Question
What is the story of the “Sudarśana Chakra”?
Answer
The Sudarshana Chakra was created by the divine architect Vishwakarma. As I discuss in this answer, Vishwakarma's daughter Sanjana married Surya the sun god. But she couldn't withstand his brilliance, so she ran away to the Earth. Eventually Surya found her, and he told Vishwakarma to reduce his brilliance so that Sanjana would be able to be around him. So Vishwakarma reduced Surya's brilliance an eighth, and then fashioned that excess brilliance into various weapons including the Sudarshana Chakra, as described in the Vishnu Purana:
To diminish his intensity, Viśwakarman placed the luminary on his lathe, to grind off some of his effulgence; and in this manner reduced it an eighth, for more than that was inseparable. The parts of the divine Vaishńava splendour, residing in the sun, that were filed off by Viśwakarman, fell blazing down upon the earth, and the artist constructed of them the discus of Vishńu, the trident of Śiva, the weapon of the god of wealth, the lance of Kártikeya, and the weapons of the other gods: all these Viśwakarman fabricated from the superfluous rays of the sun.
Chapter 78 of the Markandeya Purana (page 137) provides more detail about what was made from the briliance:
The earth was engendered by that portion of his effulgence which was identical with Rik - the etherial region was created by what was identical with Yajur and heaven by what was identical with Saman. The Divine Architect, made with those fifteen divisions of his effulgence that had been exhausted, the trident of Siva, the discus of Vishnu, the dreadful maces of Vasus, Sankara and the fire god, the conveyance of the god of riches and other shining weapons of Yakshas, Vidyadharas and other celestials. Thenceforward the Divine Sun bears only the sixteenth portion of his effulgence, which was thus distributed into fifteen divisions by the celestial Architect Viswakarman.
But Vishnu didn't get the Sudarshana Chakra directly from Vishwakarma; he got it from Shiva, as the sage Upamanyu describes to Krishna in the Anushasana Parva of the Mahabharata:
The discus which thou bearest, O sinless one, was given unto thee by Mahadeva.... Wonderful and irresistible in energy it was given unto thee by that illustrious god. In consequence of its blazing energy it was incapable of being gazed at by any person save Siva the wielder of Pinaka. It was for this reason that Bhava (Siva) bestowed upon it the name of Sudarsana. From that time the name Sudarsana came to be current in all the worlds.
Note that Upamanyu says "thou" only because Krishna is an incarnation of Vishnu, not because it's how Krishna himself got the Sudarshana Chakra. Krishna actually got it from Varuna the ocean god, as I discuss in this answer. And since you asked about the power of the Sudarshana Chakra, here's how Agni the fire god describes it to Krishna in the Adi Parva of the Mahabharata:
With this, O slayer of Madhu, thou shalt be able without doubt to vanquish in battle even foes that are not human. With this weapon, without doubt, thou shalt be superior in battle to men and gods, and Rakshasas and Pisachas, and Daityas and Nagas. And thou shalt certainly be able with this to smite all. And, O Madhava, hurled by thee in battle at thy foes, this weapon will irresistibly slay the enemy and again come back into thy hands.
The Srimad Bhagavatam gives a similar description of its power:
Set into motion by the Supreme Personality of Godhead and wandering in all the four directions, the disc of the Supreme Lord has sharp edges as destructive as the fire of devastation at the end of the [Yuga]. As a blazing fire burns dry grass to ashes with the assistance of the breeze, may that Sudarśana cakra burn our enemies to ashes.
It should also be noted that when the demon Hayagrivasura stole the Vedas, he also stole Vishnu's Sudarshana Chakra, so Vishnu got it back after killing him in his Matsya incarnation, as Sugriva says in the Kishkindha Kanda of the Ramayana. (The translation of that verse is inaccurate though, because it makes it sound as if Hayagrivasura always had it.)
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