Actually he is specifying the speed of light. Your objection is common, but his commentary says specifically "tatha ca smaryate" or "it is remembered here" and since the Rg Veda verse in question is specifically glorifying the light aspect of the sun (it brightens the sky, and travels very fast), it is reasonable assumption to make that Sayana is speaking about light here.
I would disagree with that statement. Many ideas and knowledge that the Greeks first had came from India (when Alexander the Great established trade routes between the two countries ). One of these is the Pythagoras theorm which is attributed to Pythagoras but yet was first mentioned 300-400 years in the Baudhayana Sutras of
Taittiriya branch of the
Krishna Yajurveda (dated by historians to be compiled 7 to 8 century BCE ). The sutras itself state many advanced mathematical ideas like Pythagoras theorem and also an approximation of the root of 2. The exact text is is below and is an example of mathematics in the Vedas:
dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī,
cha yatpṛthagbhūte kurutastadubhayāṅ karoti.
"A rope stretched along the length of the
diagonal produces an
area which the vertical and horizontal sides make together." (this is essentially Pythagoras' theorem)
Copying the the rest directly from Wiki:
Baudhāyana sutra .61-2 gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the
square root of 2:
samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet
tac caturthenātmacatustriṃśonena saviśeṣaḥ
"The diagonal [lit. "doubler"] of a square. The measure is to be increased by a third and by a fourth decreased by the 34th. That is its diagonal approximately"
That is,
which is correct to five decimals
Other theorems include: diagonals of rectangle bisect each other, diagonals of rhombus bisect at right angles, area of a square formed by joining the middle points of a square is half of original, the midpoints of a rectangle joined forms a rhombus whose area is half the rectangle, etc."
So there is the proof that Shivji requires of Mathematics in the Vedas. Even Pythagoras therem was known by the Veda before Pythagoras himself!
He knew the speed of light! Even if we interpret is your way, the light interpretation is stronger simply because his estimates match very closely to modern estimates. There is no way that it is possible for a culture at that time (when westerners thought that light didn't even have a speed!) to do know that. This for me is proof that the Vedas can also speak confidently about material claims and be verified by science.
I am afraid the Vedas claim that from the start. The Aitareya Brahmana (3.44) declares:
"The Sun does never set nor rise. When people think the Sun is setting it is not so. For after having arrived at the end of the day it makes itself produce two opposite effects, making night to what is below and day to what is on the other side. Having reached the end of the night, it makes itself produce two opposite effects, making day to what is below and night to what is on the other side. In fact, the Sun never sets."
No this does not specifically say the earth is spherical, but advanced astronomical concepts are mentioned, and it is implied heavily here of earth's spherical nature (otherwise I would it ta'k about the opposite effects)? As for the term Bhu Gola, I shall have to search the Vedas, I think I did see the verse in Rg Veda that mentioned "Bhugolam". I am certain the Bhagavatam also used the word Bhugolam to refer to earth. However the former evidence I provided stands. As for the Puranic conception, representing Jambhudwipa as a series of concentric circles refers to our solar system with each circle being a set of planetary systems.
This article gives a very in depth analysis of those verses of the Bhagavatam using the knowledge given in Surya Siddhanta. It is long, but worth the read.
Yes I will post a few here:
evaṁ kālo ’py anumitaḥ
saukṣmye sthaulye ca sattama
saṁsthāna-bhuktyā bhagavān
avyakto vyakta-bhug vibhuḥ
.
"One can estimate time by measuring the movement of the atomic combination of bodies. Time is the potency of the almighty Personality of Godhead,
Hari, who controls all physical movement although He is not visible in the physical world." (SB 3.11.3)
kalalaṁ tv eka-rātreṇa
pañca-rātreṇa budbudam
daśāhena tu karkandhūḥ
peśy aṇḍaṁ vā tataḥ param
(Lord Kapila said): On the first night, the sperm and ovum mix, and on the fifth night the mixture ferments into a bubble. On the tenth night it develops into a form like a plum, and after that, it gradually turns into a lump of flesh or an egg, as the case may be.
māsena tu śiro dvābhyāṁ
bāhv-aṅghry-ādy-aṅga-vigrahaḥ
nakha-lomāsthi-carmāṇi
liṅga-cchidrodbhavas tribhiḥ
"In the course of a month, a head is formed, and at the end of two months the hands, feet and other limbs take shape. By the end of three months, the nails, fingers, toes, body hair, bones and skin appear, as do the organ of generation and the other apertures in the body, namely the eyes, nostrils, ears, mouth and anus." (SB 3.31.1-2)
Now as a biology student, I must point out that this version of events in the Bhagavatam fully support and are verified by modern day embrology. The rapid division of the cells from the moment of conception (and subsequent formation of the Blastocyst) does make it look like a bubble (due to it being multicelluar and a hollow inside, like a bubble, see below image). The formation of the limbs etc also are on point (though modern embryology is more specific here).
Even the Bhagavatam's calculation of Kalpa dates the age of the universe to be billions of years (9 billion if I remember while the modern estimate is 13.7 billion), while societies at that time thought earth was only millions or even thousands of years old.