கொவ்வைச்செவ்வாயில் குமிழ் சிரிப்பும்
பவளம்போல் மேனியிற் பால்வெண்ணீரும்
- Thevaaram by Thirunaavukkarasar
A blend of art, religion and science in India:
Consider the following Tamil verse by Udumalai Narayana Kavi:
“ஆவணி ரோஹிணியில் அஷ்டமியிலே
அஷ்டஜாம நேரத்திலே அவதரித்தோனே”
which translates to:
“The one who was born in the midnight hour of Āvaņi-Rohiņi-Ashtami”.
This verse was part of a much larger Bharathanatyam sequence (“Parkkadal Alaimele”) from the 1960 Tamil film Raja Desingu performed by Padmini.
This verse pertains to the birth of Krishna which is celebrated as Janmäshtami. This year, all Hindu Panchangas fixed Aug 28th as Janmäshtami day. Here’s why:
This exactly matches what is described in the verse!
I recently spotted an image in a iOS app (Deluxe Moon from Lifeware Solutions) that clearly lays out the different types of zodiac that are prevalent today viz. astronomical, sidereal and tropical.
The astronomical zodiac is defined by IAU (International Astronomical Union). The sidereal zodiac is the one used by the Hindu astronomical system and corresponds pretty much to the IAU definition except:
I have explained all this in an earlier post.
The tropical zodiac is identical to the sidereal zodiac on all respects except for the starting point. It uses the Sun’s position at Vernal Equinox as the First Point of Aries. Due to the precession of the equinoxes this point keeps falling back (wrt to the sidereal zodiac) by approximately 1º every 70 years. As a result of this, today two zodiacs are offset significantly and the First Point of Aries is well inside sidereal Pisces, as can be seen in the above figure. This zodiac is best suited for defining seasons (the seasons are predominantly decided by the Sun’s position with respect to the equator and the two tropics). Even in the Hindu system, which defines six seasons of two Rashis each, should be read with respect to this tropical zodiac to produce seasons that best match today’s reality. I have discussed this in greater detail in my monograph on the Hindu calendar.
The Astronomical Clock (Orloj) in Prague is an amazing invention considering it was first constructed in 1401 AD (coincident with the Vijayanagar Empire and Delhi Sultanate in India). In addition to showing the hour, the Orloj also shows the zodiac positions of the Sun and the Moon as well as the phases of the Moon. It even models the North-South movement of the Sun between the tropics!
The following animation shows the Orloj in action:
This animation illustrates all of the above using an Orloj Simulator available at www.orloj.eu. Keeping the hour at 12 Noon, this animation steps through 365 days starting from March 20 (Vernal Equinox). Three movements vie for our attention:
The zodiac ring rotates clockwise under the sun, i.e. the sun moves anti-clockwise around the zodiac and comes back to its starting position (the First Point of Aries) at the end of 365 days.
The moon too rotates anti-clockwise across the zodiac rapidly. The color of the moon transitions between full white (full moon) and full black (new moon) thus indicating the phases of the moon.
The Sun moves up and down the hour hand (which is stationary at 12 noon). Its movement is limited by the Tropic of Cancer (the golden ring encircling the Roman Numerals) and the Tropic of Capricorn (the golden ring encircling the globe in the center). It transits the equator (the golden ring in-between the other two) twice a year. This movement is of course nothing but the Uttarayana and Dakshinaya of the Hindu Calendar.
Continuing with our investigation of the Orloj, let us now consider the position of the Sun with respect to the Tropics and the Equator in the following snapshot of the Orloj simulator:
The Sun is between the Equator and the Tropic of Cancer; this means the Sun is over the northern hemisphere, i.e. it is either Summer or Fall in Prague (you need some context to fix which is the correct season; if the Sun is getting closer to the Equator day after day, then the season is Fall else Summer)
This further implies the following:
Due to the way the hour “Hand” is constructed, the Sun will never come directly over the Tropic of Cancer and will stop slightly short. The same effect cascades to the Equator and the Tropic of Capricorn, i.e. when the Sun if over the Equator, the Orloj will show it slightly below the Equator.
The above solstice and equinox observations can be made in another, easier fashion – using the zodiac dial. Since the tropic zodiac starts with Vernal Equinox, the following annotated snapshot illustrates the position of the Sun on the Zodiac dial on the equinoctial and solstitial days:
Note that these four positions are highlighted by two crossbars across the zodiac dial making the sign of a cross.
The Orloj models sunrise-unequal hours-sunset as well the four solstitial and equinoctial points by moving the disc of the Sun up and down the hour hand. This movement models the movement of the Sun between the two tropics, which of course causes the lengthening and shortening of day and night thus varying sunrise and sunset times. A perfect example of killing two birds in one stone!
If you are interested in the science behind the construction of the Orloj, check here.
Continuing our investigation of the Orloj, let us now consider the position of the Sun with respect to the unequal hours (aka Babylonian Time) in the following snapshot:
Though the hour “hand” is pointing to VI, the Sun is positioned on the line demarcating the first unequal hour, hence it is one unequal hour after sunrise.
