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Line 16: − + − + + − + − Even when the Moon’s latitude exists, a partial eclipse of the Sun will be possible provided the parallax in latitude is less than half the sum of the diameters of the eclipsed and eclipsing bodies. Thus at places where the equinoctial midday shadow is 1 digit, parallax in latitude is always less than half the sum of the eclipsed and eclipsing bodies. Where the equinoctial midday shadow is 5 digits, there the parallax in latitude is sometimes less and sometimes equal to half the sum of the diameters of the eclipsed and eclipsing bodies. + + + − In the case of a solar eclipse too, at places where the equinoctial midday shadow is 1 digit and the distance of the Earth’s shadow or the Sun from the Moon’s ascending node amounts to 14 degrees, a solar eclipse is impossible. + − + − At those very places, if the said distance is less than 14 degrees, there is a possibility of a solar eclipse. + − + − Where the equinoctial midday shadow is 5 digits and the said distance is 16 degrees, a solar eclipse is impossible. But if the said distance is less than 16 degrees, there is a possibility of a solar eclipse. − When the parallax in latitude amounts to half the sum of the eclipsed and eclipsing bodies, then, if the Moon’s latitude is zero, a solar eclipse does not occur. Where the equinoctial midday shadow is 9 digits, there the parallax in latitude is sometimes less than, sometimes equal to, and sometimes greater than half the sum of the diameters of the eclipsed and eclipsing bodies. When the former is equal to or greater than the latter, a solar eclipse is not possible provided the Moon’s latitude (at new Moon) is zero.+ − + − But all this happens only when the longitude of the eclipsed body is equal to that of the Moon’s node.+ + + − When the distance of the Shadow or the Sun from the Moon’s node is 12 degrees and also if the Moon’s velocity per day amounts to 12 degrees 20′, a lunar eclipse certainly does not occur anywhere. When this distance is less than 12 degrees and the Moon’s velocity greater than 12 degrees 20′, then there is a possibility of a lunar eclipse. But when the distance is 13 degrees and the Moon’s velocity 13 degrees 20′, even then a lunar eclipse is impossible. + − + − When the distance is less than that (and the Moon’s velocity greater than 13 degrees 20′), there is a possibility of a lunar eclipse. + − + − Again, when the distance of the Shadow or the Sun from the Moon’s ascending node exceeds 14 degrees and also if the Moon’s velocity is 14 degrees 20′, a lunar eclipse is impossible. (In fact) when the distance is 14 degrees, a lunar eclipse is always impossible. In that case, the Moon’s velocity does not play any role. Hence, one should proceed to calculate a lunar eclipse only when the said distance is less than 14 degrees.+ − − === Negation of Eclipses === − In a place where the equinoctial midday shadow is 9 digits and the Sun is at the last point of the sign Gemini, the length of the day amounts to 36 ghaṭīs; and when at the end of the sign Sagittarius, the day amounts to 24 ghaṭīs. Where the equinoctial midday shadow exceeds 9 digits, there is no habitation. Hence, knowledge of occurrence of eclipses for those places is of no use. − − People do not live beyond 600 yojanas from the equator. The region lying north of that is inaccessible to man. − − All this has been explained in detail in the Aryabhatasiddhanta. + + + + + + +
Editing
Mallikarjuna Suri enumerates the possibility of an eclipse as discussed in the Aryabhatasiddhanta as follows:
Mallikarjuna Suri enumerates the possibility of an eclipse as discussed in the Aryabhatasiddhanta as follows:
=== Total Eclipse ===
=== Total or Partial Eclipse ===
Adding 6 signs to the Sun at a parva (full moon or new moon), one gets the Earth’s shadow. This is the eclipser of the Moon.
Adding 6 signs to the Sun at a parva (full moon or new moon), one gets the Earth’s shadow. This is the eclipser of the Moon.
* When it is equal to the Moon’s node, we have a total eclipse of the Moon.
* When it is equal to the Moon’s node, we have a total eclipse of the Moon.
* A solar eclipse will also be total provided the Moon’s latitude corrected for parallax happens to be zero at that time.
* If the Moon’s latitude corrected for parallax happens to be zero at that time, we have a total solar eclipse.
