Astronomical Foundation to Vedic Astrology
In study of Vedic Astrology, a major roadblock one finds is to visualise the theory.
While abundant quality content is available to learn the study of Horoscopes, the scope remains limited to it. Understanding the Horoscopes is in itself a core subject that needs scholarly supervision. However, they do not provide a view to the “why”.
If you read your Horoscope, you would find the positions of various planets at the time of your birth. Also, their angle determines the extent of their influence in your life. You might also have heard of Shani entering a wrong house and the subsequent term of Sadhe Sati (Seven and half years of misfortune). And definitely, the detailed analysis of how everything affects the various aspects of your life. But in the physical universe, where exactly do planets enter, against what line do they subtend angles, and how do we define a period of stay? These questions remain unattended!
This is my attempt to explain the same.
Understanding the Jargons
Ancient Indian Astronomers, like the Greek, had predominantly considered the Earth as the centre of the solar system. According to their theory, the Sun, the Moon, and all other planets, considered together as Grah (ग्रह), revolve around the Earth. And each of them transitions from one sector to the other. In general, Rashi (राशि) is a standard notation for a thirty degree sector.
Twentieth Shloka of the first chapter of Surya Siddhanta defines it as the 12th part of a Chakra (चक्र). One Rashi consists of 30 Ansha (अंश) and one Ansha contains 60 Kala (कला). And each Kala contains 60 Vikala (विकला). In the modern units, this becomes:
But wait! Did you read that the Sun revolves around the Earth?
That absolutely makes sense. Let us find out!
The Geocentric Concept
We all are aware of the fact that the Earth and all other planets revolve around the Sun. The Gravitational pull of the Sun ensures that the loop doesn’t break.
However, considering the kinematics, there is another perspective, well within the bounds of Newtonian Physics.
For a moment let us consider the Sun and the Earth as the only heavenly bodies and forget the rest of the planets in the Solar system.
This model would somewhat look like:
Earth revolves around the Sun at the angular velocity of roughly 1 degree per day (How? Figure out!) But this is under the assumption that the Sun is at rest. Which, it is not! But, it doesn’t matter!
As per the theory of relative motion, a body is in motion if the relative separation between the body and the observer changes over a period of time. Thus, if the observer is also moving in the same direction as the subject, and with the same speed, distance between them does not change and thus, the subject is at rest for the observer.
If you have not been through the gripping relative motion problems in your senior secondary classes, following examples could help you understand this concept:
Most traditional example:
A truck is moving towards the East at a speed of 30Km per hour through a farm. In the same direction, a car is moving at the speed of 100 Km per hour. A farmer observes the same from the field, while an astronaut observes it from space.
For the truck driver, car is going towards East at a speed of (100- 30 =) 70 Km/h
For the car driver, truck is going towards West at a speed of (100- 30 =) 70 Km/h
For the farmer, the truck is going towards the East at 30 Km/h. Also, the car is going towards the East at the speed of 100 Km per hour.
For the astronaut, farm and farmer are moving towards East at a speed of approximately 1600 Km/h (Speed of Earth’s surface due to rotation)
Truck is moving towards the East at 1630 Km/h approx.
Car is moving at 1700 Km/h towards East
While the example we considered is for a unidirectional motion, the same can be used to understand the relative motion in 3 dimensions. Back in the school days, we used a simple thumb rule: If you want to observe the motion from the reference of a body, reverse all it’s vectors and give them to all other bodies. And bring the observer’s body at rest. This can be clarified from the following example:
Suppose 3 saucers are flying in space, and are observed by an observer on the Earth. The direction and speed of each saucer A, B & C are mentioned by the corresponding velocity vectors.
Now, suppose the observer sits on the saucer A. As per the mentioned rule, bring A to rest, reverse all its vectors and give it to every other body:
You can see, the vectors (speed along with directions) were reversed and added to all other bodies. Also, now Earth seems to be moving down at 100m/s and towards A at 20m/s.
Similarly, if the observer sits on the saucer B, the motion would look like:
Try to figure out how it would look like, if the observer now jumps and sits on saucer C.
Do it now! I am sure you will do it right!
Now, back to the Sun & Earth system.
