How do I find the day of the week for any date?

There are two popular formulas that you can use to find the day of the week for a given date. You should be careful when you use these formulas, though, because they only work for the Gregorian calendar. (People in English-speaking countries used a different calendar before September 14, 1752.)

Zeller's Rule

The following formula is named Zeller's Rule after a Reverend Zeller. [x] means the greatest integer that is smaller than or equal to x. You can find this number by just dropping everything after the decimal point. For example, [3.79] is 3. Here's the formula:

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] - 2*C.

k is the day of the month. Let's use January 29, 2064 as an example. For this date, k = 29.

m is the month number. Months have to be counted specially for Zeller's Rule: March is 1, April is 2, and so on to February, which is 12. (This makes the formula simpler, because on leap years February 29 is counted as the last day of the year.) Because of this rule, January and February are always counted as the 11th and 12th months of the previous year. In our example, m = 11.

D is the last two digits of the year. Because in our example we are using January (see previous bullet) D = 63 even though we are using a date from 2064.

C stands for century: it's the first two digits of the year. In our case, C = 20.

Now let's substitute our example numbers into the formula.

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] - 2*C= 29 + [(13*11-1)/5] + 63 + [63/4] + [20/4] - 2*20= 29 + [28.4] + 63 + [15.75] + [5] - 40= 29 + 28 + 63 + 15 + 5 - 40= 100.

Once we have found f, we divide it by 7 and take the remainder. Note that if the result for f is negative, care must be taken in calculating the proper remainder. Suppose f = -17. When we divide by 7, we have to follow the same rules as for the greatest integer function; namely we find the greatest multiple of 7 less than -17, so the remainder will be positive (or zero). -21 is the greatest multiple of 7 less than -17, so the remainder is 4 since -21 + 4 = -17. Alternatively, we can say that -7 goes into -17 twice, making -14 and leaving a remainder of -3, then add 7 since the remainder is negative, so -3 + 7 is again a remainder of 4.

A remainder of 0 corresponds to Sunday, 1 means Monday, etc. For our example, 100 / 7 = 14, remainder 2, so January 29, 2064 will be a Tuesday.

The Key Value Method

This method uses codes for different months and years to speed up the calculation of the day of the week. You might even be able to memorize the codes. We'll use December 16, 2482 as an example.

Take the last 2 digits of the year. In our example, this is 82.

Divide by 4, and drop any remainder. 82 / 4 = 20, remainder 2, so we think "20."

Add the day of the month. In our example, 20 + 16 = 36.

Add the month's key value, from the following table.

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

1 4 4 0 2 5 0 3 6 1 4 6

The month for our example is December, with a key value of 6. 36 + 6 = 42.

If your date is in January or February of a leap year, subtract 1. We're using December, so we don't have to worry about this step.

Add the century code from the following table. (These codes are for the Gregorian calendar. The rule's slightly simpler for Julian dates.)

1700s 1800s 1900s 2000s

4 2 0 6

Our example year is 2482, and the 2400s aren't in the table. Luckily, the Gregorian calendar repeats every four hundred years. All we have to do is add or subtract 400 until we have a date that is in the table. 2482 - 400 = 2082, so we look at the table for the 2000s, and get the code 6. Now we add this to our running total: 42 + 6 = 48.

Add the last two digits of the year. 48 + 82 = 130.

Divide by 7 and take the remainder. This time, 1 means Sunday, 2 means Monday, and so on. A remainder of 0 means Saturday. 130 / 7 = 18, remainder 4, so December 16, 2482 will be on the fourth day of the week-- Wednesday.

Here is a standard method suitable for mental computation:

(1) Take the last two digits of the year.(2) Divide by 4, discarding any fraction.(3) Add the day of the month.(4) Add the month's key value: JFM AMJ JAS OND: 144 025 036 146(5) Subtract 1 for January or February of a leap year.(6) For a Gregorian date, add 0 for 1900's, 6 for 2000's, 4 for 1700's, 2 for 1800's; for other years, add or subtract multiples of 400.(7) For a Julian date, add 1 for 1700's, and 1 for every additional century you go back.(8) Add the last two digits of the year.(9) Divide by 7 and take the remainder.

Now 1 is Sunday, the first day of the week, 2 is Monday, and so on.

Comments by me:

(a) You would have to memorize the key values of Step 4.(b) You would have to memorize the century values of Step 6 or 7.(c) A remainder of 0 would give you Saturday at the end.(d) You could cast out 7's as you go along if you wish, to keep the number small, and then step 9 is redundant.(e) You can do steps (1 and 2), 3, 4, 5, and 6 in any order. As soon as someone starts to tell you the date "July ..." you can do step 4, and probably reject doing step 5; then when he says "... 8th..." you can do step 3. When he says "... 19 ..." you can do step 6. This makes it seem as though you have done all the calculation after hearing the date, whereas you have done some of it *while* hearing it.

The example of July 8, 1954, would go like this:

(1) 54 (2) 54/4 = 13 (3) 13 + 8 = 21 (4) 21 + 0 = 21 (5) 21 - 0 = 21 (6) 21 + 0 = 21 (8) 21 + 54 = 75 (9) 75 - 7*10 = 5 <--> Thursday.

Casting out 7's would give:

(1) 54 (2) 6 (3) 0 (4) 0 (5) 0

(6) 0 (7) 5 <--> Thursday

The reasons why this works are fun to figure out. You might like totry it. If we can be of further assistance, let us know.

Here is a formula for finding the day of the week for ANY date.

N = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2

where d is the number or the day of the month, m is the number of the month, and y is the year. The brackets around the divisions mean to drop the remainder and just use the integer part that you get.

Also, a VERY IMPORTANT RULE is the number to use for the months for January and February. The numbers of these months are 13 and 14 of the PREVIOUS YEAR. This means that to find the day of the week of New Year's Day this year, 1/1/98, you must use the date 13/1/97. (It sounds complicated, but I will do a couple of examples for you.)

After you find the number N, divide it by 7, and the REMAINDER of that division tells you the day of the week; 1 = Sunday, 2 = Monday, 3 = Tuesday, etc; BUT, if the remainder is 0, then the day is Saturday, that is: 0 = Saturday.

