# How did the authors of Surya Siddhanta find the diameters of other planets in the solar system?

The Surya Siddhanta, "a Sanskrit treatise in Indian astronomy from the late 4th-century or early 5th-century CE" is truly a great work.

But how was it possible for the writers to find the exact values of the diameters of different planets and the distance between the sun and the earth?

Also, are there any mistakes in this book?

If there's any problem in my question please inform me.

• This site works better asking about very specific problems you might encounter in your day to day work or study. Speculating about supernatural influence in a religious work is outside the scope of this site, and asking users to review an entire work to list all mistakes or errata isn't really a great fit for this type of Q&A. – Robert Cartaino Apr 16 '18 at 20:18
• It looks like an interesting book, but I also don't understand what exactly you ask. The Wikipedia article (your link) explains how the astronomical knowledge in the book is based on ancient Greek astronomy. The table in the article lists the parameters from the Surya Siddhanta together with Greek and modern value. It looks to me that the the Surya Siddhanta has similar accuracy as the Greek. This knowledge developed over centuries of observations, and nothing in that Wikipedia article seems unusual to me. Can you be more specific which facts surprise you? – Stephan Matthiesen Apr 17 '18 at 7:43
• @StephanMatthiesen I edited it to clarify my question, you can have look – Abu Safwan Md farhan Apr 17 '18 at 8:11
• Ah, I think I understand now. Perhaps you should change the title and ask specifically "how did the Surya Siddhanta know the diameter of planets?" Your question was (before you edited it) still hard to understand because there are many different astronomical data in the text. Precise value for the period of planets are NOT surprising because you can easily observe them, but values for the diameter are difficult, so that is a fair question. It might be better suited in the history of science stackexchange. – Stephan Matthiesen Apr 17 '18 at 10:49
• Actually it is a really good question how they measured the diameters of planets (if the Wikipedia article is correct...) without good telescopes, and now I would like to know the answer too! – Stephan Matthiesen Apr 17 '18 at 10:56

The authors assume a geocentric universe (first thing that is wrong). They then assume that the planet Mars has the same apparent diameter as a globe 30 yojana in diameter (about 150 miles) in the same orbit as the moon, from a perspective at the centre of the Earth. This is just stated, and appears to be supposition. It is an incorrect figure. It is conceivable that some kind of system for sighting through a pinhole could be used for this estimate. This method tends to over estimate the apparent size of planets.

They next claim that the other planets have apparent sizes that would be the same as globes with diameter 37.5 (Saturn), 45 (Mercury) 52.5 (Jupiter) and 60 yojana (Venus). These form an arithmetic sequence with a common difference of 7.5, but apart from that, these values seem to be arbitrary (and are wrong). They might have been based on some kind of pinhole observations, but rounded to a simple sequence for the sake of the poetry or for easier memorisation.

There is uncertainty about the ancient value of the yojana. A different conversion to miles will give different values throughout.

Using this assumption and the distance already calculated to the moon they calculate the apparent angular diameter of each planet. The actual values they get are wrong, In fact, the angular diameter varies as the planet's distance varies.

        calculated value modern observed value
Mars       2 arcmin      (actually 0.06 - 0.39)
Saturn     2.5 arcmin    (0.25 - 0.34)
Mercury    3 arcmin      (0.08 - 0.17)
Jupiter    3.5 arcmin    (0.51 - 0.83)
Venus      4 arcmin      (0.16 - 1.05)


As you see the calculated values are much too large (ie wrong). They are comparable with values supposed to have been found by Hipparchus, but without a known observational basis. Tycho Brahe also gave similar values, found by sighting through a pinhole. This simple method doesn't give a good estimate of the angular size. The simple pattern in the calculated values is due to the original assumption that the globes were in an arithmetic sequence.

There is then a calculation of the geocentric orbital radii of the planets. They assume that Venus, Mercury and the Sun all orbit at a distance of 3.4 million miles. This is a significant underestimate, especially for the sun (this is wrong). The distances to Mars, Jupiter and Saturn were also underestimated.

One can then combine the apparent angular diameter (which is too large) with the calculated distance (which was too small) to obtain an estimate of the planetary diameter. When this is done, it gives exceedingly good estimates of the diameter of Mercury and Saturn (within 1%). A good estimate for the diameter of Mars (about 10% out), and a poor estimate for Venus and Jupiter (about 50% of the accepted modern values).

It is clear that there is much that is wrong. A combination of overestimates of some values and underestimates of others cancels out to give some impressive looking figures for two out of five planets. But do note that the estimates for Jupiter and Venus were a long way out, and all the numbers which the calculations were based on were wrong. In total there are 15 values calcuated here 5 apparent diameters, 5 geocentric distances and 5 actual diameters. Of these only 2 values are impressively accurate.

They did better than other pre-telescopic observers, but it isn't clear that they obtained values by anything other than luck.

Source

• As a sidebar, is it atmospheric scattering that makes planets appear larger than they are to the historic scientists in your answer, or is that not really a factor? (no good way to measure things that small might be the entire answer). Perhaps that's a new question but it seems related enough to ask here. – userLTK Apr 20 '18 at 3:47
• Not certain, as I can't find details of Brahe's experiment. It is probably something like "set up pin hole. Measure time for which planet is visible through pinhole as Earth rotates, convert time to angular size." A 1arcmin disc would be visible for about 4 seconds. There are lots of inaccuracies: non-zero size of pinhole, diffraction at pinhole, moving one's head slightly. These all tend to overestimate size. – James K Apr 20 '18 at 9:55

Here is a comment on the physics behind planetary diameters which are derived from the nebular hypothesis proposed by the rshis of long ago (and reproposed in the 18th century). The planets condensed from a solar nebula!

