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How many times does Krishna incarnate in a day of Brahma?

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We know that there are four ages [yugas], namely Satya, Tretā, Dvāpara and Kali. These four together comprise one divya-yuga. Seventy-one divya-yugas constitute one manv-antara. There are fourteen manv-antaras in one day of Brahmā. manv-antara is the period controlled by one Manu. The reign of fourteen Manus equals the length of one day (twelve hours) in the life of Brahmā, and the night of Brahmā is of the same duration. These calculations are given in the authentic astronomy book known as the Sūrya-siddhānta. This book was compiled by the great professor of astronomy and mathematics Bimal Prasād Datta, later known as Bhaktisiddhānta Sarasvatī Gosvāmī, who was our merciful spiritual master. He was honored with the title Siddhānta Sarasvatī for writing a commentary on the Sūrya-siddhānta, and the title Gosvāmī Mahārāja was added when he accepted sannyāsa, the renounced order of life.

The present Manu, who is the seventh, is called Vaivasvata [the son of Vivasvān]. Twenty-seven divya-yugas [27 x 4,320,000 solar years] of his age have now passed.The names of the fourteen Manus are as follows: (1) Svāyambhuva, (2) Svārociṣa, (3) Uttama, (4)Tāmasa, (5) Raivata, (6) Cākṣuṣa, (7) Vaivasvata, (8) Sāvarṇi, (9) Dakṣa-sāvarṇi, (10) Brahma-sāvarṇi, (11)Dharma-sāvarṇi, (12) Rudraputra (Rudra-sāvarṇi), (13) Raucya, or Deva-sāvarṇi, (14) and Bhautyaka, orIndra-sāvarṇi.

At the end of the Dvāpara-yuga of the twenty-eighth divya-yuga, Lord Kṛṣṇa appears on earth with the full paraphernalia of His eternal Vraja-dhāma.Now is the term of Vaivasvata Manu, during which Lord Chaitanya appears. First Lord Kṛṣṇa appears at the close of the Dvāpara-yuga of the twenty-eighth divya-yuga, and then Lord Chaitanya appears in the Kali-yuga of the same divya-yuga. Lord Kṛṣṇa and Lord Chaitanya appear once in each day of Brahmā, or once in fourteen manv-antaras, each of seventy-one divya-yugas in duration.

From the beginning of Brahmā’s day of 4,320,000,000 years, six Manus appear and disappear before Lord Kṛṣṇa appears. Thus 1,975,320,000 years of the day of Brahmā elapse before the appearance of Lord Kṛṣṇa. This is an astronomical calculation according to solar years.

Ref >> Srila Prabhupada Vani.

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