Astronomical Calculations and Differences Between Western and Vedic Astrology

When somebody asked me why is there a difference between their zodiac signs from what western astrology says to that of the vedic astrology, my first answer was a silent sigh with my mind going over the entire details of the answer. My second answer was the shorter version of it. They differ because western astrology uses Sun sign and ours uses Moon sign.

I thought I will write here the details of the first answer because the second answer is bound to have follow up questions if the person is really interested to understand the reason behind the difference. However, this may be a little too intricate and confusing. The reason I am writing it so detailed is, it takes a while to really understand it by reading multiple things at multiple places on the net. Just trying to explain it my way, which I think I am making an effort to simplify the things. However, this might have a lot of other things explained that may really not directly link to the above question, but definitely needed to have the correct overview of this detailed answer. I will not use the 'terminologies' a lot (like equinoxes, sidereal, tropical longitudes, zenith point, etc). I will use simple words like vertical line, point, date etc and not use new words so that you are unburdened and don't have to learn new words to understand the concept. Once you have the hold on the concept, you may refer the internet where 'terminologies' are used, but at that time you will be able to relate it to your understanding.

To understand the final answer, there are some concepts that one needs to first understand; which I was thinking I was taught fully in our high school astronomy classes, but unfortunately was very much incomplete.

First of all, let us assume you are aware of Copernicus theory of the Solar System. Sun is the center of the system of 9 planets revolving around it in the order - Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. This entire system is trying to revolve around a black hole at the center of the Milky way galaxy. The solar system is towards the outer boundaries of this spiral galaxy and sun is within the black hole's gravity to be called as a part of the Milky way galaxy. Sun, along with this system is trying to revolve around the center of this black hole. I say trying because, the Sun is not expected to live long enough to be able to even put one full round around this galaxy. By the time he is 30 degrees ahead, the Sun would be a pulsar with all his planets destroyed. Okay, now. This entire galaxy along with the black hole till solar system and other stars within, is slowly moving away in one direction that is not same as the direction of other galaxies around it, but when this galaxy and others are together visualized, they seem to move away from each other yet not going near to anything as if they are dots on a balloon that is being blown up. The center of that balloon trying to move everything away from each other is unknown and is said to have originated from a big bang. May be that is the case or may be it is an oscillating universe with all points moving away from each other and then coming together after a threshold. Anyway, let us assume this much was taught in the high school to us all. We would probably also know that the earth is revolving around the Sun and Moon is revolving around the earth. Also Moon's revolutional orbit is not in the same plane as of Earth's orbit around the Sun. There is a small tilt of about 5 degrees because of which Solar and Lunar eclipses do not happen every 15 days. Earth's rotation plane (equatorial plane or the 90 deg to the line of North to South pole) itself is inclined 23.5 degrees to the revolutional plane giving rise to seasons. All this you would already know.

Now a few things you may know or may not, depending on the interest in this subject or the time you have given to it.

With this huge universe, when you say you are witnessing something, you need a reference point. To witness the galaxies expanding from each other, you need to stand at a point away from the galaxies. When you are talking about solar system, you are standing at a point above that plane to visualize the solar system as the Copernicus model. Now to understand the answer to our question, come back to earth and let that be the reference point. Geographically let us assume you are in India.

Go to an open field or top of the terrace and find out which is north. Lie down facing the sky putting your head towards north and feet towards south and stretch your hands either side. The place you are lying down is the reference point. Now, keep the Copernicus theory aside and see the observable universe. On your left had is the east and right hand west. Sun rises from east and hour by hour moves west till it is dark again. Did you notice? at 12 noon, you expected Sun to be right on top burning you face directly, but Sun was rather a little low and not exactly to the top peak? That is because you are in India, a little south to the equator. So the sun never actually comes right on top. If you were lying down at a place on Equator, Sun would have shone right on top. The lower you go, this rise to set path of Sun will bend further and further away till at south pole, it feels as if sun rise started at left and always was on horizon and moved west. Being in India, it will not be that deep, but definitely not at 90 degrees like one expects. 



