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The first day when the sun begins to move north and enter the zodiacal sign of Capricorn is called Makara-sankranti, and the first day when the sun begins to move south and enter the sign of Cancer is called Karkata-sankranti

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Expressions researched:
"The first day when the sun begins to move north and enter the zodiacal sign of Capricorn is called Makara-sankranti, and the first day when the sun begins to move south and enter the sign of Cancer is called Karkata-sankranti"

Srimad-Bhagavatam

SB Canto 7

The first day when the sun begins to move north and enter the zodiacal sign of Capricorn is called Makara-saṅkrānti, and the first day when the sun begins to move south and enter the sign of Cancer is called Karkaṭa-saṅkrānti. On these two days of the year, one should perform the śrāddha ceremony.
SB 7.14.20-23, Translation and Purport:

One should perform the śrāddha ceremony on the Makara-saṅkrānti (the day when the sun begins to move north) or on the Karkaṭa-saṅkrānti (the day when the sun begins to move south). One should also perform this ceremony on the Meṣa-saṅkrānti day and the Tulā-saṅkrānti day, in the yoga named Vyatīpāta, on that day in which three lunar tithis are conjoined, during an eclipse of either the moon or the sun, on the twelfth lunar day, and in the Śravaṇa-nakṣatra. One should perform this ceremony on the Akṣaya-tṛtīyā day, on the ninth lunar day of the bright fortnight of the month of Kārttika, on the four aṣṭakās in the winter season and cool season, on the seventh lunar day of the bright fortnight of the month of Māgha, during the conjunction of Maghā-nakṣatra and the full-moon day, and on the days when the moon is completely full, or not quite completely full, when these days are conjoined with the nakṣatras from which the names of certain months are derived. One should also perform the śrāddha ceremony on the twelfth lunar day when it is in conjunction with any of the nakṣatras named Anurādhā, Śravaṇa, Uttara-phalgunī, Uttarāṣāḍhā or Uttara-bhādrapadā. Again, one should perform this ceremony when the eleventh lunar day is in conjunction with either Uttara-phalgunī, Uttarāṣāḍhā or Uttara-bhādrapadā. Finally, one should perform this ceremony on days conjoined with one's own birth star (janma-nakṣatra) or with Śravaṇa-nakṣatra.

The word ayana means "path" or "going." The six months when the sun moves toward the north are called uttarāyaṇa, or the northern path, and the six months when it moves south are called dakṣiṇāyana, or the southern path. These are mentioned in Bhagavad-gītā (8.24-25). The first day when the sun begins to move north and enter the zodiacal sign of Capricorn is called Makara-saṅkrānti, and the first day when the sun begins to move south and enter the sign of Cancer is called Karkaṭa-saṅkrānti. On these two days of the year, one should perform the śrāddha ceremony.

Viṣuva, or Viṣuva-saṅkrānti, means Meṣa-saṅkrānti, or the day on which the sun enters the sign Aries. Tulā-saṅkrānti is the day on which the sun enters the sign Libra. Both of these days occur only once within a year. The word yoga refers to a certain relationship between the sun and moon as they move in the sky. There are twenty-seven different degrees of yoga, of which the seventeenth is called Vyatīpāta. On the day when this occurs, one should perform the śrāddha ceremony. A tithi, or lunar day, consists of the distance between the longitude of the sun and that of the moon. Sometimes a tithi is less than twenty-four hours. When it starts after sunrise on a certain day and ends before the sunrise of the following day, the previous tithi and the following tithi both "touch" the twenty-four-hour day between the sunrises. This is called tryaha-sparśa, or a day touched by some portion of three tithis.

Śrīla Jīva Gosvāmī has given quotations from many śāstras stating that the śrāddha ceremony of oblations to the forefathers should not be performed on Ekādaśī tithi. When the tithi of the death anniversary falls on the Ekādaśī day, the śrāddha ceremony should be held not on Ekādaśī but on the next day, or dvādaśī. In the Brahma-vaivarta Purāṇa it is said:

ye kurvanti mahīpāla
śrāddhaṁ caikādaśi-dine
trayas te narakaṁ yānti
dātā bhoktā ca prerakaḥ

If one performs the śrāddha ceremony of oblations to the forefathers on the Ekādaśī tithi, then the performer, the forefathers for whom the śrāddha is observed, and the purohita, or the family priest who encourages the ceremony, all go to hell.