Vedic Astrology is a Vidya & not a Science:
By a Vidya is meant, a subtle system of spiritual-knowledge, discovered by the Vedic Rishis and having as its essential hall-mark, its recurrent focal-theme of the presence of Divinity [Isvara or Parabrahma]- at the very heart of every aspect of nature, as well as in the very bosom of man’s consciousness. In this sense, all Hindu Vidyas are manifestly ‘Isvara [Divinity]-centred’ or ‘centered around the Devatas [Deities]’, rather than being in the nature of the ‘Sciences’-such as we know them in our own day -with their characteristic aloofness from the ‘spiritual’ and the ‘consciousness’ aspects of our human life. This fundamental distinction between the Sciences, on the one hand and the Hindu Vidyas on the other, will have to be constantly borne in mind, if we are to reap a more bountiful harvest as a result of our turning to Vedic astrology and its powerful Remedial Measures.
The natural Vedic self-consistency between the existence of numerous Vedic Devatas [Deities] on the one hand and a unique Godhead [Parabrahma] on the other, may be seen in the following passage of a modern Vedic Rishi, who has had a substantial role to play in creating an intense awareness of the paramount importance of the Vedas, which he held to be the original well-spring of India’s timeless spiritual culture:
“It is a marked, an essential feature of the Vedic hymns that although the Vedic cult was not monotheistic in the modern sense of the word, yet they continually recognize, sometimes quite openly and simply, sometimes in a complex and difficult fashion, always as an underlying thought, that the many godheads whom they invoke are really one Godhead,-One with many names, revealed in many aspects, approaching man in the mask of many divine personalities.”
– Sri. Aurobindo 
Even renowned Jyotish Acharyas[authoritative learned teachers of Jyotisha or Vedic astrology, according to a certain definitive school of learning]are often seen referring to Vedic astrology as a ‘Science’ [6, 7]. Although one can advance three sound reasons in support of such a perception; yet when we look at this whole question from more fundamental considerations, the ‘scientific’ nature of Vedic astrology is seen to be only of very limited validity.
On the grounds that Vedic astrology is ‘quantitative’ like Mathematics, Statistics, Engineering or Theoretical Physics, and is also highly ‘systematic’ like the modern Sciences; this perception of the Jyotish Acharyas does indeed have a certain validity. Moreover, Vedic astrology also has that other hall-mark of the modern ‘Sciences’- namely, the development of this system of knowledge occurring always only as a result of the constant mutual-interaction between empirical data from human lives on the one hand and the theoretical formulation of the astrological sutras on the other. This is exactly like the constant interchange in the Sciences between theory and experiment. Thus some similarities do exist between the methods of Vedic astrology and the modern methods of the Sciences.
However, in spite of these similarities, when we look into the Vedic-origin and the philosophical & inherently spiritual-orientation of Vedic astrology, we see that it will be more consistent to classify it as a Vedic or Hindu Vidya, and set it apart from the modern Sciences, since these two systems of knowledge, in so far as their philosophical foundations are concerned, are actually poles apart.
We had emphasized that Vedic astrology is ‘quantitative’ and also a subtle system of knowledge. Now, there are many quantitative and subtle systems of knowledge, in our modern civilization as well, like the examples we have cited above. However all these differ from the Vedic systems, only because, they are part of a larger modern materialistic world-view, which does not recognize the existence of the ‘spiritual’ dimension of life nor of the underlying Divine presence, permeating the whole of man’s world as well as the world of nature. This sharp contrast between the systems of modern knowledge, called the ‘Sciences’ and the ancient Vedic spiritual-systems of knowledge, called the Vidyas, makes it abundantly clear in which sense Vedic astrology may be deemed to be a ‘Science’ and in which sense, it may be deemed to be an ‘esoteric species of knowledge’, a Vedic Vidya– but never a ‘Science’.