As you see in India - Wikipedia image
As you see at Equator - Wikipedia image
At the polar region - Wikipedia image
  
This line/trajectory/locus/path of the Sun is called 'ecliptic'. Ecliptic is the apparent path of the Sun around the earth.


Ecliptic - Wikipedia image


Just like Sun, even moon because of earth daily rotation, feels as if he rises and sets. Moon has his own movements and depending on the phase, sometime is visible and sometimes not. But, if seen on a full moon day, moon appears on east (your left hand) and moves west (right hand) but again not always come right on top of your head. This would be the same type of movement for other planets too. If you see the considerably bright Venus, it moves from east to west. All planets move from your left hand towards your right hand. In fact all stars you see at night, you can see them move from left to right! All this happens because of earth's rotation. Now while still lying down, assume you see the ellipse - the path of Sun. Over many days if you observe, one fact becomes clear.

All planets and moon and Sun move within 18 degrees of this ellipse. That is if the movement of the Sun were to be on a 18 degree wide belt, all planets and moon too appear on the same belt - round the year for ages. This belt is called Zodiac belt. It is a 18 degree wide belt. If you stretch your hand and point the sky with the index and little finger stretched away from one another with middle finger and ring finger closed with the thumb, that distance is 15 degrees plus a distance of a thumb post that. This is a crude method of degree measurements our ancient men had. The width of little finger is 1 degrees, width of thumb is 2 degrees, width of index and middle and ring finger together is 5 degrees, width of a closed fist is 10 degrees and 15 degrees is what I just told. This belt is of 18 degrees and is called Zodiac belt that is divided into 12 'almost' equal parts called zodiac signs.

Now, let us assume you are lying down in this way to mark the position of Sun everyday at say 12 noon, assuming you have the ability to view the background star as well on the zodiac belt. Due to the tilt of earth's axis, the point keeps on moving up and down the vertical line in a pendulum fashion. The point where Sun is seen at 12 noon today is probably a little below the point where Sun is seen tomorrow at the same time. This movement has a simple harmonic motion of 1 year and every 6 months the point reverses its direction. To explain clearly, say you started this test in December end. You marked on a graph x axis with days starting from December till the next December. Y axis with the width of zodiac belt. First day you mark a point where you saw the Sun on zodiac belt. When you try to do the same tomorrow, you will see the Sun is slightly above it's yesterday's point. keep on doing it daily, till sometime in June mid. You will see the point at which Sun is seen is coming more and more above, towards your face, towards north. Post June mid, again the point starts falling back downwards. This observable up and down movement of Sun is what is called Uttarayana and Dakshinayana movements. If you were to do this exercise from Dec 2012 to Dec 2013, you will see on your graph that the bottom most point of Sun will be on Dec 21st and a mid point is seen on March 20th, then a top point seen on 21st June, again to the mid point on Sept 22nd and again the bottom most point on Dec 21st. This Dec 21st lowest point of Sun's position is called Southern Solstice. Top most point is called Northern Solstice. Mid point where Sun is moving towards Northern Solstice is called Northward Equinox and the mid point where Sun is moving towards Southern Solstice is called Southern Equinox. Now this Southern Solstice which is the Dec 21st date where Sun starts moving north is what is celebrated as 'Sankranti'. But from long time till these days, Jan 15th is celebrated as Sankranti and not Dec 21st. Let us see why that date difference is, later. But understand that conceptually Sankranti is the time of Uttarayana, the time when Sun starts moving northwards.





Now you know that Sun rises in the east and sets in the west making a path called ellipse. Then there is a year round up and down movement that can be visualized as a perpendicular line to this ecliptic. The rotation of earth is what makes us visualize the left to right path of ellipse while the revolution of earth is what will make us trace the vertical path of Sun's movement.

Now, as mentioned, the Zodiac belt is divided into 12 and Sun appears to be in one of the 12 zodiac signs at a given time. Instead of a point marking the sun's position, now start visualizing and using the vertical line as the Sun, moving horizontally across the zodiac belt, with the exact Sun's position somewhere on the vertical line.

