Of the fourteen branches of learning basic to our Vedic religion, I have so far dealt with siksa, Vyakarana, Chandas and Nirukta. These four form part of Sadanga (the six limbs of the Vedas). I will now speak about Jyotisa, it being the first of the remaining two of the Sadanga. Jyotisa, which is the science of the celestial bodies and the eye of the Vedapurusa, consists of three "skandhas" or sections. So it is called "Skandha-trayatmakam". Sages like Garga, Narada and Parasura have written samhitas (treatises) on this subject. The sun god, in disguise, taught the science to Maya, the carpenter of the Asuras. The work incorporating his teachings is called the Suryasiddhanta. There are treatises on astronomy written by celestials and sages and ordinary mortals. Of them some are by Varahamihira, Aryabhata and Bhaskaracarya. In recent times we had Sundaresvara Srautin who wrote a work called Siddhanta-Kausthubham.
Why is Jyotisa regarded as the eye of the Vedapurusa?
What purpose is served by the eye? Near objects may be perceived by the sense of touch. With our eyes we learn about distant objects. Just as our eyes help us to know objects that are distant in space (that is just as we see distant object with our eyes), Jyotisa sastra help us to find out the position of the heavenly bodies that are distant in time (their configuration many years ago in the past or many years hence in future).
We can find out directly the positions of the sun and the moon and other heavenly bodies. Just as we can know near objects, even if we are blind, by feeling them with our hands, we can learn about the positions of the heavenly bodies near in time even without the help of astronomy. What is 50 feet away is to be perceived by the eye. Similarly, if you want to know the position of planets 50 years ago or 50 years hence, you have to have recourse to Jyotisa.
We cannot, however, form a full picture of near objects only by feeling them. For instance, we cannot know whether they are green or red. For this, we must see them with our eyes. Again, even if we are able to see the planet with our naked eye, we will need the help of astrology to find out its effects on our life, how its positions in the heavens will influence our destiny.
This is the reason why Jyotisa is called the eye of the Vedapurusa. Vedic rituals are performed according to the position of the various planets [and the sun and the moon]. There are rules to determine this. The right day and hour [muhurta] for a function is fixed according to the position of the celestial bodies. Here again, Jyotisa performs the function of the eye.
This Anga of the Vedas is indeed called "nayana" which word means "to lead". A blind man needs to be led by another. So it is the eye that leads. Astronomy / Astrology is the eye that enables us to fix the hours for Vedic rituals.
For a general background, please see here