Astronomy of Makar Sankranti
By Ameya L Gokhale
Makar Sankranti is a festival in India which is celebrated in winter. It is famous for recipes of sesame and jaggery which are particularly good for health during the winter. Let us try to understand the astronomy behind that festival.
Makar means zodiac sign of Capricornus and Sankraman means transition. From the two words it becomes clear that the sun transitions into Capricornus on that day. Capricornus can also have following 3 meanings:
1) Indian Capricornus (nirayan – which doesn’t consider precession)
2) Western Capricornus (sayan – which considers precession)
3) Capricornus constellation
For the purpose of Sankranti, of course the Indian Capricornus is assumed as the standard. Since it is the 10th zodiac sign, its starting point is 9×30=270 degrees from first point of Aries (Indian). When sun arrives at this point, it transitions into Capricornus. It is the time of hard winter in India and so there has been a tradition of eating recipes of sesame and jaggery on its occasion and also of wearing black clothes. So, this festival is tightly coupled with seasons than other Indian festivals.
Now, let’s think about Sankranti dates. You might be aware that it comes on 14th or 15th January. But, exactly why and when does it come on 14th or 15th? Table no. 1 shows few Sankranti dates. Please look at only first two columns for now.
|Year||Festival date||Time of sun’s Capricornus transition|
|2001||14th Jan||5:10 am, 14th Jan|
|2002||14th Jan||11:19 am, 14th Jan|
|2003||14th Jan||5:30 pm, 14th Jan|
|2004||15th Jan||11:43 pm, 14th Jan|
|2005||14th Jan||5:41 am, 14th Jan|
|2006||14th Jan||11:54 am, 14th Jan|
|2007||14th Jan||6:07 pm, 14th Jan|
|2008||15th Jan||12:07 am, 14th Jan|
Examining the table, we can roughly infer that Sankranti occurs on 15th Jan in a leap year. But wait! It is just a temporary state at that time and Sankranti slowly moves forward. Let us see how.
Now take a close look at column 3. You will find that the transition into Capricornus occurs 6 hours 9 minutes* later every year. This surplus of 9 minutes is very important. In 4 years Sankranti moves forward by 24 hours 36 minutes, but the leap year pulls it backwards by only 24 hours. (Because of extra day taken in leap year, Sankranti gets pulled in previous day.) These surplus 36 minutes slowly keep pushing Sankranti forward.
Now again look at the 3rd column in table no 1. Look closely at 2004 and 2008. Why was Sankranti celebrated on 15th Jan in those years? Because transition into Capricornus was after sunset. So we found one more rule that – “If transition into Capricornus occurs after sunset, Sankranti is celebrated on the next day”.
To understand it better, let’s take a look at the graph for those 8 years (figure 1). Y-axis shows the year and X-axis shows the time of day. The forward motion of Sankranti is clearly visible in it. The dotted line on the graph represents the sunset at Mumbai on 14th January (6:19 pm). You can easily see that in 2007, the entry into Capricornus was just before sunset. In 2011, it happened after sunset and so Sankranti was celebrated on 15th Jan. In short, the pattern of Sankranti which previously was 14-14-14-15, changed to 14-14-15-15 in the period 2009-2012. Few years later it will become 14-15-15-15; few years later it will be 15-15-15-15; it will keep shifting forward like that. But in exactly how many years? It takes about 40 years to change Sankranti pattern. If the sunset is just missed by 1-2 minutes, it can get delayed to 44 years. On the other hand if it can catch up with sunset a little early, it changes in 36 years. If you miss a bus by 1 minute, you have to wait for 10 minutes for next bus – it is analogous to that. But, 40 years is far more common.
Now here is one interesting thing. At Kolkata, sun sets at 5:19 pm on 14th Jan. As a result, the Sankranti pattern there would have changed 8 years before that at Mumbai i.e. in 2003! So, the pattern also depends upon your location on Earth.
Can we work out this 40 years cycle through calculations? It’s easy. Sankranti’s new pattern (14-14-15-15) started in the period 2009-2012. In that period, sun’s entry in Capricornus in 2010 was at 12:30 pm. For the pattern to change again, this entry should move forward till 6:19 pm – by about 6 hours = 360 minutes. Entry into Capricornus moves forward at the rate of 36 minutes per 4 years. So, in order to move ahead by 360 minutes, it will take 4×360÷60 = 40 years. So, the pattern will change to 14-15-15-15 in the period 2049-2052.