The vertical line of sun's up and down motion is used as Sun's reference from here because, for now, let us not think about exact sun's position on this line, but the exact position of this vertical line with respect to the zodiac belt. Just remember, on Dec 21st, Sun is at the lowest point of this line and on June 21st, Sun is at the topmost point of this line.

Year after year, if you keep marking the lowest and topmost points of Sun, that is exactly of 1 year duration. However, over the years, you will see that with reference to the zodiac belt behind the Sun, the vertical line drawn on the day of the lower-most Sun - Dec 21st this year - will not be the same in a few more years. Say you witnessed the vertical line with lower most Sun on top of a particular Pisces zodiac star, Next year, when the Sun is lower most on the vertical line, he is a little towards your right hand when you are still lying down as I asked you to. The Sun's vertical line with the lower-most Sun's position has actually moved nearly 1 second angle. It is very small to notice because the exact angular difference from last year's lower-most Sun's vertical line behind a zodiac to this years is 50.29".

That is the vertical line has moved a little less than 1 second to your right. Visualize that on the lower most Sun's position on 2012 is on Dec 21st and the zodiac you see behind is Pisces. If you are still lying down as I said, you are seeing Pisces on your front with Sun at noon but you still can see the stars behind. On your right is the Aquarius zodiac followed by Capricorn. On the left of Pisces you see Aries followed by Taurus. 



Apparent Sun in Pisces with Aquarius on the right and Aries on the left


Next year in 2013 when you try to see the vertical path of Sun against the same background, it would seem a little on the right. Not significant because as mentioned below, the stretched hand with little finger's width is the apparent 1 degree. Divide that little finger width into 60 parts, Now, in 2013, the vertical line would have moved right not fully of 1 part of that 60 parts - a little lesser. So it is very small movement but a definitive movement of 50.29" seconds a year. The lowest point of Sun's path thus keeps on moving towards right at this rate year after year.

This movement happens because of the movement of earth's axis' movement such that the north pole of axis not pointing constantly to a star but rather over years encircling a set of stars. Let me not talk about that here, but just have the understanding that this movement of apparent Sun's vertical path is happening not because of earth's rotation or revolution, but because of the revolution of earth's north pole's point of the axis around a set of starts. Currently that axis points pole star or Dhruva star, but remember that it won't do so always. This concept is precession of equinoxes which I will deal at some other time. Forgetting the why, just remember the vertical line is not at the same place this year as it used to be last year - has moved a little right.



Earth's axis revolves around a set of apparent stars

Understanding till here and clarity about the vertical line with reference to the background zodiac is crucial to move forward. Because I am going to talk about another vertical line that may confuse you.

Now, you were doing all the calculations based on the time of say 12 noon every day. Now lets get into that time. Forgetting Sun for the time being, looking at only the zodiac belt, if you are sticking to the clock in the hand and noting things down at 12 noon exactly, the star that you saw at 12 noon at one point today will seem to move a little 'right' tomorrow. No, its not very complex, because, the reason for this is, earth's rotation is not exactly 24 hr clock but 23 hrs, 56 mins 4 seconds a day. So even if your clock shows 12 noon, earth doesn't need the full 24 hrs of your clock to rotate fully around itself. Some 3 mins before itself, it has rotated full one round, right? That is the reason, the star you saw at one point yesterday seems be at the same point at 23 hrs 56 mins 4 secs itself and at 12 noon today is a little more to your right, west. remember? everything seems to move west as time goes by, right? So knowing that 24 hrs is not what we want to base our observations, take off that watch and just remember that a day is 23 hrs 56 min and 4 sec.

The star that is found at a particular point at a particular time will appear at the same point the next day at 23 hrs 56 min and 4 seconds. Now instead of 'a star', let us fix a star. But let us choose a star that is within the zodiac belt, we don't want to go far away from the belt and get confused. Let us take the 'Speca' star (Chitta) which is the brightest star in Virgo (Kanya). With this earth's rotation for an year, the star is expected to return to the same observable point at the same time after the earth has made 365.25 rotations. So after so many rotations, you, lying down the terrace can see Speca/Chitta star at the same place at the same time as you had seen the last year. This would be true for not just Speca/Chitta but to any star within the zodiac. It can be Speca or Aldebaran or the Sun itself. That is even the Sun takes 365.25 days to return to the same place in the sky. Now let us draw a vertical line parallel to the earlier vertical line of Sun's lowest most point line.

