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Keeping Time with the Skies - Luni-solar calendars

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A Solar Year is the time taken by the Earth to complete one revolution around the Sun, which is approximately 365.2422365.2422 days.

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A Lunar Month (Synodic Month) is the time interval between two consecutive New Moons (Amavasya) or Full Moons (Purnima), lasting approximately 29.5329.53 days.

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A Lunar Year consists of 1212 lunar months, which totals approximately 354.36354.36 days (12×29.5312 \times 29.53).

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The difference between a Solar Year and a Lunar Year is roughly 10.8810.88 days per year. Without adjustment, lunar festivals would drift through different seasons over time.

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Luni-solar calendars, such as the Indian National Calendar and various regional Panchangs, reconcile this difference by adding an extra month, known as 'Adhik Maas' or 'Purushottam Maas', approximately every 32.532.5 months.

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A 'Tithi' is a lunar day in the Hindu calendar, defined by the 12∘12^\circ increase in the longitudinal separation between the Moon and the Sun.

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The 'Uttarayan' starts when the Sun begins its northward journey after the Winter Solstice, while 'Dakshinayan' starts when the Sun begins its southward journey after the Summer Solstice.

📐Formulae

1 Solar Year≈365.24 days1 \text{ Solar Year} \approx 365.24 \text{ days}

1 Lunar Month≈29.53 days1 \text{ Lunar Month} \approx 29.53 \text{ days}

1 Lunar Year=12×29.53≈354.36 days1 \text{ Lunar Year} = 12 \times 29.53 \approx 354.36 \text{ days}

Annual Difference=365.24−354.36=10.88 days\text{Annual Difference} = 365.24 - 354.36 = 10.88 \text{ days}

Total Tithis in a Lunar Month=30\text{Total Tithis in a Lunar Month} = 30

💡Examples

Problem 1:

Calculate the approximate difference in days between the Solar calendar and the Lunar calendar after a period of 33 years.

Solution:

10.88×332.64\begin{array}{r} 10.88 \\ \times 3 \\ \hline 32.64 \end{array}

Explanation:

Since the lunar year is shorter than the solar year by approximately 10.8810.88 days, we multiply this annual difference by 33. The result, 32.6432.64 days, is roughly equal to one full lunar month. This is why an 'Adhik Maas' (extra month) is added every 2.52.5 to 33 years to keep the calendar aligned with the seasons.

Problem 2:

If a Lunar Year is taken as exactly 354354 days and a Solar Year as 365365 days, find the difference in days over 55 years using vertical subtraction for the annual difference.

Solution:

Annual difference: 365−35411\begin{array}{r} 365 \\ - 354 \\ \hline 11 \end{array} Total difference over 55 years: 11×5=55 days11 \times 5 = 55 \text{ days}

Explanation:

By subtracting the length of the lunar year from the solar year, we find a gap of 1111 days per year. Over 55 years, this gap accumulates to 5555 days, which would cause significant seasonal shifting of festivals if not corrected by a luni-solar system.