Western scholars Thibeau and Whitney argued that the early Indians did not have any conceptions about Maths and Astronomy and the calculations of the Cosmological Cycles ( One Cosmological Cycle = 4.32 billion years ) were looted from the Greeks and the Romans.

On the other hand, another Western scholar, the Rev Ebenezor Burgess who translated the Surya Siddhanta into English, differed from them saying that the early Indians were pioneers of Astronomy and Maths.

In Aryabhateeyam, Maha Bhaskareeyam and Brahma Sphuta Siddhanta, to mention 3 major astronomical treatises, Bhuja was Sin, Koti was Cos and Sparsa was Tan. Bhuja chapa was Arc Sine of an angle (Asin), Koti Chapa was arc cosine of an angle ( Acos )& Sparsa Chapa was arc tangent of an angle(Atan). Sin was Bhujajya/ Trijya, Opposite Side/Hypotenuse and Cos was Koti Jya / Trijya, Adjacent Side/Hypotenuse. All trignometric funtions which we know as Sin, Tan and Cos had Sanskrit names and Spherical Astronomy and Spherical Trignometry were well developed in India !

Kala Hora has been defined as 1/12th of a day

Dina Dwadasamso Matha Kalahora

If Thursday, then the ruler of the first hour is Jupiter ( Jove or Thor’s day, Thursday)

Pathi tasya poorvasya varadhi nadha

Nisayam thu vareswarath panchamadya

The ruler at night is the fifth lord

meaning on a Sunday, after sunset, the first hour is ruled by Venus

as per the rule

Arka Sukra Budhas Chandra Manda Jeeva Dharasutha

Sun, Venus, Mercury, Moon, Saturn, Jupiter and Mars.

Why is Monday after Sunday ?

The answer is given by the sequential order of Planetary Hours or Kala Hora

On Sunday, at surise, the first hour or Kala Hora is ruled by the ruler of Sunday, the Sun. So after 21 hours, the 22nd hour is ruled by Sun, the 23rd hour by Venus and the 24th hour by Mercury and the 25th hour, that is next day is ruled by Moon and so the next day is Moon’s day or Monday !

Planetary Hour = Duration of day /12

Duration of Day = Sunset – Sunrise
Duration of Night = Sunrise – Sunset

The duration of Night and Day varies and it is not exactly 12 hours. So in the program formulae should be given for finding out Planetary Hours !

We have said before that the mean longitude of the planet should be subject to a trignometric correction to get the Vikshepa Vritteeya Sphuta or Reduction to Aphelion. Then it is reduced to Ecliptic by the formula

Sin h = 1 – Cos l Sin Y Cos Y / Cos l

The longitude thus obtained is subjected to another trig correction, Reduction to Perihelion or Sheegra Kriya. The term Trignomety, it must be mentioned, is derived from the Sanskrit Trikonamithi and Geometry, from Jyamithi. Brahma Gupta in his mathematical treatise Brahma Sphuta Siddhanta defined Jya as 5 degrees of 1/6 th of a Zodiacal Sign. Bhujamsa, he said, is radius multiplied by modern sine. In hoary times, Astronomy was sister to Astrology and both were united by Mathematics. Astronomy and Maths ( Ganitha ) is one the Three Skandas ( branches ) which constitue Jyothisha or Astro Physics. Samhita ( Philosophy ) and Hora ( Astrology ) were the other branches.

The Longitude of Gulika is the longitude of the Ascendant at the time of Gulika’s rise.

Gulika rises at different times on different days. Saturday he rises at 4 Nadis, that is 4*24 minutes, after sunrise.

Once the calculation of the Asc is carried out, the computation of Gulika’s longitude becomes easy

In the Western system, the Moon’s mean longitude is subjected to 6 trignometric corrections. ( There are actually 300 ).

In the Indian Sidereal System, the Moon is subjected to 14 trignometric corretions, the Chatur Vidha Jya samskara. All the major perturbations of the Moon- the Parallactic Equation, the Evection, the Variation, the Annual Equation – are taken into consideration.

Sunrise = 6 Hours + Equation of Time – C, the Ascensional Difference – R, the refraction correction

Sunset = 18 Hours + Equation of Time + C + R

Computation of Sunrise and Sunset are necessary for an Astrology program. Sunrise varies from latitude to latitude. Also the Ascendant.

From Aries to Libra is the Northern Celestial Hemisphere. When the Sun is in the Northern Hemisphere, days have more duration.

From Libra to Aries is the Southern Celestial Hemisphere. When the Sun is in this Hemisphere, nights have more duration.

The Great Circle called the Zodiac, ” the oblique line that beareth all planets”, as Dante called it, is divided into 4 quadrants of (360/4) 90 degrees.

The First 90 degrees is Odd
The Second 90 degrees is Even
The Thirdt 90 degrees is Odd
The Fourth 90 degrees is Even

“Oja yatra guanira kotir apara meshadi jookadhi kau”

The distance traversed by a planet is called Bhuja & the untraversed distance is Koti.

We give below the equation of Bhuja

In the First Quadrant, if a planet traverses 42 degrees, the bhuja is 42 degrees

In the first 90 degrees, the same longitude
In the Second 90 degrees, longitude = 180- longitude
In the Third 90 degrees, longitude = longitude – 180
In the Fourth 90 degrees, longitude = 360 – longitude

This equation of Bhuja should be applied for all astro mathematical calculations.

The Zodiac Software was developed according to the principles of Vedic Spherical Astronomy & Trignometry.

The longitudes measured along the Ecliptic are called true longitudes and the longitudes measured along the Vishuvat Vritta, the Celestial Equator, are known as Right Ascension.

When we say the Right Ascension of East Point, we mean the East Point along the Celestial Equator. The Right Ascension of the Meridian Cusp( RAMC ), is the longitude of the MC or Mid Heaven measured along the Celestial Equator.

The formula for computing the MC , the Madhya Lagna is as follows

tan K = tan R /cos w

where is the K is the longitude of the MC, and R, Sidereal Time converted into degrees.

180 degrees from the Madhya Lagna or the MC is the IC, the Imum Caeli or Patala Lagna.

The formula for computing the Ascendant is

Tan L = Sin E / cos E cosw – Sin w Tan A

The Ascendant is a point on the Celestial Horizon. The Eastern Celestial Horizon

First compute E, the Right Ascension of East Point, the East Point lying on the Celestial Equator and this E is subjected to the trignometric correction referred to as above.

The Celestial Horizon is known as Kshithija. w is the maximum declination of the Sun, The Soorya Parama Kranthi. A is the latitude of the place.

The Eastern Point on the Celestial Horizon is Udaya Lagna
180 degrees from it is the Astha Lagna or the Descendant