Apply the same concept here. For an observer on the Earth, how does the motion of the Sun look like? It’s something like the figure below.
For the observer on the Earth, it seems that the Sun is revolving around the Earth at a speed of one degree per day. And that is the reason why most of the ancient astronomers considered that the Earth is the centre of the universe.
Thus, the prominent solar system design, with the Earth revolving around the Sun is correct, assuming that the observer sits at the Sun. It is called the Heliocentric model (Helius+ Centre).
The observation that the Sun revolves around the Earth is also correct in the 2 body system, assuming the observer sits at the Earth. It is called the Geocentric model (Geo+ Centre). Overall validity of the model depends on the trajectory of other planets. We’ll get into that.
But what about the spin of the Earth? Geocentric model also takes into account the spin of the Earth. And that is the reason the sun revolves around the Earth in 365 days, 6 hours and 12 minutes. Not 24 hours.
Motion of other planets
Twenty fifth shloka of the first Chapter of Surya Siddhanta mentions that the planets move towards the West and then stop. This indicates a change in direction of the motion of planets.
It is obviously clear that if all the planets revolve around the Sun in the solar frame of reference, observation of their motion from the Earth cannot be an ellipse. There has to be an unusual path that the planets follow, if they are expected to be revolving around the Earth. Let us try to develop that path.
Following chart shows the time taken by each planet to complete one revolution around the Sun, in the Heliocentric model. Deriving from the same, we can determine the angular speed of each planet around the Sun.
For simplicity, let us try to draw the trajectory of Jupiter, as observed from the Earth. For this, let us plot the actual position of Jupiter over the periods it subtends the angle of 5 degrees at the centre of the Sun. As evident from the table above, in the same period, the Earth subtends an angle of 60 degrees at the centre of the Sun.
In the Heliocentric model, for two revolutions of the Earth, this is shown as follows:
In the centre is the Sun. First circle shows the path of the Earth, while the second circle shows the path of Jupiter. For every thirty degree angle segment run by the Earth, Jupiter subtends 5 degree angle against the Sun. Points on the third circle show the position of Jupiter, as observed from the Earth.
You can observe that from 1 to 2 Jupiter runs clockwise, then changes direction and runs counter clockwise till 7, then changes direction again and runs clockwise till 9 and then again changes direction. This can be represented along the perpendicular axes as follows:
Rearranging the relative distance between the two planets along the x-axis, and the motion of the projection along the y-axis, we get a grid with relevant points. Connecting all those, we get the path of Jupiter, as observed from the Earth:
In the above trajectory, Earth is somewhere between point number 7 & 11 on the ‘y’ axis. And it does not move from it’s position. You can observe that Jupiter goes away from the Earth, comes closer, cuts its own path, changes direction, goes away and cuts its own path. This cycle repeats itself.
Jupiter is considered just as an example, as it offers easy calculations. Any planet would behave in the same way. Although the size and detailing of the path would change.
Ancient astronomers across the civilisations, including India, perceived it as the epicyclic motion. They considered that the planets revolve around an intangible point, which revolves around the Earth. That is:
The Moon and the Sun revolve around the Earth in ellipse, while any general planet revolves around an intangible point A in ellipse, which further revolve around the Earth in an ellipse. The path thus created by the planet looks like the one shown earlier.
In further sections, unless stated otherwise, consider all the discussions in the Geocentric model.
Manifestation of Rashi
With Nakshatra (नक्षत्र) or the constellations as reference, a circle around the Earth (with radius equal to the distance between the Earth and the farthermost planet) is divided into 12 equal sectors. Each of these is equal to 1/12th of 360 degree i.e. 30 degree angle. Each sector is called a Rashi.
As all the planets revolve around the Earth, they transition from one Rashi to the other. Their position in the Rashi, in combination with the position of other planets, has the influence over our lives, which is widely covered in the subject of Astrology.