As an example, let's check it out on today's date, 3/18/98. Plugging the numbers into the formula, we get;

N = 18 + 2(3) + [3(3+1)/5] + 1998 + [1998/4] - [1998/100] + [1998/400] + 2

So doing the calculations, (remember to drop the remainder for the divisions that are in the brackets) we get;

N = 18 + 6 + 2 + 1998 + 499 - 19 + 4 + 2 = 2510

Now divide 1510 by 7 and you will get 358 with a remainder of 4. Since 4 corresponds to Wednesday, then today must be Wednesday.

You asked about New Year's Day, so let's look at this year, 1/1/98. Because of the "Very Important Rule," we must use the "date" 13/1/97 to find New Year's Day this year. Plugging into the formula, we get;

N = 1 + 2(13) + [3(13+1)/5] + 1997 + [1997/4] - [1997/100] + [1997/400] + 2

N = 1+ 26 + 8 + 1997 + 499 - 19 + 4 + 2 = 2518

Now divide 2518 by 7 and look at the remainder: 2518/7 = 359 with a remainder of 5. Since 5 corresponds to Thursday, New Year's Day this year was on a Thursday.

In your FAQ, you give the following formula for finding the day of theweek for a given date:

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] - 2*C

But in your archive, you give a different formula:

N = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2

Obviously these two formulas are equivalent, but I can't see why. Why the 2m? Why the +2? Could you be so kind as to explain thisequivalence? I guess I'm trying to understand why the formula works; what is the underlying idea. The 2m and the +2 throw me.

The first thing to do is to note the differences:

In the FAQ,

f = k + [(13*m-1)/5] + D + [D/4] + [C/4] - 2*C

"m" is the month number starting with March as 1; "k" is the day of the month; the year is given by C, the century, and D, the last two digits; in the result, 0 means Sunday.

In the alternative formula,

N = d + 2m + [3(m+1)/5] + y + [y/4] - [y/100] + [y/400] + 2

"m" is the month number starting with January as 1; "y" is the year; in the result 0 means Saturday.

So if we try to write the latter using the variables of the former, wewill have to replace

d with k m with m+2 (so March is 3) y with 100C+D and subtract 1 from N to get f (so Sunday is 0).

We get

f = N-1

= k + 2(m+2) + [3((m+2)+1)/5] + (100C+D) + [(100C+D)/4] - [(100C+D)/100] + [(100C+D)/400] + 2 - 1

= k + 2m + 4 + [3(m+3)/5] + 100C + D + [25C + D/4] - [C + D/100] + [C/4 + D/400] + 1

= k + 2m + 4 + [3m/5 + 9/5] + 100C + D + 25C + [D/4] - C - 0 + [C/4] + 0 + 1

= k + [10m/5 + 4 + 3m/5 + 9/5 + 1] + 124C + D + [D/4] + [C/4]

= k + [(13m + 4)/5 + 6] + D + [D/4] + [C/4] + 124C

= k + [(13m-1)/5 + 7] + D + [D/4] + [C/4] + 124C

This isn't quite right, is it? Unless

7 + 124C = -2C,

it can't be the same.

Ah! I realized what we're missing when I tried checking this by doing each calculation for a specific date: the answer is not this whole expression, but the remainder when we divide by 7. The two forms will be the same if

7 + 124C = -2C (mod 7).

And since 124 = 7*17 + 5 = 7*18 - 2, it is in fact true that the remainder of the left side, 7*(1+18C) - 2C, will be the same as the remainder of -2C. The two formulas are indeed equivalent.

The Tropical Zodiac is the position of the sun referenced against the earth’s horizon at a particular locale which gives you the seasons as a measure of the flow of time. The framework for

the 4 seasons are the 2 solstices and the 2 equinoxes. This is the one most western astrologers use.

The Sidereal Zodiac is the position of the sun referenced against the star background, as a measure of the flow of time. The framework for the star background is the constellations the sun passes in front of. This is the one astronomers use.

We can measure time by the seasons (tropical time) or by the stars (sidereal time). The sun, as the time hour hand, is common to both.

To expand on the nutshell.

Tropical Zodiac. Most people know what their birth sign is. They may be a “Leo” or a “Taurus” or one of 10 other signs of the Tropical Zodiac. What does it mean? It means that at the time of their birth, from an earth perspective, the sun was in 1 of 12 zones around the earth. Each of the 12 has an angular length of 300. 12 X 300 =3600. The frame of reference for these zones is the sun’s positions relative to the earth’s horizon. As the sun moves through the seasons its altitude changes and so do the compass bearings of its rising and setting positions. None of these signs can be directly related to a group of stars that can be seen in the skies with one's physical eyes.

            Example 1; If you were born on the March Equinox your birth sign would be 0 0 Aries and the sun would have risen exactly in the east and set in the west. The sun travelled directly over the equator all that day before crossing into the northern hemisphere the next day. March Equinox and 00 Aries are synonymous.

            Example 2: If you were born on the June Solstice your birth sign would be 00 Cancer and the sun would have risen in the northeast and set in the northwest. The sun travelled directly over the northern hemisphere Tropic of Cancer all that day. The Tropic of Cancer is as far north as the sun gets in the course of the year (for an earth based observer).  June Solstice and 00 Cancer are synonymous.

Example 3; If you were born on the September Equinox your birth sign would be 00 Libra and the sun would have risen exactly in the east and set in the west. The sun travelled directly over the equator all day before crossing into the southern hemisphere on the following day. September Equinox and 00 Libra are synonymous.

            Example 4: If you were born on the December Solstice your birth sign would be 00 Capricorn and the sun would have risen in the southeast and set in the southwest. The sun travelled directly over the southern hemisphere Tropic of Cancer all that day. This is as far south as the sun gets in a year. December Solstice and 00 Capricorn are synonymous.

            For 6 months of the year the sun travels northward until it is over the Tropic of Cancer, it then turns and travels southward until it is over the Tropic of Capricorn and turns yet again. The word tropic is derived from the Greek tropikos - belonging to a turn. The Sun turns at the solstice points. It turns from getting lower and lower in the sky at midday (heading to midwinter) to start climbing higher and higher (heading to midsummer) and vice versa.

The cross of these 4 signs is the frame of the Tropical Zodiac which is then farther subdivided into 12.

