I Lunar months: One revolution of Moon around the earth is called lunar month. There are following four types of lunar months:
(1) The Sidereal month: Period during the Moon, when observed from earth against a fixed star, moves around the zodiac once and returns to the same star. Its duration is 27.3217 mean solar days (27d 7h 43m).
(2) The Synodic month (a Lunation): It is the period between one new Moon (a conjunction of Sun and the Moon) to the next. Its duration is 29.5306 mean solar days (29d 12h 44m). It is larger than sidereal month as it indicates relation of the Moon with the Sun. During one revolution of the Moon around earth, the Sun also moves by slightly less than one sign. To catch up the Sun, the Moon has to take extra time.
(3) The Nodical month: It is time the Moon takes to complete one round from Rahu to Ketu and back to Rahu – the Moon’s nodes. Its duration is about 27.2122 mean solar days.
(4) The Anomalistic month: This is duration of time that the Moon takes to complete one revolution around the earth, in its orbit from perigee to perigee. Its duration is about 27.5546 mean solar days.
(5) The Moon revolves around earth in elliptical orbit (so does the earth around the Sun). The orbit is in constant flux due to perturbations caused by the Sun and the planets. Perigee is the point at which the Moon in orbit around the earth is at the least distance from the earth. Its reverse is called Apogee.
(6) An anomalistic lunar month is the lunar equivalent to the solar anomalistic month, which indicates the passage of the Sun around the earth from perigee to perigee or the passage of the earth around the Sun from perihelion to perihelion. Perihelion and Aphelion are to perigee and apogee, with the Sun as the center and the planets orbiting around it.
II Cycles of the Moon:
(1) Lunar year: it is a synodic year consisting of 12 synodic months, amounting to a duration of about 354 days. It contains 360 lunar dates or tithes (30 tithis in one synodic month). This year falls short of a solar year (equal to 365.25 days) by about 11 days.
(2) Luni-Solar year: If a totally lunar calendar were followed, the various seasons would fail to coincide with the lunar months, since the lunar year would end 11 days earlier than a solar year. This would mean a difference of over one month over three solar year. In order to compensate this and to make the solar and lunar calendar function side by side, a luni-solar concept has been developed so that an extra lunar month is added approximately three years or earlier. It is called an intercalary month (Adhik maasa). The various `Yugas’ consisting of 3-year cycle, 5-year cycle, 8-year cycle, 11-year cycle, 19 years cycle, 30-year cycle etc. signified brilliant attempts by Indian pre-Vedic astronomers to harmonise the solar and lunar years. The 19-year cycle appears to be most accurate `observed’ Yuga or cycle. It consists of 7 intercalary months over a period of 19 solar years. Therefore in a period of 228 solar months, there are 235 lunar (synodic months (New Moon or Full moon).
(3) The Metonic cycle: Consistent with above observation by vedic astronomers, Meton (433 BC) discovered that there occur 235 lunations in a period of 19 solar years. 19 solar years equals to 19x365.2422=6939.60 days and 235 lunations equals to 235x29.5306=6939.69. The two figures are remarkably close. It means that 19 solar years are equal to 19 lunar years and 7 lunar months.
(4) The 19 years luni-solar cycle is so accurate that the tithes or lunar dates on similar days after exactly 19 years. Even astronomical phenomenon like, eclipses recur after 19 years interval with fair precision.
(5) Adhik Maasa or Intercalary month: Sun’s ingress in to a sign is called `Sankranti’. A lunar month in which there is no solar ingress into a sign is an intercalary month or Adhik maasa. An intercalary month occurs once in about 3 years and 16 days. Roughly in three years, there is an intercalary month. That year, there are 13 lunar months.
(6) Kshaya or Omitted month: It occurs when there are two solar ingresses in one lunar year. This is rare. When there is a Kshaya maasa, there occur two intercalary months during that one-year. It occurred once in Saka 1744 & Saka 1885.
III Eclipses: There are two types of eclipsers – Solar and Lunar eclipses.
(1) Solar eclipse is caused when the Moon is in between the Sun and the earth; and the shadow of the Moon falls on the earth cutting the portion of Sun (or eclipsing the Sun) when viewed from the earth. This occurs on New Moon day, when the Sun and the Moon are conjunct and happen to lie on same side of the earth. Since the orbit of the Moon is tilted at an angle of approximately 5◦ to the ecliptic, the Sun-Moon-earth trio does not always fall in a straight line on every New Moon day. Therefore solar eclipse does not occur on every New Moon day.
(2) The Moon’s path cross the Sun’s path at ascending and descending nodes (i.e. Rahu and Ketu). In order that the Sun-Moon-earth falls in a straight line, Sun and Moon be fairly close to Rahu or Ketu. A solar eclipse is likely to occur if a New Moon occurs within 18 ½ degrees of a node, and certainly if distance is less than 15◦.
(3) Lunar eclipse occurs when the earth lies between the Sun and the Moon. It happens on a Full Moon day when they are in one line. Since the orbit of the Moon is tilted at an angle of approximately 5◦ to the ecliptic, the Sun-Moon-earth trio does not always fall in a straight line on every Full Moon day giving rise to lunar eclipse every Full moon day.
(4) A lunar eclipse is likely to happen when the distance between the Moon and a node is less than 12 degrees, and certainly if less than 9 ½ degrees.
(5) The Sun-Moon-earth falling in straight line repeats after every 18 years and 10 days. Therefore an eclipse is repeated exactly after this period.
Shanker Adawal
www.shankerstudy.com, www.shankarsastro.com
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