A 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. A Bengali translation of 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 translating the Sūrya-siddhānta, and the title Gosvāmī Mahārāja was added when he accepted sannyāsa, the renounced order of life.
(Sri Caitanya Caritamrta-----1:3;8-----purport).

The prathama-sandhyā is the beginning of the age. According to astronomical calculation, the age is divided into twelve parts. The first of these twelve divisions is known as the prathama-sandhyā. The prathama-sandhyā and śeṣa-sandhyā, the last division of the preceding age, form the junction of the two ages. According to the Sūrya-siddhānta, the prathama-sandhyā of Kali-yuga lasts 36,000 solar years. Lord Caitanya appeared in the prathama-sandhyā after 4,586 solar years of Kali-yuga had passed.
(Sri Caitanya Caritamrta-----1:3:29-----purport).