To compile the Tropical Zodiac no reference was made to any stars.

Let us now look at the Sidereal Zodiac. At this stage it is important to clarify the use of two words. When the word ‘sign’ is used in this article it refers to the Tropical Zodiac and ‘constellation’ refers to the Sidereal Zodiac. Both zodiacs are divided into twelve and they both use the same names, which understandably causes enormous confusion. If your birth ‘sign’ is Pisces it does not necessarily mean that the sun was in front of the ‘constellation’ of Pisces at your birth. Your birth ‘constellation’ is different to your birth ‘sign’. What earth season (i.e. sun declination or latitude) you were born in is different to what stars where behind the sun at the hour of your birth. The Sidereal Zodiac uses the physical stars visible in the night sky as their frame of reference for the sun, moon or planet’s positions in the sky. The sun, moon and planets do not transit in front of all the constellations in the sky, they only traverse in front of 12 or 13. These are the zodiacal constellations. Whether there are 12 or 13 depends on where the boundaries for the various constellations are positioned. Different cultures and systems have positioned them differently i.e. there is no universal consensus to the boundaries or even to the size of the constellations. Generally speaking the sidereal zodiac (as seen by a person standing on the earth) is that belt of stars 70 either side of the sun’s path (ecliptic) through the sky that is divided into 12 equal sized (300) constellations.

This zodiac is like a freeway with a central lane (ecliptic) on which the sun travels. The moon and planets also travel on this freeway but on different lanes. They do, however, cross each other’s lanes at times (nodes). The word sidereal is derived from Latin sidus ‘star’.

Sidereal Zodiac Wheel Diagram (Southern hemisphere perspective)

Both zodiacs use the names Aquarius, Pisces, Aries etc for their twelve fold divisions. Little wonder that there is confusion! For this article the ‘signs’ use the nomenclature Aquarius, Pisces, Aries etc., and the equivalent ‘constellations’ are named The Water Bearer, The Fish, The Ram etc.

Can the two zodiacs be compared against each other?

If we represent both of them as spokes on a wheel as done in the diagrams we can superimpose them on a single hub as, in this case, they are both geocentric and the hub is the earth. NB The sidereal zodiac can be considered from a heliocentric perspective too. To align the seasons relative to the stars we now use the sun which is also common to both zodiacs. The sun’s position at the March equinox (00 Aries) is measured against the star background and is currently near the beginning of The Fish constellation. How many degrees into the The Fish depends on which constellation boundaries you are using. By comparing the two wheels you can see that there is a difference of around 250 between them. By making this comparison over time it has been realized that the difference is increasing, the seasons are slowly moving relative to the star background by a degree every 70 odd years. This phenomenon is known as the "Precession of the Equinoxes". It takes 2160 years for the equinoxes and solstices to move backwards through each constellation. This retrograde movement determines our cultural ages. We are in the ‘Age of Pisces’ and moving towards the ‘Age of Aquarius’.

Sidereal Zodiac (outer wheel) + Tropical Zodiac (inner wheel)

A bigger picture of the zodiacs

If we now take what has just been covered and go back to the quotes at the beginning of the article we can come to a realisation that the heavenly zodiac (sidereal) is imprinted into the earth (tropical zodiac). This takes us out of the abstraction of wheels (which can be useful) into something more real, if it is correct. The forces behind the stars of the zodiac have their imprint as forces within the earth.

The question is then begged: "What is the cause of these forces, where do they come from?" On earth human beings create farms, buildings, works of art etc. That is to say from actions, deeds of beings. Do super sensible beings bring about universal forces through their actions? Creator Beings are described in mythos and sacred books across most cultures.

Mapping

If the tropical zodiac is indeed an imprint of the heavens onto the earth we could map it onto the earth and possibly learn something about the earth and its regions as a consequence.

To do this we have a heavenly start point in the sidereal zodiac at 00 of The Ram.

We have a start point in the tropical zodiac (00 Aries)

We also have a starting point on the earth at the longitude line going through Greenwich in London. Our time zones are based on these lines or meridians of longitude.

NB. The lines of longitude are based on the equator and the geographic poles.The Zodiac is not based on the celestial equator but the ecliptic so what I have said is not a strict equivalency for current times. However I have chosen to take a position that in much earlier times the Earth's axis did not have a tilt and its axis was vertical which would make the ecliptic and the celestial equator the same.

Some researchers also choose to take Jerusalem as their 00 longitude point (rather than Greenwich).

"Are these starting points arbitary intellectual constructs or has there been some subconscious wisdom at work in humanity?" is another question we have to ask.

In my work I have chosen to offset the tropical zodiac 230 (rather than 250 which you could well do) from the sidereal so in order to do this projection of the heavens onto the earth I have lined up the 00 Aries 230 back from Greenwich which takes it to the 230 West longitude going through Iceland.

NB to arrive at 230 offset from Greenwich I am using the weather researcher Dennis Klocek’s work (www.weatherdoc.com). I have done so because he is a respected current day researcher in the realm (weather) that I am investigating. I have yet to form conclusions about its validity.

Astrologers also use a system of ‘houses’ for their interpretations. What is the house system?

Essentially the sun, moon or planets position relative to the earth’s horizon can be related to four key positions –where it rises,where it culminates or reaches its highest point above the horizon - Medium Coeli, where it sets and its lowest point below the horizon - Imum Coeli.

From this fourfold framework there is a farther trisection giving 12 zones or houses. These houses are horizon dependant and latitude affected whereas the ‘signs’ are longitude dependant. There are many house systems. The chart below shows a equal-sized house system from a northern hemisphere perspective (east is on the left side).

Where the sun, moon or planet is relative to the horizon is important in weather forecasting especially for the timing of an event within a 24 hour framework. The Antipodean Astro Calendar and the Northern Hemisphere Star Calendar has the essential foundation of the house system (4 key positions -ascendant, MC, descendant and IC) built in for the moon. They can be also be deduced for the planets from the information in the calendars.

Sayana And Nirayana Chakra: Understanding Ayanamsha

By Deborah Allison

This is the second in a series of articles that highlight the unique features and tools of Vedic Astrology when compared to other astrological traditions.

