Of Natural Strength and Intercalary Months          By Govind Kumar

Natural Strength, Naisargika Bala

It is the inherent property of a celestial object, which possesses the following properties

1) This force is constant for a celestial object, not varying in time.

2) This force is proportional to the size of the diameter of the planets.

3) This force is inversely proportional to the distance, r, from the Sun.

4) It increases in the order from the farthest planet to the nearest planet to the Sun. From Saturn,Jupiter, Mars, Venus, Mercury, Moon and Sun.

5) This Force is a major factor when planets are involved in Planetary War ( Graha Yuddha ), when their longitudes are more or less identical in the Ecliptic.
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Let F1 and F2 be the Naisargika Bala of planets 1 and 2 situated in the same distance, r, from earth. Then we have

F1 = F(D1)/r
F2 = F(D2)/r

The ratio of the planetary Naisargika Bala is

F1/F2 = F(D1)/F(D2)

The solar month is 30.438030202068 days

A lunar month = 29.5305881 days

It need not be added that a lunation or synodic month means the interval between two consecutive full moons or new moons. Conjunction ( New Moon ) is 0 degrees and Opposition ( Full Moon ) is 180 degrees

Hence a solar year does not have a whole number of lunar months ( about 12.37 lunations ) So a thirteenth embolismic or intercalary month is inserted.

It was observed that 19 solar years or 19*12 = 228 solar months = 235 lunations and hence 7 Adhi Masas were found in every 19 years. An intercalary or 13th month had to be inserted in a 19 year cycle and 19/7 was the ratio. .

They are called Adhi Masas in Indian Astronomy and they were computed using the Theory of continued fractions. The Theory of contiued Fractions is attributed to Euler. This 19 year old cycle is called the Metonic Cycle, named after the Greek astronomer, Meton.

But then the Indian mathematicians correctly computed the Adhi Masas, centuries before Meton or Euler ! The Indian National Calender is lunisolar, whose dates both indicate the solar year and the moon phases and the next date when the New Moon or Full Moon will occur. The length of the synodic month is given as 29.5305879 days in the Surya Siddhanta, which is correct to six decimals. Surya Siddhanta stated that there are 15933396 Adhi Masas in 51840000 solar months !

The forces are given by ( according to Newtonian modern theories)

F1= ( M1M/r^2)
F2= ( M2M/r^2)

The ratio of the gravitational forces are

F1/F2 = M1/M2

M1 = v1 d1
M2 = v2 d2 ( v volume d density )

If d1 = d2

then

F1/F2 = V1/V2 = F(D1)/F(D2)

Therefore the ratio of the Naisargika Balas of two planets at the same identical position in the Zodiac, as defined by the Indian astronomers, is almost identical to the ratios of the modern gravitational forces of these planets if their mass densities are identical.  