The Kepler Equation, M = E- e Sin E

The Kepler equatio M = E- e Sin E can be used to compute planetary longitudes.

M is the Mean Anomaly of the planet and E, the Eccentric Anomaly. Eccentric Anomaly is an auxiliary angle used in Kepler's Equations.

e is Eccentricity of Orbit. The planet's orbit is elliptical and not circular and Eccentricity or e is always Zero at Circle, 0-1 at ellipse and one at Parabola !

The Kepler Equation can be put in a different way

E = M + e Sin E

Kepler's Laws of Planetary Motion

Johannes Kepler expounded the principles of Planetary Motion thus

1)The orbit of a planet is an ellipse, with the Sun as the focus of the ellipse.

3)The motion of a planet is fastest at Perihelion and slowest at Aphelion.

4) p1^2 / p2 ^2 = a1 ^ 3 /a2 ^3

The periods of revolutions ( sidereal period ) of two planets is equal to the cubes of their semi major axes.

Long before Kepler Aryabhata expounded the Helio centric Theory of Gravitation, that all planets circle around the Sun due to celestial gravity. If it is terrestrial gravity which is the characteristic of the earth, then it is Celestial Gravity, which is the characteristic of the Sun

R, the Magic Figure in Astronomy

R is the Radius of a Circle. It is 206265 secs and is an important figure is Astronomy

We talk about the Circles in Astronomy. The Ecliptic is a Circle, the Zodiac is a Circle and so on. And how do we measure the Radius of the Circle?

The Magic Figure of 206265 seconds is got by these derivations


Circumference = 2 Pi r

360 degrees = 2 Pi r

r = 360 degrees / 2 Pi

= 360 degrees / 2* 3.14

= 57.3 degrees

( One degree is 60 minutes and one minute is 60 seconds and hence one degree = 60*60 = 3600 seconds )

= 57.3 degrees * 3600 seconds

= 206265 seconds of arc

This is the how the Magic Figure in Astronomy, 206265 seconds, is derived !

Computation of Directional Strength

Directional Strength or Digbala is one of the Sixfold strengths. Here we give the formula for computing Directional strength

First find out the Digbala arc. For instance Jupiter has full directional strength when he is on the Ascendant. That means 180 degrees from that point, on the Descendant he is zero.


So the equation for Digabala arc is

Digbala arc = Longitude of the planet - its powerless point.

( if the difference is more than 180, subtract it from 360 degrees ).

The midpoint of the House or Bhava is taken into consideration. The midpoint of the 7th House becomes the powerless point of Jupiter

Divide the Digbala arc by 3 and you get the Digbala or Directional strength.

Definitions of some Vedic terms

Astrology is based on the Platonic Imitation Theory that the Earth
is an exact replica of Heaven. "As Above So Below" - was the form-
ula summed up by Hermes Trismegistes. We find that the pauper of
today is the prince of tomorrow and the prince of today is the
pauper of tomorrow. What is the base of all this ?

Astrology - the Science of Time - is the only science that has the
answer as it deals with natural causes and the corresponding cele-
stial causes. Since everything happens by Cause we can infer that
everything happense by two types of causes - natural & celestial.
We know the natural causes which has determined the present events.
This heavenly science deals with the celestial causes which has de-
termined the present events. Divine Providence coincides completely
with natural causes.

The Law of Correspondences of classical philosophy states that
everything on earth is an exact copy of that which is structured
in Heaven. Astrologers therefore analyse the heavenly archetype
( the horoscope ) to understand the earthly reflection.

GLOSSARY OF SANSKRIT TERMS USED
-------------------------------

LMT - Local Mean Time after the longitudinal correction is applied.

Nirayana - Sidereal viz based on the constellation of fixed stars.

Sayana - Tropical viz based on the Signs of the Zodiac.

Rasi - Zodiacal Sign . There are 12 signs of the Zodiac from Aries
to Pisces . 30 degrees of arc.

Sphutam - Celestial longitudes of planets.

Nakshatra - Star or asterism. There are 27 asterisms or stars which
tenant the Zodiac

Zodiac - A belt of the heavens 9 degrees to either sides of the
Ecliptic.

Eclipitic - The real path of the earth round the Sun.

Pada - Quarter of a star or asterism. A star is divided into 4
quarters or 4 padas.

Lord - Lord of the star. All stars have lords. For instance Alpha
Arietis or Aswathi is owned by Ketu. Revathi or Zeta Piscium is
owned by Mercury.