All Vedic astrologers have to deal with the identity crisis that inevitably occurs when clients who are used to Western chart readings, or who simply skim the "Your Horoscope" column in the local newspaper, encounter Jyotish for the first time. Even Jyotish "diehards" may not really understand why there is not alignment between something as basic as the calculation of what sign and degree a planet occupies in these two systems.

The answer lies in the point of reference used for this all- important calculation. Western Astrology relies on what is known as the Tropical Zodiac (Sayana cakra), which uses the Vernal Equinox as the point of reference. The Indian system - Jyotish - uses the Sidereal Zodiac (Nirayana cakra), which adopts a fixed star as the point of reference.

The reason for the discrepancy between these two systems is that there is a "wobble" in the rotation of the earth on its axis. As a result, the Sun does not return exactly to the same point of 0 degrees Aries each spring at the vernal equinox as observed from a fixed star. It misses by a tiny amount (around 50 seconds of arc according to the most widely used reference point). This may not seem to matter much, but when it accumulates over the years, the vernal

equinox is seen to slip back and back into the sign of Pisces then eventually Aquarius and so on. This phenomenon is known as precession of the Vernal Equinox.

At the present time, the discrepancy between these two systems is about 23 degrees, 57 minutes. This ever-increasing difference is known as the ayanamsha (moving part). If you subtract the daily specific ayanamsha from the planet's position in a Western tropical chart, you will get its location in the Vedic Sidereal Chart.

A Western Astrologer is going to fix the Vernal Equinox as 0 degrees Aries regardless of whether the Sun is actually observed against the backdrop of the stars in the constellation of Aries on that particular day and year. In fact, eventually, there can be the bizarre situation where the Sun is actually observed by astronomers in the sign of Libra and a Western astrologer says it is in Aries - the opposite sign of the zodiac! This may be a contributing factor to the typical modern astronomer's negative opinions about astrology. However, as all astrology is, at its heart, a divination system, the important thing is how well the astrologer integrates any system with the cognitive faculty of intuition.

Jyotish, in turn, always establishes the planetary position against the backdrop of the fixed stars so that real-time observation matches the chart positions. The Sayana cakra or Tropical Zodiac is used in Jyotish to a limited extend for some aspects of calendar calculations. However, the all-important mapping of the heavens for the purposes of divination strictly uses the positions of the planets against the Fixed or Sidereal Zodiac – the Nirayana cakra.

Since the stars in the constellation of Aries are very dim, the reference star used for "pointing" to the all important beginning of the zodiac of 0 degrees Aries is one of the brightest stars in the heavens. Westerners refer to it as Spica but it is known as Citra in Jyotish. Citra is the marker star for one of the 27 nakshatras that bears the same name. Its brightness is reflected in the symbolism of that nakshatras which is known as "the shining jewel." The ayanamsha based on using Citra as the reference star is known as the Citra Paksha ayanamsha or the Lahiri ayanamsha and is the most widely used in India.

However, if you have had your chart done by several Jyotishis, you may find some minor discrepancies in the positions of your planets. This is due to the fact that there are variant opinions on the ayanamsha, and in some charts, this can result in dramatic displacements either in the main chart or in some of the subtler divisional charts.

GREATNESS OF INDIAN ASTROLOGY |

Greatness of Indian vedic Astrology

Indian vedic astrology history and pioneers

Vedas are the oldest literature and compendium of multitude of Knowledge. The history of Astrology traces back to Vedic times, lakhs of years ago from now. Astrology can be divided broadly as Siddhanta Bhaga (Calculation part) and Phalita Bhaga (Predictive part). In Rigveda, the year is divided into 12 months, the special 13th month called extra month correlates the Solar and Lunar months. In Taittireeya Brahmana, the 6 seasons are described. The details of planets as gods, solar and

lunar eclipses are available in Rigveda.

The oldest available book on Astrology is ‘Rigjyothisha’, written by Lagadha. In this book, there are 5 types of years described, along with the ruling deities. The 2 ayanas (parts) of the year are also mentioned, along with their starting stars. Precision of equinoxes are explained. And the 27 stars are also given in this book.

There are 18 pioneers in Astrology, who contributed for its development. They are: 1. Surya, 2. Pitamaha, 3. Vyasa, 4. Vasishta, 5. Atri, 6. Parasara, 7. Kasyapa, 8. Narada, 9. Garga, 10. Mareechi, 11. Manu, 12. Angeerasa, 13. Lomasa, 14. Poulisa, 15. Chyavana, 16. Yavana, 17. Bhrigu, and 18. Saunaka.

Varahamihira (123 AD) wrote ‘Brihat Samhita’, a great work on Astronomy and Astrology. There are 105 chapters and 4000 verses in this book. He has shown how Astrology can be applied for the welfare of public.

Aryabhatta-I (476 AD) wrote ‘Aryabhateeya’, which comprise a great deal of Astronomy, Mathematics and Astrology. Even Astronomy of this book is spread to Arab countries. Aryabhatta-II (950 AD) wrote ‘Mahasiddhanta’, where he explained more clearly about calculation part of Astrology.

Bhaskara-I (629 AD) wrote ‘Mahabhaskareeya’, a book on astro-mathematics. Bhaskara-II (1114 AD) gave ‘Siddhanta Siromani’ where a lot of Mathematics can be found. Details of square, square root, cube, cube root, factorial values, factors of a number are explained. Details of planets, calculation of radius of earth , eclipses, and atmospheric layers ( 7 zones) above earth are discussed clearly.

Zodiac is the outer wheel from where the radiation from different celestial bodies is received, filtered and sent to earth. Indian Astrology links the planets and stars with gods. Gods are representatives of certain types of energies. The entire Zodiac chart is divided into 12 signs, starting from Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. There are 4 things to be done in a human life: Dharma (righteous path), Artha (wealth), Kaama (Desire), Moksha (Unification of soul with God). These are one by one represented by the 12 houses of the zodiac. The hidden meaning is: A man should follow righteous path to achieve wealth and fulfill his desires. At the same time he must be desirous to reach God, and find ways to finally unify himself with the super soul. The potentiality to achieve this is represented step wise by the zodiac.