You might have noticed that your Astrologer is less concerned about the periods of your life when Sun or the Moon enter the houses of misfortune. But the similar periods of Jupiter and Saturn are specifically mentioned in the Horoscope. Following are the reasons for the same:
The Sun completes the revolution around the Earth in roughly 365 days. So:
1 revolution = 360 degree
Angular speed of Sun = 360/365 ≈ 1 degree per day
Angle of 1 Rashi = 30 degree
Time = Distance/ Speed
Thus, Time spent by Sun in 1 Rashi ≈ 30/1 ≈ 30 days
Similarly, The Moon completes one revolution around the Earth in roughly 27 days. Thus:
1 revolution = 360 degree
Angular speed of Moon = 360/27 = 13.3 degree per day
Angle of 1 Rashi = 30 degree
Time = Distance/ Speed
Thus, Time spent by Moon in 1 Rashi = 30/13.33 = 2.25 days
From these calculations, we find out that the Sun and the Moon move very fast. While the Sun stays in a house for roughly a month, the Moon changes its house every 2 and a quarter days. So whatever may be the influence of their motion, good or bad, it is unlikely to stay for a longer period and thus, less significant.
As we go away from the Earth, the radius of the revolution increases, and thus, the time spent in each Rashi. Due to the epicyclic motion of the other planets, time spent in a Rashi may vary from one Rashi to the other. However, as evident from the conclusions in Astrology, Jupiter and Saturn spend many years in one Rashi. Thus, their period of influence becomes a significant part of your life.
Extent of influence at birth- Understanding ‘Bhav’
If the position of a planet within a Rashi influences anything, it is obvious that the influence of the planets transitioning from one Rashi to the other should be less, while the planet positioned in the mid of a Rashi should be maximum.
In the Vedic Astrology, the angle subtended by a planet against the reference line of a Rashi is called Bhav (भाव). And the relation between the planetary influence (considered independently) against Bhav is roughly defined by the following curve:
Thus, the influence of a planet in a Rashi is highest when it is exactly at the centre of Rashi i.e. subtending 15 degree angle with the reference lines of the Rashi. On either side of this, influence reduces, reaching to zero at the terminals.
Conclusion
Vedic Astrology stands on the foundation of the Geocentric model i.e. the Earth is at the centre of the solar system, and all other planets revolve around the Earth. While that may sound absurd at the first look, none of the principles followed violate the kinematics of classical Physics.
Visualising the geocentric model of the solar system, all principles of Vedic Astrology seem to fall in place, be it the exclusion of the Earth from the planets, less importance to the transition of the Sun and the Moon or the varying planetary influence with position. While the authenticity of Astrology may be debated, it is beyond the scope of this article.
Visualisation of the reference line of each Rashi has also not been discussed here. In the universe, where everything is in motion relative to the Earth, how the reference line is defined holds significance. This may be covered later.
Some Other Relevant Definitions:
Sankranti (संक्रांति): The day of transition of the Sun from one Rashi to the other Rashi.
There are total 12 Sankranti in a Solar YearLunar Month (चंद्र मास): Time between 2 consecutive new moons. This is approximately equal to 29.5 days
Lunar Year (चंद्र वर्ष): A period of 12 lunar months. This is equal to (29.5x12=) 354 days.
All major Hindu festivals are celebrated following the Lunar calendarSolar Year (सौर वर्ष): A period in which the Sun completes one revolution around the Earth. All Sankranti, including Makar Sankranti, are celebrated following the Solar calendar. There is roughly 11 day difference between the Lunar and the Solar year
Purushottam Maas/ Mal Maas/ Atirikta Maas (पुरुषोत्तम मास/ मल मास/ अतीरकत मास): In three years, the difference between the Lunar and the Solar year becomes approximately of 1 month. Thus, after every three years, the thirteenth month is added into the Lunar Year to balance out this difference. This thirteenth month is called Purushottam Maas or Mal Maas or Atirikta Maas. It is the only Lunar month where there is no Sankranti. In 2020 Diwali fell late because Purushottam Maas was observed before Kartik Maas- the month of Diwali
Reference
Geometric diagrams: https://www.desmos.com/geometry
All other diagrams: Microsoft Paint
Rashi image: http://www.globalgoodfortune.com/pages/maharishi_jyotish/12_rashis.html
Period of revolution of planets: https://www.exploratorium.edu/ronh/age/
Relevant definitions: Monthly Jantri by Kashmiri Sabha
Surya Siddhanta translated by Shri Kedarnath Shukla, wherever mentioned specifically
Cover image: https://wallpaperaccess.com/universe-full-hd-pc
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