There are a few scientific discoveries that are not found mentioned in Varahamihira's Brhat-Samhita.
How do heavenly bodies remain in the skies? How is it that they do not fall? Everybody thinks that it was Newton who found the answer to such questions. The very first stanza in the Suryasiddhanta, which is a very ancient treatise, states that it is the force of attraction that keeps the earth from falling.
In Sankara's commentary on the Upanisads there is a reference to the earth's force of attraction. If we throw up an object it falls to the ground. This is not due to the nature of object but due to the earth's force of attraction. "Akarsana-sakti" is force of attraction, the power of drawing or pulling something. The breath called "prana" goes up, "apana" pulls it down. So the force that pulls something downward is apana. The Acarya says the earth has apana-sakti. The Prasnopanisad (3. 8) states: "The deity of the earth inspires the human body with apana". In his commentary on this, Sankara observes that, just as an object thrown up is attracted by the earth, so prana that goes up is pulled down by apana. This means that our Upanisads contain a reference to the law of gravitation. There are many such precious truths embedded in our ancient sastras. Because of our ignorance of them we show inordinate respect for ideas propounded by foreigners, ideas known to us many centuries before their discovery by them. Our Jyotisa is also some thousands of years old. Even so it foresaw the mathematical systems prevalent in the world today.
At the beginning of the kalpa, all grahas were in alignment. But over the ages they have changed their courses. When another kalpa commences, they will again remain in alignment.
The "samkalpa" we make before the performance of any ritual contains a description of the cosmos, a reference to the time cycle, and so on. All this is part of Jyotisa.
Centuries ago, we knew not only about the earth's force of attraction but also about its revolution round the sun. Aryabhata, Varahamihira and others spoke of the heliocentric system long before the Western astronomers or scientists. Until the 16th century people in Europe believed that the earth remained still at the centre of the universe and that the sun revolved around it. They further believed that this was how day and night were created. If anybody expressed a different view he was burned at the stake by the religious leaders.
"It is the earth that revolves around the sun, not the sun round the earth", declared Aryabhata. He used a beautiful term to describe the logic behind his view : "laghava-gaurava nyaya". "Laghu" means light, small, etc and "laghava" is derived from it. The opposite of "laghu" is "guru", weighty, big, etc. "Guru" also denotes a weighty personality, a great man, like an acarya or teacher, one who has mastered a sastra. If the acarya is guru the disciple must be laghu. The student is small and "light" compared to his guru. So he goes round the latter. This is based on "laghava-gaurava nyaya". By adducing this reason for the earth going round the sun, Aryabhata combined science with a traditional sastric belief.
In the old days religious leaders in Europe were opposed to science and even burned scientists as heretics. But today we join the descendants of the very same people to make the preposterous charge that the Hindu religion stood in the way of scientific advancement, that it ignored the matters of this world because of its concern for the other world. As a matter of fact our traditional sastras are a storehouse of science.
"The sun remains still and it is the earth that goes round it. It is only because the earth revolves round the sun that it seems to us that the sun rises every day in the east and sets in the west". This is mentioned in Aitareya Brahmana of Rgveda. The text says clearly : "The sun neither rises nor sets".
That all learned people in India knew about the earth's revolution is shown by a passage in the Sivotkarsa-Manjari by Nilakantha Diksita who was minister of Tirumala Nayaka. One stanza in this work begins like this : "Bhumir bhramayati" and from it we must also gather that the author's great-uncle, Appayya Diksita, also knew about this truth. What is the content of this verse?
Siva is called "Astamurti". Earth, water, air, fire, space, the sun and the moon, the yajamana or sacrificer--they are all the personification (murti) of Isvara. Among them only the yajamana has no bhramana or motion. All the rest have bhramana, says Appayya Diksita. That he has said so is mentioned in the verse in question by his younger brother's grandson, Nilakantha Diksita.
We see that air has movement, that fire does not remain still, that water keeps flowing. When we look up into the sky, we notice that the sun and the moon do not remain fixed to their spots. As for space, it is filled with sound and it cannot be still. But the earth apparently stands still. Even so, says Appayya Diksita, it has motion. "It revolves".
Let us now consider the shape of the earth. Europeans claim that they were the first to discover that the earth is like a ball, that in the past it had been thought to be flat like a plate. All right. What word do we use for "geography"? "Bhugola sastra", not just "bhu-sastra". We have known from early times that the earth is a "gola", a sphere.
We call the universe with all its galaxies, "Brahmanda". It means the egg created by Brahma (the cosmic egg). An egg is not exactly spherical in shape, but oval. According to modern science the universe too is oval in shape. The cosmos is always in motion, so observe modern astronomers. "Jagat" is the word by which we have known it from Vedic times. What does the word mean? That which does not stand still but is always in motion, that which "is going".
In our country too there were people who refused to believe that the earth rotates on its axis. I will tell you the view of one such school of thought. The earth's circumference is about 25, 000 miles. So if it rotates once in 24 hours then it means it rotates more than 1, 000 miles an hour or 16 or 17 miles in one minute. Those who did not accept the fact of the earth's rotation tried to prove their point thus :"There is a tree in Mylapore [in Madras]. Imagine there is a crow perched on one of its branches. It leaves its perch this moment and soars high and, by the next minute, it perches itself again on the branch of the same tree in Mylapore. If the rotation of the earth were a fact how would this be possible? The crow should have descended to a place 16 or 17 miles away from where it had started.
I have not checked on how this argument was answered. But when I asked people who know modern science they said : "Surrounding the earth for some 200 miles is its atmosphere. Beyond that there are other spheres. When the earth rotates these too rotate with it". I may have gone slightly wrong in stating the view of modern science. However it be, there is no doubt that when the earth rotates, its atmosphere also rotates with it.
What are called Arabic numerals actually belong to India. This fact was discovered by Westerners themselves. The zero is also our contribution and without it mathematics would not have made any advance. Bhaskaracarya established the subtle truth that any quantity divided by zero is infinity ("ananta"). He concludes one of his mathematical treatises with a benedictory verse in which he relates zero to the Ultimate Reality.
When the divisor goes on decreasing the quotient keeps increasing, does it not? If you divide 16 by 8 the quotient is 2; if the same quantity is divided by 4 the result is 4. Divided by 2, the quotient is 8. Divided by zero? The quotient will be infinity. Whatever the number divided, the result will be infinity if the divisor is 0. Bhaskaracarya gives it the name of "khahara". "Kham" means zero, "haram" means division. Bhaskaracarya says : "I pay obeisance to the Paramatman that is Infinity".
For a general background, please see here