Theory says that Zodiac wheel starts with Aries 0 degrees, and is constant. When a top is rotating , it bends slightly and rotates. If a point is imagined on the top , it make circles. These circles will not coincide each other. There will be some deviation between each circle. Similarly, the Zodiac is also deviating slowly from its constant position. It is calculated to be around 51 seconds per year. This deviation is called Precession of equinoxes, or Ayanamsa. Indian Astrologers are not taking this

Ayanamsa into account when they calculate Planet positions. So their system is called ‘Nirayana’. But westerners apply this correction in their calculations. So western system is called 'Sayana' system. This is the major difference in Indian and Western Astrological worlds.

Sayana = Nirayana + Ayanamsa.

There are 27 stars and each star has 4 padas (quarters). Thus a total of 27 x 4 = 108 star padas will will arise, which have been distributed in the zodiac. Since 12 signs are there in the Zodiac, every sign gets 9 padas. Each pada is of 3 degrees 20 minutes duration and 9 x 3deg 20min = 30 degrees. So each sign takes 30 degrees duration.

There are planets whose role is to bestow the results of past deeds, done either in this birth or carried from previous births. Planets merely transmit the results which we earlier stored in the form of radiation. There are 9 planets identified: Sun, Moon, Mars, Jupiter, Saturn, Mercury, Venus , Rahu (Ascending Node) and Kethu (Descending Node). All the planets are not comfortable in all the signs. A planet is comfortable in its exaltation, or friendly or own house. Then it may give good results. A planet is not comfortable in enemy camp, and can give bad results.

Each planet aspects its opposite planet, i.e, the house and planet in 7th from it. Additionally, Jupiter has 5th and 9th aspects. Mars has 4th and 8th aspects. And, Saturn has 3rd and 10th aspects.

By observing the inter-relationships between the signs, planets, stars and their positions, we can understand the inherent capabilities of a human being, his thought process, and his weaknesses, and finally conclude what he has in store for his future. Various Dasa- systems are developed to know what planets are currently influencing a human being and promoting him to do what kind of things.

Indians call planets 'Grahas'. Graha means that which catches. Grahas are those which catch the human beings and shed their influence on them. Grahas affect all inanimate and animate objects in this world. This is the reason Grahas are also personified as gods by Indians. Another greatness of Indian Astrology lies in providing remedial measures for various problems faced by human beings. The remedies are mentioned by sages in various works and also in Vedas. But the suitability of a remedy for a case is to be judged by a competent astrologer.

Indians see Astrology in every thing. It became a part and parcel of their culture. For them Astrology is ‘VedaChakshu’, the guiding eye for molding their future and attaining self- realization.

A TALE OF TWO ZODIACS

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By Antardwipa Dasa, (edited by ShyamasundaraDasa)

Over the course of 2012, a number of articles have been published regarding the tropical and sidereal definitions of the zodiac, and which of these is to be used for Vedic astrological purposes. These publications have mostly urged for a new approach to jyotish (Vedic astrology); although the authors generally claim that their presentations are actually the most traditional. One such article is, The 12 Signs of the Zodiac, by Vraja Kishor das. Some of the ideas presented therein are misleading, and therefore, for my own edification, and for the satisfaction of those who are knowledgeable, I would like to present the following to the esteemed readers.

For those not familiar with this ongoing discussion, the basic question under debate is, “Where does the circle of the zodiac begin? ” Or, framed in greater detail, “When constructing a horoscope, do we use the longitudes of planets as measured from the position of the sun when it is at the vernal equinox (tropical zodiac) or from a specified fixed star (sidereal zodiac)?”

This question has at times been hidden behind the inquiry as to whether the sidereal rasis (signs of the zodiac) match the constellations that exist as patterns of stars in the sky. Vraja Kishor presents the argument that there are thirteen constellations that make up the zodiac, and that they are of varying sizes; some larger than thirty degrees and some smaller. As such, these constellations do not match the twelve rasis of the sidereal zodiac. He concludes, therefore, that the zodiac signs (rasis) have nothing to do with the stars, and as a result:

“Once we realize that the zodiac signs have nothing to do with stars, we don’t really feel compelled to use the stars to define where they begin. In fact we feel quite compelled to use the point where the center of space is, where the equinox is, where the ecliptic crosses the equator.”

Although it is unclear what is meant by the term ‘center of space’, we shall ignore that and focus on his rejection of sidereal rasis. Vraja Kishor clearly believes that the rasis have nothing to do with the stars. This can be seen in another of his articles, Reconciliation of the Tropical and Sidereal Zodiacs, where he states:

“There is a sidereal zodiac in Indian astrology, and probably in all ancient great astrological systems. Yet this sidereal zodiac is not twelve but twenty-eightfold!”

We must note, however, that the statements of the Jyotir Veda reveal this assertion to be false, and that there is in fact an authentic twelve-fold division of the stars. To prove this, we may begin by referring to the Surya-siddhanta 1.28. Vraja Kishor also quotes this verse, and correctly points out that it describes a rasi as being the geometrical division equal to one-twelfth of the circumference of a circle. Unfortunately, it appears that he has not fully grasped the significance of this.

All circles may be divided in this twelve-fold way, with the first thirty degree arc being known as Mesha, the second known as Vrishabha, and so on; covering the twelve familiar names of the rasis used in jyotish. This is the standard treatment given to arcs in traditional Indian geometry. Being applicable to all circles, it is nonsensical to claim that the circle of stars is not similarly composed of these same twelve rasis. Thus, it is irrelevant whether or not the visible constellations match the twelve sidereal rasis, because the sidereal zodiac is a circle, and therefore it naturally contains twelve divisions known as rasis.

More importantly though, this verse describing the layout of rasis on a circle comes immediately after a verse stating that planetary revolutions are to be counted from the end of Revati nakshatra. That the nakshatras are constellations of stars is undeniable and is accepted by all authors. Thus, in Surya-siddhanta 1.27, a specific point amongst the fixed stars is referenced as the point of zero degrees longitude, or the beginning of the circle of revolution, and then in the next verse, the divisions of that circle into twelve rasis is described. Considering the content and placement of these verses, it is unwise to conclude that the rasis have nothing to do with the sidereal zodiac, or that sidereal rasis are not presented in the Vedic texts.

To make this argument even more compelling, we may consider the Sanskrit terminology used. Surya-siddhanta 1.27 states:

tesam tu parivartena pausnante bhaganah smrtah

“The planets’ revolutions are counted complete at the end of Revati nakshatra.”

