In astronomy, we call this Right Ascension. To track the location of the Sun, I used Stellarium, a software that is used by a large number of observers for accurate positioning.
On 13th April, 20:23:00 UTC+05:30, the Sun was at 1h 28m 19.99s. Where would the Sun be at subsequent years at the exact same day at the exact same time? Here's a tabulated result:
| Date/Time | Location (RA) | Recession from previous | Recession from first measurement |
| 2020-04-13 20:23:00 | 1h 28m 19.99s | - | - |
| 2021-04-13 20:23:00 | 1h 27m 23.11s | 56.88s | 56.88s |
| 2022-04-13 20:23:00 | 1h 26m 26.49s | 56.62s | 113.15s |
| 2023-04-13 20:23:00 | 1h 25m 28.46s | 58.03s | 171.53s |
| 2024-04-13 20:23:00 | 1h 28m 13.65s | -165.19s | 6.34s |
We can see that through the three non-leap years, the error accumulates quite dramatically, reaching almost 3 arc minutes. Then it kind of compensates with the error with the leap year correction, but never quite catches up to the exact amount.
But before we go any further, we need to inspect one more thing. In my explanation above, I said that the Sun's apparent position moves back about 50.3 arc seconds every year. However the observations above show that it is around 57 arc seconds and varies each year. What's going on here?
The reason for that is that the amount by which the position recedes is not a fixed rate of 50.3 arc seconds per year. The latest formula adopted by the IAU stands as follows:
Cumulative precession (arc seconds) = 5028.796195t+1.1054348t2+0.00007964t3−0.000023857t4−0.0000000383t5
Here, the term t refers to Julian Centuries. But explaining that is going to be another series of posts, so I am going to leave it at that ;) But at this point it is sufficient to note that as time passes, smaller parts add up to that 50.3 arc seconds.
Now let's get back to the problem at hand. Was Knox's observation simply explainable by the precession? As the formula for calculating precession is quite complex, I decided to use the aid of a simulator for this. As before, my tool of choice was Stellarium.
To find out what the New Year could've been "back then", I started going in reverse from 2020 New Year time and tried to simulate at which date and time on each of the years the Sun would be at the same position.
| 13-Apr-2020 | 20:23:00 |
| 14-Apr-2019 | 14:08:23 |
| 14-Apr-2018 | 8:06:23 |
| 13-Apr-1920 | 5:05:43 |
| 11-Apr-1820 | 13:39:51 |
| 09-Apr-1720 | 22:19:50 |
| 08-Apr-1620 | 7:04:05 |
| 08-Apr-1660 | 13:17:49 |
| 08-Apr-1661 | 19:19:10 |
| 09-Apr-1662 | 1:31:09 |
| 09-Apr-1663 | 7:37:16 |
| 08-Apr-1664 | 13:42:22 |
| 08-Apr-1665 | 19:57:33 |
| 09-Apr-1666 | 1:59:50 |
| 09-Apr-1667 | 8:15:46 |
| 08-Apr-1668 | 14:34:52 |
| 08-Apr-1669 | 20:34:55 |
| 09-Apr-1670 | 2:45:48 |
| 09-Apr-1671 | 8:54:58 |
| 08-Apr-1672 | 14:58:54 |
| 08-Apr-1673 | 21:14:13 |
| 09-Apr-1674 | 3:14:31 |
| 09-Apr-1675 | 9:25:56 |
| 08-Apr-1676 | 15:42:01 |
| 08-Apr-1677 | 21:39:24 |
| 09-Apr-1678 | 3:53:04 |
| 09-Apr-1679 | 10:10:39 |
| 08-Apr-1680 | 16:17:38 |
As you can seem the New Year date recedes back to 11th by around early 19th century and goes to 8th and 9th of April during the time Robert Knox was a prisoner in Sri Lanka. This is still far from the end-March dates that are mentioned by Knox on his publication though.
This is where a calendar change comes in. Up until 1582, Europeans were largely using the Julian calendar. From 1582 on wards the new calendar introduced as the Gregorian calendar (named after Pope Grogory XIII who was behind its development) became gaining popularity. However, Britain did not switch to this calendar till 1752, and when it did, there was a loss of 11 days from the Julian calendar to the Gregorian calendar. Brits went to sleep on 2nd September 1752 on the Julian calendar and woke up on 14th September on Gregorian calendar.
Given that Knox's book was published in 1681, his dates invariably refer to the Julian calendar. When you adjust for that calendar change, we get the dates of 08th and 09th April on the Gregorian calendar as 28th and 29th on the Julian calendar. It appears that his observations and the calculations Sri Lankans used at the time were pretty perfect.
But, all mystery is not solved yet. One of Knox's passages where he mentions about the New Year reads as follows:
They reckon their Time from one Saccawarsi an ancient King. Their year consists of 365 days, They begin their year upon our Eight and twentieth day of March, and sometimes the Seven and twentieth, and sometimes, but very seldom, on the Nine and twentieth. The reason of which I conceive to be, to keep it equal to the course of the Sun, as our Leap year doth.
But based on the simulations during the time when he was a prisoner, the New Year has fallen almost all the time on 28th and 29th of March and never on 27th. So what happened? Was he off by a day? Was he simply mistaken? Or are the simulations off by some amount?
I would be very glad if I knew the exact answer, but for the moment, I am content in knowing that the approximation works :)
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