Concept in Indian astronomy and astrology
In Indian astronomy and astrology, vyatipāta and vaidhṛti (or, vaidhṛta) are two moments in the regular motion of the sun and the moon in the zodiac characterized by their certain special relative positions. These terms are also used to denote two of the 27 "Nityayoga"-s: "vyatipāta" is the 17th "nityayoga" and "vaidhṛti" is the 27th "nityayoga".
Definitions.
Sūrysiddhānta defines "vyatipāta" and "vaidhṛti" as follows ("Sūrysiddhānta" Chapter IX "Pātādhikāra" verses 1 and 2):
The term "pāta" in the present context means literally "fall," and hence also either "fault, transgression," or " calamity." The term was probably first
applied to the moon's nodes, because they were the points of danger in her revolution, near which the sun or herself was liable to fall into the
jaws of Rāhu. Why the time when the sun and moon are equally distant from the equator should be looked upon as so especially unfortunate is not easy to discover. When the equal declinations are of opposite direction, the aspect is denominated "vaidhṛta", or "vaidhṛti". It has been noted above that it is the
name of the last "nityayoga". The name of the other aspect ("pāta"), which occurs when the sun and moon are equally removed from the
equator upon the same side of it, is "vyatipāta", which may be rendered "very excessive sin or calamity." This, too, is the name of one of the
"nityayoga"-s, but not of that one which occurs when the sum of longitudes of the sun and moon is 180 degrees.
The specification that the "pāata"-s take place when the sum of longitudes equals a circle or a half-circle respectively, or when the two luminaries are equally distant from either solstice, or either equinox, is not to be understood as exact: this would be the case if the moon had no motion in latitude; but owing to that motion, the equality of declinations, which is the main thing, occurs at a time somewhat removed from that of equality of distance from the equinoxes: the latter is called "madhyapāta", "the mean occurrence of the "pāta"."
Chapter XI "Pātādhikāra" of "Sūrysiddhānta" is devoted entirely to a discussion on "vyatipāta" and "vaidhṛti". Among other things, the chapter discusses the malignant aspects of the "pāata"-s, methods to find the longitude of the sun and moon when their declinations are equal, methods to determine the duration of the aspect, and the moment of its beginning and end, etc. According to Burgess: "Of all the chapters in the treatise, this is the one which has least interest and value."
Records of "vyatīpāta"-s in stone inscriptions.
This term "vyatīpāta" appears in several stone inscriptions. The contexts of the inscriptions may be grants, donations to temples, records of death of war heroes, self-immolation of saints or women committing sati. A detailed study of these inscriptions has yielded valuable information about eclipses and other celestial events like planetary conjunctions. 
References.
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