Thus, a bhagana (planetary revolution) is counted as complete with respect to the end of a constellation of stars, Revati, which is also known as Paushna. After Revati comes Ashvini, and therefore, Ashviniis taken as the first nakshatra when considering the longitude of planets. Then in verse 1.28, it is said:

vikalanam kala sastya tat sastya bhaga ucyatetat trimsata bhaved rasir bhagano dvadasaiva te

“Sixty seconds (vikala) make a minute (kala); sixty of these, a degree (bhaga); thirty of the latter is composed a sign (rasi); twelve of these are a revolution (bhagana).”

The term ‘bhagana‘ has been used in both of these verses. The circle of one revolution of a planet is known as a bhagana. After being described as beginning at the end of Revati nakshatra, it is then said to be composed of twelve rasis, each of which is thirty degrees. Thus, it is clear that these two verses, when taken together and understood correctly, indicate that the zodiac of twelve rasis, through which planetary movement is to be reckoned, has a beginning that is fixed in relation to the stars. Hence, it is clearly a sidereal zodiac composed of twelve rasis.

Furthermore, the term ‘bhagana‘ indicates that planetary longitudes are to be reckoned against the background of the stars. ‘Bhagana‘ literally means ‘the multitude of stars’, and thus it indicates the circle of the stars, or sidereal zodiac. That this very same term is used to describe a single revolution of each of the planets indicates that their movements are measured on this sidereal zodiac.

Aside from this, Vraja Kishor quotes other verses from the Surya-siddhanta to establish that a tropical definition of the rasis is given in that authentic text. Importantly, these other quotations do not nullify the explanation just given. Rather, it must be acknowledged that the Jyotir Veda describes both the nirayana cakra (sidereal zodiac) and the sayana cakra (tropical zodiac), and that each of these zodiacs is composed of twelve rasis. Thus, providing instances of a tropical definition does not discredit, nor override, the other statements that present and define the sidereal zodiac.

From the above, it is evident that simply knowing of the existence of the two zodiacs is not sufficient; one must also know how and when to use each appropriately. In this regard, we find in the Surya-siddhanta, 3.10, that the tropical zodiac is described as being used for the determination of kranti (declination), chaya (the shadow of the sundial) and caradala (length of time for signs to rise). Of course, other unspecified applications are also implied in this verse by the use of the word ‘adikam,’ which means ‘beginning with’ or ‘et cetera‘. Verses 3.46 − 49 describe some of these other calculations that are made with the help of the sayana cakra; in particular, the calculation of the lagna (ascendant) and madhyalagna (meridian).

What is important to note, is that planetary longitude is not listed amongst the items that are to be calculated using the tropical zodiac. Rather, Jyotir Veda presents the sidereal zodiac as the fixed basis of calculation, and all longitudes are naturally determined according to that measure. This is highlighted by the arrangement of chapters within the Surya-siddhanta: the first two chapters provide all calculations for determining the true longitude of the planets. It is only after such longitudes are calculated, that the topic of ayanamsa is presented in the third chapter. This calculation (the ayanamsa) is then used to calculate the tropical zodiac, which in turn is necessary for determination of the other elements mentioned above. Thus, ayanamsa plays no part in the calculation of planetary longitude, and because of this, it is logically impossible for the tropical zodiac to play any role in the calculation of such longitudes. Thus, the sidereal zodiac is the basis of longitude calculation and expression.

We may add that, by themselves, the terms ‘nirayana‘ and ‘sayana’ provide evidence that the longitudes of planets are to be measured against the sidereal zodiac. Before illustrating this, however, it should be noted that some speak of the use of the sayana longitude of the sun to calculate the lagna as some sort of evidence that the tropical zodiac is actually the only correct one. For example, Vraja Kishor states:

“The ascendant is by nature tropical, and is the very foundation of a natal horoscope. That the thing upon which the entire horoscope revolves is intrinsically tropical is surely a profound point for consideration.”

We agree that one should consider the implications of this method for calculating the lagna, but not for the same reason as Vraja Kishor. Rather, by careful consideration of the terminology used, one will see that actually it is the sidereal longitudes of planets that are to be used in a horoscope, not the tropical.

It is clear from the astronomical texts that the lagna is to be calculated by using the sayana (tropical) longitude of the sun. There is no confusion about this. The lagna thus calculated is, however, properly called the “sayana lagna. ” This can be seen from the Bengali translation of Surya-siddhanta given by Srila Bhaktisiddhanta Sarasvati Thakura. In the translation to 3.47, which is the final verse in a series that describes the calculation of the lagna, he parenthetically includes the word ‘sayana‘ before ‘vlagna‘ to clarify what is being referred to.

So, by Surya-siddhanta we calculate the longitude of the sayana lagna. Considering that the term ‘sayana’ means ‘ with ayana’, it follows that the sayana lagna is equal to ‘lagna with ayanamsa‘ or ‘lagna plus ayanamsa‘. A natural consequence of this is that the longitude of the lagna (alone and without addition of anything) is equal to the sayana lagna minus the ayanamsa. [ie. lagna = (lagna + ayanamsa) - ayanamsa] Thus, the Sanskrit terminology actually makes it clear that the ayanamsa needs to be deducted so

as to arrive at the lagna that is used along with the sidereal planetary longitudes that were calculated in the previous chapters.

These terminological subtleties are usually missed by the casual reader of sastra; partly due to the incorrect approach that they take and partly due to the esoteric presentation of the texts themselves. However, both of these causes for misunderstanding can be eradicated by studying under the guidance of a bona fide teacher. Indeed, this is the prescribed manner in which the sastra is to be approached. Thus, for those who neglect the teachings of previous authorities, the verses of the Vedic scriptures are impenetrable. For this reason, we must follow our revered preceptors in order to understand what is actually being given.