*When the Moon’s latitude exists, if the parallax in latitude is less than half the sum of the diameters of the eclipsed and eclipsing bodies, a partial eclipse of the Sun will be possible .
=== Partial Solar Eclipse ===
=== Possibility of a Solar Eclipse ===
A solar eclipse is possible when,
# The equinoctial midday shadow is 1 digit and the distance of the Earth’s shadow or the Sun from the Moon’s ascending node is less than 14 degrees.
# The equinoctial midday shadow is 5 digits and the distance of the Earth’s shadow or the Sun from the Moon’s ascending node is less than 16 degrees.
=== Possibility of a Lunar Eclipse ===
A lunar eclipse is possible when,
# The distance of the Shadow or the Sun from the Moon's node is less than 12 degrees and the Moon’s velocity greater than 12 degrees 20′, then there is a possibility of a lunar eclipse.
# The distance of the Shadow or the Sun from the Moon's node is less than 13 degrees and the Moon’s velocity greater than 13 degrees 20′.
=== Negation of a Solar Eclipse ===
=== Negation of a Solar Eclipse ===
A solar Eclipse does not occur if,
# The Moon’s latitude is zero when the parallax in latitude amounts to half the sum of the eclipsed and eclipsing bodies.
# The Moon’s latitude (at new Moon) is zero when the parallax in latitude is equal to or greater than half the sum of the diameters of the eclipsed and eclipsing bodies.
# The equinoctial midday shadow is 1 digit and the distance of the Earth’s shadow or the Sun from the Moon’s ascending node amounts to 14 degrees.
# The equinoctial midday shadow is 5 digits and the distance of the Earth’s shadow or the Sun from the Moon’s ascending node is 16 degrees.
=== Negation of a Lunar Eclipse ===
=== Negation of a Lunar Eclipse ===
A lunar eclipse does not occur when,
# The distance of the Shadow or the Sun from the Moon’s node is 12 degrees and also if the Moon’s velocity per day amounts to 12 degrees 20′.
# The distance of the Shadow or the Sun from the Moon’s node is 13 degrees and the Moon’s velocity 13 degrees 20′.
# The distance of the Shadow or the Sun from the Moon’s ascending node exceeds 14 degrees and the Moon’s velocity is 14 degrees 20′.
# The distance of the Shadow or the Sun from the Moon’s node is 14 degrees. In that case, the Moon’s velocity does not play any role.
=== Observations ===
# At places where the equinoctial midday shadow is 1 digit, parallax in latitude is always less than half the sum of the eclipsed and eclipsing bodies.
# At places where the equinoctial midday shadow is 5 digits, the parallax in latitude is sometimes less and sometimes equal to half the sum of the diameters of the eclipsed and eclipsing bodies.
# At places where the equinoctial midday shadow is 9 digits, the parallax in latitude is sometimes less than, sometimes equal to, and sometimes greater than half the sum of the diameters of the eclipsed and eclipsing bodies.
# One should proceed to calculate a lunar eclipse only when the distance of the Shadow or the Sun from the Moon's node is less than 14 degrees.
# In a place where the equinoctial midday shadow is 9 digits and the Sun is at the last point of the sign Gemini, the length of the day amounts to 36 ghatis; and when at the end of the sign Sagittarius, the day amounts to 24 ghatis.
# Where the equinoctial midday shadow exceeds 9 digits, there is no habitation. Hence, knowledge of occurrence of eclipses for those places is of no use. For, people do not live beyond 600 yojanas from the equator. The region lying north of that is inaccessible to man.
Tamma Yajva and Ramakrshna Aradhya too have included the above discussion of the possibility of an eclipse in their commentaries on the Suryasiddhanta.<ref>Aditya Kolachana, K. Mahesh & K. Ramasubramanian, Studies in Indian Mathematics and Astronomy, Hindustan Book Agency.</ref>
Tamma Yajva and Ramakrshna Aradhya too have included the above discussion of the possibility of an eclipse in their commentaries on the Suryasiddhanta.<ref>Aditya Kolachana, K. Mahesh & K. Ramasubramanian, Studies in Indian Mathematics and Astronomy, Hindustan Book Agency.</ref>
== References ==
== References ==
<references />
<references />