Ayanamsa - Precessional Distance. It was observed that the Tropi-
cal Zodiac precedes 1 degree in every 72 years. It takes 25920
years to precede 360 degrees and this is called the precession of
the Equinoxes.

Chitra Paksha Ayanamsa - The Indian Govt adopted this Ayanamsa for
all astronomical calculations. ( There are other Ayanamsas formulated
by scholars.)

Ahargana - No of days elapsed from the beginning of Kali Era which
started from 3102 BC as per the Hindu Calender.

Thithi - Lunation . When the Moon is within 12 degrees from the Sun
it is the First Lunation or Prathama. When Moon is within 24 degrees
from the Sun it is the Second Lunation or Dwitheeya.

Thriteeya - Third Lunation
Chathurthi - Fourth Lunation
Panchami - Fifth Lunation
Shasthi - Sixth Lunation
Sapthami - Seventh Lunation
Ashtami - Eighth Lunation
Navami - Ninth Lunation
Dasami - Tenth Lunation
Ekadasi - Eleventh Lunation
Dwadasi - Twelvth Lunation
Thrayodasi - Thirteenth Lunation
Chaturdasi - Fourteenth Lunation
Pournami - Full Moon. Moon 180 degrees from the Sun
Amavasya - New Moon. Conjunction of the Moon with the Sun.

Nithya Yoga - There are 27 Nithya Yogas. Period during which the
joint motion in longitude of Sun and Moon amounts to 13 degree 20
minutes of arc.

Shukla Paksha - Bright Fortnight - 15 days after the New Moon.
Krishna Paksha - Dark Fortnight - 15 days after the Full Moon.

Dasa - Period of Directional Influence. Saturn's period is 19
years Jupiter's 16, Mars 7, Moon 10 Sun 6 Venus 20 Rahu 18 Ketu 7.
When a person is born he is born in a certain star. It is ruled
by a planet. This planet is ruling at the time of birth. Say
a child is born in a star called Zeta Piscium or Revathi. Its
lord is Mercury and Mercury Dasa will be ruling at the time of
birth. After 17 years it will be replaced by Ketu Dasa for 7
years and after 7 years Venus dasa for 20 years.

KETU - Moon's Descending Node . Caput Draconis.

RAHU - Moon's Ascending Node . Cauda Draconis.

Ashtavarga - Benefic points of planets in a Rasi or Zodiacal
Constellation.

Sarvashtavarga - Total benefic points in the 12 signs.

Rasi Chart - Map of the heavens at the time of birth.

Navamsa Chart - 1/9th division of the Rasi Chart.

Bhava Chart - Chart based on the Ascending Degree. ex - Suppose
the ascending degree of a man is 20th degree of Cancer. This point
is taken as the mid-point of Bhava and 15 degrees to either side
is taken as the Ascendant House. So the Ascendant house or the
First House is from 5th degree of Cancer to the 5th degree of Leo.

LAGNA - Ascendant - The Eastern Horizon of the place. The Sign
rising at the eastern horizon. For instance if the date of birth
is say 05th JAN the sign rising at the Eastern Horizon at the time
of Sunrise is Sagittarius. This is known as Sagittarius Ascendant
or Dhanus Lagna.

GUL - Gulika a satellite of Saturn.

Bhava Sphutam - Longitudes of Houses ( Bhavas ).

Arambha _ Starting Point
Madhya - Mid-point
Anthya - End-point

Ayana - Solstice . There are 2 two types of Ayanas _ Uttarayana
and Dakshinayana ( Northern progress of the Sun and Southern
progress of the Sun). When the declination of the Sun is North
- Uttarayana. When the declination of the Sun is south - Dakshi-
nayana).

Rithu - 2 months. There are 6 Rithus in a Year.

Chandra Vela Chandra Kriya and Chandra Avasthas - Subtle States
of the Moon.

Saptha Varga - Points attained by planets.
Subha Varga - Benefic Points.
Papa Varga - Malefic Points.

Drekkana - Decanate . 10 degrees of a Sign.
Hora - 1 hour. 15 degrees of a Sign.
Sapthamsa - 1/7th Division of a Sign.
Dwadasamsa - 1/12th division of a Sign.
Trimsamasa - 1/30th division of a Sign.

Apahara or Bhukthi - Sub -period of a planet. In a ruling Dasa
there will be sub-periods of other planets.