Calendar System -Part III

Continued from previous post

Solar Day:

Before I begin I would like to summarize what we have discussed so far and what need to be always kept in mind.

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(In old Indian system of Astronomy the units of measurement of time were Danda,Pala and Viplava.

60 Danda (or Gahtika)=1 day=24 hours

60 Pal(or Bighatika)= 1 Danda

60 vipal=1 Pal.

So 1 Danda=24 minutes and 1 Pala=24 second

Further we know that in relation to Time we have 1 hour=60 minute=3600 second, but in closed loop positional astronomy (circular or elliptical) 1 degree=60 minute=3600 second. So, the two has to be interpreted as per context. Just as, we  have said that presently(2000 AD) vernal equinox is shifting back by 72 years per degree or 50 second per year (viz. 72*50 second=3600 second=1 degree)

Indian Almanac  shows sunrise/sunset time in both the units that is in Hour/Minute/Second and Gahtika/Pal.

Further Zodiacal belt consists of 27 Asterisms or Constellations. Asterism is a group of stars. There are different numbers of stars in different Asterism ranging from 3 to 30. There is, however, a little difference between Asterism and Constellation. An Asterism may consist of more than one constellation. There are total 88 constellations discovered so far. But for practical purpose we can take the two to represent the same thing.    

In tropical system the belt of 27 asterisms is divided into 12 signs. In Indian or sidereal system it is divided into 12 Rashis. The span of Rashi is slightly greater than that of Sign. All the planets move in this belt, as seen from earth, in anticlockwise direction (GeoCentric view). Earth also precess around normal to ecliptic plane in anticlockwise direction. As a result Vernal equinox and the beginning point of each sign of tropical system also moves in clockwise direction. We have discussed that tropical belt is little shorter than sidereal belt. Sidereal belt starts at 0 degree Aries end ends at exactly same point 0 degree Aries. But tropical belt starts at around 5 degree Pisces which is the vernal equinox point presently (2000 AD) but ends a little earlier because by the time Sun is likely to come back to the starting point, Vernal equinox point would have shifted behind by 50 second. In both the system the belt starts with Aries sign and continues ahead in the identical  order. But in tropical system this beginning point is moving behind in clockwise direction. So it appears that entire zodiacal belt is moving in clockwise direction with the same rate. To remind the order of Signs or Rashis in anticlockwise direction is-ARIES, TAURUS, GEMINI, CANCER, LEO, VIRGO, LIBRA, SCORPIO, SAGITTARIUS, CAPRICORN, AQUARIUS, PISCES.

It need not be reminded that  Earth has been divided into longitudes and latitude. The longitude at Greenwich, UK, is taken to be standard from the point of view of standardizing time.-Indian standard time is based upon 83.20 degree longitude and is ahead of Greenwich mean time by 5.30 hours( a change of 4 minute of time per degree). We may discuss this issue while discussing the three concepts of time –that is Local, Standard and Sidereal.

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We will discuss the concept of ‘Day’ first followed by that of ‘Month’.

One Solar/tropical day is the time taken by earth in two successive sunrises. The mean tropical day is 24 hours. But in this process earth has to rotate by 361 degree in space, which is 1 degree more than the same for one rotation of earth around its own axis. Earth rotates around its own axis by 360 degree in 23 hours 56 minute and 4 second( so approximately 1 degree in 4 minute). This time is called sidereal day. By the time earth rotates by this 360 degree around its axis it also moves ahead by around 1 degree along ecliptic. So from earth it appears that sun is going back ( in heliocentric view) by the same rate.  So, for the sunrise the time taken is 4 minutes more than the sidereal day time, or say span of tropical day is 4 minutes more than that of sidereal day. Sidereal day may be called the length of day as measured with respect to a fixed star or point in heaven. But position of Sun is not fixed, as discussed. It appears to be going back by a rate of  1 degree per tropical day because of earth’s movement along ecliptic. So with respect to Sun the length of tropical day, that is time taken between two sunrises, is 4 minute more than time taken by earth to rotate around its axis. So, though it appears that in the process earth has rotated by 360 degree around Sun, but basically it has rotated by 361 degree in space. Regarding the issue of temporal day and night, the time of the two go on varying throughout the year in a fixed pattern, but the total time for day+night is always 24 hours. It is almanac issue because rate of rotation of earth around its axis is not constant, only that total time taken per day+night is constant.  However these 24 hours is also a mean figure. Actually the solar day also differs from day to day, though very minutely, due obliquity of ecliptic with earth’s equator or say due to obliquity of Sun’s path. But for reckoning purpose it is standardized as exactly 24 hours of clock. Sidereal day is used only for Astrological concept of sidereal time. As we will see that in Indian systems day is also measured on Lunar basis called Tithi. It is the time taken by moon to move ahead in ecliptic by 12 degree.  One Tithi  comes to be around .984353 days and may start anytime in day or night. We will come back to this issue in Lunar Section.

In Solar/Sidereal systems, such as Indian system, the day begins with Sunrise. In Lunar system, such as Islamic, day begins with Sunset. However Christian day, which is of course Solar/tropical, begins with 12 ‘o’ clock night. Practically we know that for official purpose we follow Christian day.

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Solar Month:

Tropical month stands for time taken by Sun to travel through one Sign. It comes to be 30.47 days as an average. Similarly sidereal month stands for time taken by Sun to travel through one Rashi. This comes to be 30.48 days as an average. We have already discussed the difference between Sign and Rashi. Lunar month is a little different issue. Sidereal months are named in accordance with the Sun occupying a particular Rashi. But in India practically Luni-Sidereal(Religious)  and Luni-Tropical(official) systems are followed as per which months are named in accordance with the near full-moon occupying a particular Asterism at a given time of the year. We will discuss this issue next. Names of Tropical month as followed in European Calendars are based on Christian Calendar. However number of days to be 30-31 or even 28 in a month is matter of convention followed in Christian Calendar which though begins with January but is still tropical in nature. We will discuss these issues later on in the context of Christian Calendar.

In this context the issue of Sun itself being mobile or say moving around due to a system of Binary star is of no consequence for Calendar system. However it may be correlated with precessional motion of the earth. According to some the precession by whole 360 degree may not be possible.

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Lunar: To be continued……….

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