These two lines are not always same and do not overlap every year. The vertical line of lowest most point of Sun and the vertical line of return of Sun after 365.25 days varies year after year because of the precession of equinoxes. That is due to the change in the direction of the axis that points to the pole star, there will be a difference between these two vertical lines and the difference is 50.29 seconds a year. This difference is called ayanamsha.

There was a particular time when the difference between these two lines was 0 degrees. Mathematically if you go on subtracting 50.29 seconds difference each year to the now difference between these two vertical lines which is 24 degrees, you will at one point in the history see that the difference was 0. Earlier to that time, the difference would be negative, that is one line crosses over the other line in the opposite direction.

All till now is astronomy basics. If you understand till here, you will be able to understand astrological systems.

What you understood till now is what is available as per today's observations. This is how Sun is visualized over different zodiac signs looking from earth.






This calculation is not what is used in astrology. This is what is readily available from Google, Nasa, etc as of today. This data is readily downloadable on the net.

Western Astrology:

When at one point in time the difference between two vertical lines was zero, Greeks defined the boundaries of the zodiac. They called a person to be of a particular zodiac if Sun was in that particular zodiac when he was born. These dates are now revised to the observable Sun's lowest and top most points in the western astrology. Since Dec 21st onwards, as of now, the sun starts moving northwards on the vertical line, Dec 22nd till Jan 20th is called Capricorn and then Jan 21st till Feb 19th is Aquarius, Feb 20th till March 20th is Pisces, March 21st to April 20th is Aries, April 21st to May 21st is Taurus, May 22nd till June 21st (the topmost point of Sun on the vertical line) is Gemini, June 22nd to July 22nd is Cancer, July 23rd till Aug 22nd is Leo, Aug 23rd till Sept 23rd is Virgo, 24 Sept till 23rd Oct is Libra, 24th Oct till 22nd Nov is Scorpio and 23rd Nov till 21st Dec, the bottom most position of Sun, is Sagittarius. That is the western astrology (Fagan, Bradley, Burgess, Colebrooke, etc till the latest Linda Goodman and others) base their predictive astrology, on the first vertical line we talked about which sees the highest and lowest points of Sun on the vertical line each divided by 30 degrees movement of sun.

This however will keep changing over the years and based on the ephemeris (position of Sun and other planets), keep on changing the dates after every few years to adjust to the actual positions.

The start and end dates of each zodiac hence would keep changing based on the movement of the vertical line and the start of Capricorn would keep shifting backwards in date, because the line as we discussed will keep moving west. So the dates above are good for a few years to come after which they would be revised.

Greek Astrology:

This is the same western astronomy, when the difference between the start and end times of these zodiacs was zero. That is because the vertical line with bottom most sun was not on Dec 21st during the days of Greek (Ptolemy, Socrates, Plato, etc), but a date farther away on the calendar from that. Aries started 15th April till 15th May from the now 21st March to 20th April and Capricorn started from Jan 15th till 14th Feb. This also happened to be the time around 499 AD.

Before telling the details about Vedic astrology, a few points to note.

The difference between the two vertical lines we spoke about is currently 24 degrees. It will go on increasing till 27 degrees after which because of the revolution of the axis pointer's apparent motion of return, will start coming down from 27 degrees back to 0 degrees and then extend till 27 degrees on the other side.

Historically 0 degree difference happened during 499 AD and till 2299 AD it slowly keeps moving right till the difference between the two lines becomes 27 degrees. After 2300 AD, it starts decreasing from 27 degrees back to zero degrees in 4099 AD then go from 0 degrees to -27 degrees in 5899 AD. This pendulum type simple harmonic motion of the vertical line will keep happening.

According to this type of motion, the western astronomical dates need to be upgraded by and by as and when the difference is growing significantly.

So, the western or Greek astrology uses the apparent position of the Sun with respect to the 30 degree wavelength of the Sun's lower most point on the winter solstice to mark the beginning of Capricorn.