This is nicely illustrated by Srila Bhaktisiddhanta Sarasvati Thakura’s translation of Surya-siddhanta 3.17 – 19. Therein, the process is described for calculating the corrected longitude of the sun from the shadow of the sundial. This is stated by our most esteemed translator as being the sayana longitude of the sun; which is natural as the size of the shadow on the sundial changes according to the sun’s movement on the tropical zodiac. While this is straightforward, the potential misunderstanding arises in the final verse of this section, where a further process is described for finding the mean longitude of the sun from his corrected longitude. In this verse (3.19), the corrected longitude of the sun is simply referred to with the pronoun ‘tat‘, meaning ‘that’. Thus, it may appear to be referring to the very same sayana corrected longitude that was used in the first half of the sloka. However, Srila Bhaktisiddhanta Sarasvati Thakura places the word ‘nirayana‘ in parentheses to show that the measure being referred to is the corrected longitude of the sun without the addition of the ayanamsa.

Thus, after dealing with sayana longitude, the Surya-siddhanta again reverts to the use of nirayana longitude in the same verse, without any definite specification of this use within the verse itself. Without the guidance of a learned teacher, this reversion is easily missed. Thus, we should conclude that when the Surya siddhanta is studied under the authority of one who actually knows the subject matter, then all such topics are easily understood by the student. In contrast to this, it is due to a lack of proper training that the present trend towards incorrect conjectures is manifesting amongst today’s astrologers.

Furthermore, within Vedic astrology, the sidereal zodiac is established as the fixed zodiac. Because it is considered fixed, it naturally follows that it is the basis upon which all measures of movement are considered. The tropical zodiac, on the other hand, is not fixed, and therefore, it is not the appropriate circle upon which to measure the longitude of planets. Srila Bhaktisiddhanta Sarasvati Thakura in his Bengali translation of the Surya-siddhanta, 3.11, confirms the movable nature of the tropical zodiac. Therein, he states in connection with the calculation and measurement of the ayanamsa:

antaramsa parimane krantivrtta calita haya

“By the degrees of difference the circle of the sun’s declination has moved.”

Thus, he has described that it is the kranti-vritta (the circle of the sun’s declination) that moves. This kranti-vritta is the tropical zodiac. As such, the sidereal zodiac is fixed, and the tropical zodiac moves with respect to it. Being of changeable longitude itself, it is not appropriate to consider the tropical zodiac as the basis for measuring longitude.

Therefore, it must be the sidereal zodiac alone that is employed as the circle of longitude for describing planetary movements and constructing horoscopes.

This fixed nature of the sidereal zodiac is also presented in the Srimad-Bhagavatam. For example, in 5.22.11, it is said:

tata uparistad dvi-laksa-yojanato naksatrani merum daksinenaiva kalayana isvara-yojitani sahabhijitasta-vimsatih.

“There are many stars located 200,000 yojanas [1,600,000 miles] above the moon. By the supreme will of the Supreme Personality of Godhead, they are fixed to the wheel of time, and thus they rotate with Mount Sumeru on their right, their motion being different from that of the sun. There are twenty-eight important stars, headed by Abhijit.”

Herein, the nakshatras are described as being fixed to the wheel of time. The reason for their fixity is also given; it is the will of the Supreme Personality of Godhead. Thus, it is established by the Lord that the sidereal zodiac is a fixed measure of the wheel of time. Being the sole fixed measure of this movement, it is a natural consequence that they remain the reference point to which all other movements are made.

Like the other planets, the sun moves with respect to this wheel of time, as can be seen from Srimad-Bhagavatam, 5.22.2:

sa hovacayatha kulala-cakrena bhramata saha bhramatam tad-asrayanam pipilikadinam gatir

anyaiva pradesantaresv apy upalabhyamanatvad evam naksatra-rasibhir upalaksitena kala-cakrena dhruvam merum ca pradaksinena paridhavata saha paridhavamananam

tad-asrayanam suryadinam grahanam gatir anyaiva naksatrantare rasy-antare copalabhyamanatvat.

“Sri Sukadeva Gosvami clearly answered: When a potter’s wheel is moving and small ants located on that big wheel are moving with it, one can see that their motion is different from that of the wheel because they appear sometimes on one part of the wheel and sometimes on another. Similarly, the signs and constellations, with Sumeru and Dhruvaloka on their right, move with the wheel of time, and the antlike sun and other planets move with them. The sun and planets, however, are seen in different signs and constellations at different times. This indicates that their motion is different from that of the zodiac and the wheel of time itself.”

Here, it is noteworthy that the rasis and nakshatras are described as moving with the wheel of time. As we saw above, it is the stars that are fixed to this wheel, and consequently moving with it. Therefore this verse indicates that the rasis and nakshatras are being defined in relation to the stars that are fixed to the wheel of time. Hence, in Srimad-Bhagavatam, a sidereal definition of the rasis is also given.

The sun, in his orbit, moves through these sidereal rasis in the course of a year. Thus, a year of the sun is being defined with respect to the fixed, sidereal zodiac. Additionally, this verse states that the motion of the planets is different from that of the zodiac. As such, the zodiac being referred to cannot be based on the orbit of any of the planets,

including that of the sun. It must therefore be the zodiac that is made of the stars; the sidereal zodiac. Considering these points, it is again evident that the sidereal zodiac is the fixed reference point from which measures of movement are considered, and this is the conclusion presented within the Srimad-Bhagavatam.

Furthermore, in 5.22.5, we find the following:

atha sa esa atma lokanam dyav-aprthivyor antarena nabho-valayasya kalacakra-gato dvadasa masan bhunkte rasi-samjnan samvatsaravayavan masah paksa-dvayam diva

naktam ceti sapadarksa-dvayam upadisanti yavata sastham amsam bhunjita sa vai rtur ity upadisyate samvatsaravayavah.

“The sun-god, who is Narayana, or Visnu, the soul of all the worlds, is situated in outer space between the upper and lower portions of the universe. Passing through twelve months on the wheel of time, the sun comes in touch with twelve different signs of the zodiac and assumes twelve different names according to those signs. The aggregate of those twelve months is called a samvatsara, or an entire year. According to lunar calculations, two fortnights—one of the waxing moon and the other of the waning—form one month. That same period is one day and night for the planet Pitrloka. According to stellar calculations, a month equals two and one quarter constellations. When the sun travels for two months, a season passes, and therefore the seasonal changes are considered parts of the body of the year.”

