User:Partha Shakkottai/sandbox

Planetary diameters How were the planetary sizes determined by the ancient Rishis? What are the possible scaling rules? Let us define

D = Planetary diameter

R= Orbit radius

M = planetary mass ~ D^3

T = Orbit time = 2 Pi/ Omega

I = angular momentum = Integral of R^2 dm .Omega ~ R^2 D^3/ T

Possible relations: (This law of gravitation is most unlikely to be known so early in History)

If force is G M_sun M_planet /R^2 = Mplanet. Omega^2 R

R^3. Omega^2 = constant

R^3 ~T^2

Snow plow theory:

Larger radii sweep more particles leading to bigger planets

D^3 ~ 2Pi R no pf particles ~ 2Pi R n. volume ~ 2 pi R R. thickness

~ R^2 if thickness is fixed, n being number density

Or

D^3 ~ R^2

Thin disk:

In this case the planet grows to bigger than the thickness and

D^3 ~ R^3 or D ~ R

It appears that ancients assumed the last possibility. The planetary diameter scales with the orbital size.

Body mile(D) “Relative Size  `Relative size (modern)

Mercury 3008. 0.38         3.87E-01

Venus 4011.00      0.50          7.20E-01

Earth 8.00E+03     1.00          1.00E+00

Mars 3.77E+03      0.47          1.52E+00

Jupiter 4.16E+04   5.20          5.19E+00

Saturn 7.39E+04   9.24E+00        9.53E+00

Relative size is from Surya Siddhanta and is compared to modern measurements of orbits compared to Earth’s orbit. Venus and Mars have the most disagreement. They are the rocky planets. The agreement is very good in general. Especially good for gas giants!

Conclusion: The vedas predicted planetary sizes using the acretion model from the initial solar nebula. So it automatically means they were the first to hit upon the idea of sun-centered planetary system!

This also means Indian Astronomy was developed by Indians with no input from the Greeks. No others have planetary diameters! The kalachakra was a giant astronomical clock and was used to calculate orbits of planets visible to the naked eye from which planet sizes were determined, a far cry from the flat earth theory of Christianity! See

https://www.quora.com/How-was-kalachakra-used-in-Indian-Asronomy

This uses four dials, one of which is the Zodiac, the same as the Greek one, most likely copied by the Greeks, an exact translation from Sanskrit! For fixed stars, the kalachakra uses bright stars with Sanskrit names. The Indians have been observing stars from long enough to know the period of nutation of Earth is 25,000 years. At least 5000 years of data is required.

Rg Veda is variously dated from 1500 BC to 8000 BC (from internal evidence on the order of time when River Saraswati was still flowing). (The internal reference also mentions a big earthquake that made River Saraswati stop flowing.)