It is now easy to understand that the time when the Sun rises above/sets below the horizon must be the time of sunrise / sunset respectively. The following simulation snapshot shows the time of sunrise at Prague on the 25th Jul:
The Sun is beginning to peep over the horizon at Prague at close to 4:30 AM (4:22 AM to be exact, as shown by the simulator). A quick check on the internet shows 5:22 AM as the sunrise time at Prague. The discrepancy is due to daylight saving time which the ancients who built this clock did not account for.
Since this clock does not have a minute hand it is of course not possible to read 4:22 accurately; based on the position of the hour “hand”, one can only read this, at best, as “sunrise is around 4:30 AM”. Also, it is visually difficult to determine when the Sun is beginning to “peep over” the horizon! Hence, the accuracy of these time readings is, of course, quite limited.
Further, the saffron area labeled “Aurora” demarcates dawn which is rather large in Summer, as it should be.
To understand this ingenious arrangement even better, let us look at sunrise in winter, i.e. six months later on the 25 Jan, 2014:
The clock now shows sunrise close to 8 AM (7:46 AM to be exact, as shown buy the simulator, which corresponds with my internet reference, since there is no daylight saving time in effect in winter). Also note that the dawn (Aurora) is much smaller now (though it is covered by the central disc which is a Polar projection of the Earth). Observe that there is a saffron are which runs right through the “night” indicating there are days when twilight merges with dawn without an intervening night!
Sunset works in a similar fashion – when the golden disk of the Sun goes completely below the horizon, the Sun is deemed to have set and twilight starts. It is worth noting that the Orloj keeps rotating the outermost Arabic numerals dial in such a way that 24 coincides with the time of Sunset, thus implementing the Italian hours.
The saffron colored area below the horizon represents dawn (aurora) and twilight (crepusculum) on the left and right sides of the dial respectively. The horizon itself is marked as ortus (rising) and occasus (setting).
Given the zodiac corresponds to seasons, it is possible to use the Orloj to read the seasons too. I will cover that in my next post.
After having written about the astronomical clock in Venice, I recently heard about another one in Prague built in 1410 AD (603 years back!).
An amazingly ingenious astronomical clock, this Prague Astronomical Clock (Orloj in the Czech language) shows
Of course it requires some training to read all this right. I bought an iPhone app that simulates the Orloj in order to study it in more detail. Here is my annotated guide to the Orloj:
I have not annotated the outermost Arabic numerals (they are not very useful; they represent a timescale, called Italian time, which starts a day from Sunset!) and the small yellow star which helps read sidereal time with respect to vernal equinox (right, something so obscure cannot be very useful).
Now we can read the Orloj snapshot shown above as follows:
While all this is interesting enough, what is mind-boggling is the series of time measure that are modeled by the position of the disc of the Sun. More on that in my next post.
Of places in Venice I found a zodiac clock (originally built in 1493 and restored multiple times):
This clock shows the time is approximately 18:30 (there is no minute hand), the Sun is in Gemini and the Moon is nearing full moon (the disk in the center representing the Earth).
Is this clock showing the tropical or sidereal zodiac?
I checked Stellarium for the date (the photo was taken on 21 May 2013, and the clock shows 18:25):
As can be seen from the above screenshot, the Sun was right around Taurus and had not yet moved into Gemini, hence this clock is not showing the sidereal zodiac surely.
Stellarium shows that the Sun’s Ecliptic longitude was 60° 37′ 58.6” at that time. Hence, by the tropical zodiac the Sun 37′ 58.6′ inside Gemini, i.e. barely inside Gemini. Hence this clock is showing the tropical zodiac.
The clock shows significant traversal insider Gemini and that is quite inaccurate. Clearly the zodiac dial moves along with the hour hand but slightly faster, at a rate that enables the hour hand to traverse the entire zodiac ring in one year. Something seems to have gone wrong with the rate of rotation.
The Moon phase on the other hand seems to be more accurate:
On May 21st, the Moon was waxing and four days away from a full moon. Assuming the Moon dial rotates anti-clockwise (one full rotation in 30 days) that seems just about right – in a few more days the Moon and the Sun will be in opposition on the clock.
Google Earth published some startling time lapse images from 1984 – 2011 showing how a glacier in Alaska and a lake in Azerbaijan have shrunk dramatically (among others).
Here is the image showing the decimation of Columbia Lake, Alaska, presumable due to global warming:
Then I checked Google Earth myself and this is what it shows today (in May 2013):
Same story with Lake Urmia:
Here is what Google Earth shows today:
What exactly is Google Earth (and NASA and others) trying to do here?
Tomorrow (24th Apr) noon the Sun transits right over Bangalore on its march towards the tropic of Cancer.
The above screenshot from Stellarium shows the Sun crossing the meridian over Bangalore at 12:17 and RA/DE (of date) shows a declination of 12 Deg 56 Mins which places the Sun somewhere over South Bangalore.
The Sun crosses 13 Deg N sometime in the night and the next day – the 25th – will find it transiting North Bangalore.
So, listen to Sheryl Crow and go soak up the Sun
And stop complaining about global warming and how hot Bangalore has become. It is all local, buddy! Nothing global about it.