Vedic Astrology:

Instead of the simple harmonic motion of this sort, first and foremost, we normalized all the calculations to 0 degree. The best standardization that can be applied by an inventor of zero. Surya Siddhanta, Siddhanta Siromani of Bhaskaracharya, Aryabhaatiyam of Aryabhata, Varahamihira, Sayanaacharya and everyone in the vedic Siddhanta ganita, formed a system where, all calculations of the positions of all planets, Sun will be based on 0 degrees of this line and a factor of Ayanabhaga added/subtracted from this to arrive at the actual sayana siddhanta positions, otherwise, based on subtracted/added Ayanamsha to arrive at Nirayana siddhanta position. This is applicable to all except the Moon. Moon's position is calculated with a different equation mathematically with Aldebaran star (Rohini) as the starting point of observed position each month. However since Moon revolves around the sun along with the earth as if it is not a different entity and the observed moon's position is not impacted by earth's tilt since moon has to stick with earth and tilt it's orbital plane with the earth itself. So there is no question of the first vertical line calculated same way for moon as we did for the sun to vary yearly.

So, the vedic astrologers used Moon to identify the zodiac sign of a person. The zodiac that moon occupies at the birth time is what is taken as the zodiac of the person. This varies every ~2.5 days and hence cannot be give a "set of specific to and from dates" but accurately the position can be calculated. However, the system does not change with a simple harmonic motion of the moon and hence it is more fixed.

That is, we say to arrive at the exact 'observable' position of the planets and Sun, apply the Ayanamsha correction to the Nirayana calculated positions. It is not correct to assume vedic astrology is only Nirayana system and not saayana. But, all theory, predictions, results, etc are documented as per 'nirayana' that is at 0 degrees of Ayanamsha AND to actually calculate the sun rise time and to see the graha change the raashi or bhaa chakra, you need to apply the Ayanamsha correction to the same and see the saayana aspect of it.

Now a days softwares just reverse engineer the same to accurately reverse calculate the Nirayana positions from the tropical data. The positions can either be calculated based on equations given in Surya Siddhanta or based one ephemeris data from google and the like, which gives the positions as of today and then subtracting the ~24 degrees from the tropical ephemeris data, you get the data that can be cast at 0 degrees or Nirayana.

We also have the system called Tajaka where we also cast a Nirayana system chart like the western system - where every year of Tajaka is said to begin at the time when Sun is at the same degree minute and seconds as it was when a person was born. This system however even though it takes into account the the ayanamsha correction to be put, is based on the exact value that can be calculated for Ayanamsha. So, as per our ancient texts, this would be kept as an approximate annual casting and not the actual birth chart cast with a dasha.

So, our vedic astrology depended mainly on moon's position to determine the raashi of a person while it calculated the position of Sun and other planets with a Nirayana equation. Now a days the positions of Sun's and other planet's positions are calculated based on the available tropical data minus the ayanamsha value to arrive at the 0 degree position of the difference between the two vertical lines we discussed. So it has become very important these days to the modern softwares to know the exact values of the ayanamsha. Ayanamsha is calculated in various ways prescribed by Fagan-Bradley or Ptolemy or Burgess or NC Lahari or Krishnamurthi or BV Raman or as per Surya Siddhanta or even based on any given fixed star. There are about 20 famous ways which differ slightly in the value because of a different way to calculate it. Let me take that up in a different write up.

To answer the main question now in a slightly different way which I hope you can understand now, the western astrology uses a just-in-time position of Sun with respect to a just-in-time position of the winter solstice date to spread a 30 degree sun's movement and whichever zodiac the date falls in, would be the zodiac of the person. But the dates itself will vary after a few decades or centuries.

Vedic astrology on the otherhand uses the position of the moon in a particular zodiac as of the time the person is born, so that the solstices need not be considered, and then positions the Sun and other planets in the chart as if the chart is cast at 0 degrees of ayanamsha (Nirayana) and casts Tajaka charts based on the Sun's position but again normalizing to the nirayana 0 degrees.

Hope the longer version answer makes sense.