The planets are too far away to estimate diameters without powerful telescopes.Diameters can be estimated only by scaling rules based on physics.

“The Surya Siddhanta also estimates the diameters of the planets. The estimate for the diameter of Mercury is 3,008 miles, an error of less than 1% from the currently accepted diameter of 3,032 miles. It also estimates the diameter of Saturn as 73,882 miles, which again has an error of less than 1% from the currently accepted diameter of 74,580. Its estimate for the diameter of Mars is 3,772 miles, which has an error within 11% of the currently accepted diameter of 4,218 miles. It also estimated the diameter of Venus as 4,011 miles and Jupiter as 41,624 miles, which are roughly half the currently accepted values, 7,523 miles and 88,748 miles, respectively.” from the wiki at https://en.wikipedia.org/wiki/Surya_Siddhanta

[The Surya Siddhanta is the name of a Sanskrit treatise in Indian astronomy from late … It calculates the earth’s diameter to be 8,000 miles (modern: 7,928 miles), diameter of moon as 2,400 miles (actual ~2,160) and the distance between moon …

How were the planetary sizes determined? What are the possible scaling rules? Let us define

D = Planetary diameter

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:

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.

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. 0.383.87E-01

Venus 4011.00 0.50 7.20E-01

Earth 8.00E+03 1.001.00E+00

Mars “3.77E+03 “0.47 1.52E+00

Jupiter 4.16E+04 5.205.19E+00

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

( Ignore the. I had to use it to line numbers up.) 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 27,000 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 because of tectonic shifts.)

No luck was involved! Just thinking smart!

Let me add background information on astronomy of ancient India. There were many before Aryabhata. Box 3. Indian Astronomers before Aryabhata

“As mentioned in the Chandogya Upanishad (VII.1.2, 4), nakshatra-vidya (science of asterisms) was among the core disciplines of study in the Vedic era. Astronomers were called nakshtra-darsa (star-observers) or gal}aka. The sage Atri (who was among the originators of the oldest Vedic hymns) and his descendants were distinguished for expertise in accnrate edipse prediction and planetary astronomy. The Rg-Veda describes a solar eclipse observed by Atri (dated 3928 BCE in [5], p.1l6; [6], pp.173-l74). The Taittiriya Brahmana (Ill.lO.9) eulogises Ahina, Devabhaga and for attaining bliss due to their absorption in the science of the Sun, i.e., astronomy ([7], pp.20-2l); sage Matsya is also mentioned (1.5.2, 1) in the context of astronomy. Garga is the most ancient astronomer referred to in post-Vedic treatises. The Mahahharata (XII.59.ll) refers to him as the court-astronomer of the great King Prthvi. TIte cpic (IX.37.14-17) mentions that a holy tirtha on the Sarasvati was named after the as Garga-srota ("stream of Garga"). This was the sacred place where Vrddha Garga performed ascetic penance for self-purification and attained mastery over astonomy. Rishis of high merit and rigorous discipline l1sed to assemble here to acqllire thc profollnd knowledge of astronomy from the venerated Rshi.

Ancient Indian traditions mention a list of 18 astronomy texts called siddhiintm.; ("established theories") named after SfIrya, Pitamaha, Vyasa, Vasistha, Atri, Parasara, Kasyapa, Narada, Garga, Marici, Manu, Ailgira, Lomasa, Plllisa, Cyavana, Yavana,Brughu and Saunaka.

Varahamihira (505-587 CE), himself a prominent astronomer, also mentions Asita-Devala, Maya, Badarayalla and Nagllajit. Many of the treatises by the above astronomers got lost even by the time of Varahamihira; None are available in their original forms.

While considerable astronomical knowledge is embedded in early Vedic literatures, the oldest available treatise devoted exclusively to astronomy is the Vedanta Jyothisha (G. 1300 BCE vide [6]) composed by sage Lagadha. The Vedanga era represents a transitional pcriod in Indian civilisation when the Vedic culture was on the wane and there was a consequent attempt to organise and formulate the extant knowledge and systematise them into various branches called shastras .

Aryahhatlya (499 CE) is the earliest extant astronomy treatise after the Vedanga Jyotisha. It was composed during the "Classical Age" of post-Vedic India. Towards the beginning (Ganita 1) and the end (Gola 48-50) of his text, Aryabhata had made a general acknowledgement of his predecessors." from

https://www.ias.ac.in/describe/article/reso/011/05/0058-0072 by Amar Kumar Dutta.

More info on why I am doing this: Surya Siddhanta is dated by wiki which says : Surya Siddhanta is a Hindu text on astronomy from late 4th-century or early 5th-century CE[1] Above is verse 1.1, which pays homage to Brahma.[2 Some scholars refer to Panca siddhantika as the old Surya Siddhanta and date it to 505 CE.[17] https://en.wikipedia.org/wiki/Surya_Siddhanta

It is pretty old and gives a list of planetary diameters.

Now we have to explain how the data was known for orbit radii and how planetary diameters were calculated. They didn’t have telescopes and such in those days.

Data must have been available for whatever method was used before Surya Siddhanta.

Now I show the data was available . ( Kak says “ My discovery that the Rgveda is an altar of mantras came rather suddenly. Although I had been studying the altars described in the Shatapatha Brahmana for several months, I had never thought of any connection of these with the Rgveda. It was while reading some unrelated matter the idea flashed that the Rgveda itself is a symbolic altar. “)

It is worth reading Subash Kak’s “The Astronomical Code of the Ṛgveda (Third Edition) “ for a fascinating insight into Hindu Civilization and Astronomical knowledge.