|1969 – 1972||14-14-14-15|
|2009 – 2012||14-14-15-15|
|2049 – 2052||14-15-15-15|
|2089 – 2092||15-15-15-15|
|2101 – 2104||16-16-16-16|
|2125 – 2128||16-16-16-17|
Table no 2 shows future patterns of Sankranti – let’s observe them closely. Everything looks normal till 2089 – pattern is changing every 40 years. But the numbers for 2101-2104 are quite unexpected. 40 years are not yet over, but Sankranti has already jumped by 1 day in all 4 years. Usually Sankranti pattern just “shifts” by a day. But here Sankranti has jumped outright. What’s going on there? 2100 is not going to be a leap year! It is going to be an ordinary year of 365 days. So, Sankranti won’t get pulled backward the way it gets due to a leap year (see figure 1). It will move ahead by a day forever. As per the rules of Gregorian calendar that we use, if a year is fully divisible by 100 it has to be fully divisible by 400 in order to be a leap year. So the years 2100, 2200, 2300 are not leap years; but 2000, 2400 are, so Sankranti will get pulled back in those years.
Following are our conclusions so far:
1) Sankranti follows a 40 year cycle due to which it slowly moves forward (average 9 minutes/year)
2) Sankranti follows a 100 year cycle due to which it takes a 1 day jump. But, it does not apply every 400 years.
3) Sankranti’s total forward motion is the result of superposition of both the cycles.
So, can we calculate the total rate of forward motion of Sankranti? That calculation also is quite simple. As per 40 year cycle’s rate of 9 minutes/year, Sankranti would move 9×400 = 3600 minutes in 400 years – that’s 2.5 days. And as per 100 year cycle, it will move by 3 days in 400 years (because 3 leap years get skipped). So, in 400 years Sankranti moves by 2.5+3 = 5.5 days. This is the average rate.
Till now we saw “what” happens; now let’s try to find “why” it happens. We take 365 or 365 number of days in a year because we can’t take fraction values. But the real duration of year is not an integer but a fraction. It takes 365.2564 days for Earth to revolve around sun “relative to stars”. This value is nothing but 365 days 6 hours 9 minutes. It is this 6 hour 9 minute difference that causes delay in sun’s entry into Capricornus. This gives us the reasoning of 40 year cycle. The cause of the 100 year cycle lies in the fixed (nirayan) style of zodiac belt that Indian astronomy uses – we assume the first point of Aries to be fixed and unaffected by Earth’s precessional motion (we will come to it shortly). The year “relative to stars” that we saw above is called “sidereal year”. It is “nirayan”. The fixed Indian zodiac belt uses this year. There is a second type of year. The time it takes for Earth to revolve around the sun “relative to vernal equinox” is called as “tropical year”. Its duration is 365.2422 days or 365 days 5 hours 48 minutes. It takes account of moving zodiac belt due to Earth’s precessional motion. Our Earth is a giant top and its axis of rotation precesses just like the top and traces a cone in the space. It causes the vernal equinox and the western zodiac belt to move backwards. The seasons depend upon vernal equinox and as a result the tropical years is always in sync with the seasons whereas sidereal year has got nothing to do with seasons. Precisely for this reason the Gregorian calendar also follows tropical year. Due to a leap year in every 4 years its average number of days becomes 365.25 days. To take it as close as possible to 365.2422, leap years are skipped every 100 years. As a consequence of this, Sankranti takes jump of 1 day. Now know the reason behind 100 year cycle too. The root cause of the problem is the use of fixed (nirayan) zodiac belt.
This proves that Sankranti will keep going out of sync with seasons. Sayan and nirayan sankrantis were together about 1800 years ago. Today the difference has accumulated to 24 days, which is a big difference. It will go into February in another 1200 years. This definitely needs a repair. But what is the solution? Use of sayan zodiac belt is the fix. With this the Sayan Makar Sankranti would always be nearby 22nd December. In principle this is the right day because it is meant to be celebrated when the sun is at its southernmost point. Instead of sticking to old traditions it is important to improve them.
Sayan Makar Sankranti also has its own 32 years (not 40 years) cycle and 100 years cycle, but they operate in “opposite” directions. 32 years cycle moves sayan Sankranti “backwards”, while 100 years cycle pushes it “forward”. So, net effect almost cancels out and it always falls nearby 22nd December.
Before ending the essay, let me tell one interesting thing. As per tradition, the sesame and jaggery recipes are consumed starting Sankranti up to “Rath Saptami” (Maagh Shuddha Saptami). In future, will the forward motion of Sankranti cause it to move even ahead of Rath Saptami? This is a good problem for amateur astronomers and needs in depth knowledge of Hindu calendar. Will be you be able to find the answer?
[* 9 minutes is average. Elliptical orbit causes the value to slightly differ. ]