Here it is stated that the sun god passes through twelve months on the wheel of time, and in so doing passes through the twelve rasis beginning with Mesha. It has already been established that the stars are fixed to the wheel of time, and hence the sidereal rasis are also fixed to the wheel of time. Therefore, the twelve divisions of the wheel that are being referred to in this verse must also be measured with respect to the stars. Consequently, the division of zodiac into twelve rasis that is being described is sidereal.

Furthermore, in this verse it is said, “According to stellar calculations, a month equals two and one quarter constellations.” The Sanskrit terminology for ‘two and a quarter constellations’ is ‘sapadarksa-dvayam‘ and many of the authorized commentators make notes regarding this. Srila Sridhara Svami, Srila Vijayadhvaja Tirtha, Srila Viraraghava Acarya, Srila Jiva Gosvami, Srila Visvanatha Cakravarti Öhakura and Srila Bhaktisiddhanta Sarasvati Thakura all state that with regards to solar measures, a month is the time taken for the sun to cover two and a quarter nakshatras. Thus, there is no doubt that solar time is measured with respect to the sun’s movement against the stars, and that the twelve rasis are also defined according to the same stars. Srimad Vijayadhvaja Tirtha is very explicit with regards to the rasis, and he states in his commentary:

krttika-pada-yukta-asvini-bharanyau mesa ityadi kramena boddhavayam

“It should be understood that Mesha is Ashvini, Bharani and the first quarter of Krttika. The other rasis follow similarly.”

Thus we have shown that the Vedic scriptures describe a sidereal zodiac consisting of twelve rasis that remain aligned with the fixed stars, and that the calculation of solar time is based upon the sun’s movement through this fixed zodiac. Similarly, the movement of all other planets is calculated in the same way.

At this point, it should again be noted that the Srimad-Bhagavatam does provide descriptions of the tropical zodiac. There is however, no need for me to quote these as Vraja Kishor has done so nicely. But as mentioned above in relation to the Surya-siddhanta, evidence in favor of a tropical zodiac does not refute the evidence for the sidereal zodiac, as both the sidereal and tropical zodiacs are factual and are described in the Vedic literatures. The important point is using them for the correct purposes, and from the above statements of Srimad-Bhagavatam and Surya-siddhanta, it is clear that the sidereal zodiac is the correct basis for measuring planetary longitude.

As if the aforementioned were not enough, we may also quote from the writings of Varaha Mihira, who lived some fifteen hundred years ago. He wrote extensively on all areas of Vedic astronomy and astrology, and in his Brihaj-jataka, 1.4, he states:

mesasviprathamanavarksacaranah cakrasthitarasayah

“The signs of the zodiac, Mesha etc., are represented successively by the nine padas (quarters) of the several nakshatras commencing with Ashvini.”

Here, this great authority clearly states that the rasis are each composed of nine quarters of the nakshatras. This is equal to two and a quarter nakshatras, which is the same measure as sapadarksa-dvayam that was quoted above from Srimad-Bhagavatam. As previously stated, everyone accepts that the nakshatras are groups of stars. Thus, the rasis, as defined by Varaha Mihira, are divisions of the sidereal zodiac.

While this is clearly in support of the authenticity of the sidereal rasis, some may claim that by Varaha Mihira’s time, knowledge of the true nature of the rasis had already been lost. Indeed, Vraja Kishor has posited that some time in the last two millennia, astronomers in India forgot how and when to distinguish between the two zodiacs, and as a result of this ignorance, began to describe rasis according to the fixed stars. He has suggested that, due to the decline of knowledge in Kali-yuga, astronomers and astrologers in India “became locked into thinking that the tropical measurements and the stars were identical.”

However, this proposition is not supported by the writings of Varaha Mihira; an author of such repute that astronomers and astrologers have been studying his writings ever since he penned them. In his Brihat-samhita, 3.4, Varaha Mihira states:

“If the sun should change his course before reaching Makara, he will bring evil in the west and south; and if he should do so before reaching Kartaka, he will bring evil in the north and east.”

In this text, Varaha Mihira is describing the directional changes that occur at the solstices. These changes in the northward and southward movement of the sun are fixed in relation to the rasis of the tropical zodiac; as it is in relation to the solstices and the equinoxes that the tropical zodiac is defined. Therefore, the sun always turns north at the beginning of tropical Makara.

However, in this verse it is described that the change from southward movement to northward movement can occur before the sun reaches the beginning of Makara rasi. The Makara rasi being referred to must, therefore, be the sidereal rasi, as it cannot be the tropical counterpart. It is clear from this that Varaha Mihira correctly distinguished

between the two zodiacs, and as such, his definition of the rasis as being sidereal was not a case of a lack of knowledge on his part.

Therefore, at a time when the sidereal and tropical zodiacs were closely aligned, this renowned author was describing rasis as being fixed according to the stars and that the tropical zodiac was moving with respect to them. This is the same conclusion that we have drawn from the Srimad-Bhagavatam and the Surya-siddhanta.

Finally, even though the ayanamsa was small, perhaps even zero, during Varaha Mihira’s life, it is clear from his writings that he was fully aware of both the sidereal and tropical zodiacs, and did not confuse one with the other. His ongoing fame has ensured that his writings have remained prominent till the present day; including his distinguishing between the sidereal and tropical zodiacs. Indeed, his works are still considered to be essential studies for anyone who is serious about learning the science of astrology. This is very significant evidence that Vraja Kishor’s ‘decline in knowledge’ theory is patently wrong.

In conclusion, it is foolhardy to claim that the Jyotir-veda does not use a sidereal zodiac that is divided into twelve rasis. Rather, we have shown that an authentic sidereal zodiac certainly existed in the Vedic astronomical and astrological tradition. Furthermore, we have seen that it is this zodiac that is the fixed basis upon which planetary movements are measured. Therefore, it is the sidereal zodiac, and not the tropical zodiac, that should be used for constructing a horoscope, as the longitudes of planets are properly measured only on the sidereal circle.

Having established all this, we are now in a position to respond to the following question posed by Vraja Kishor das:

“Beside force of habit, injured pride, the paralysis of shock, or fear of change – is there anything that would stop us all from embracing the unequivocal tropical definitions of the zodiac found in all the ancient and classical literature of the world?”

By the grace of guru and Krsna, we can confidently answer that the statements of sastra and the previous acaryas safely stop us from making such a grievous error.