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Keeping Time with the Skies - Lunar calendars

Grade 8CBSE

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

🔑Concepts

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A lunar month is the time interval between two consecutive new moons (Amavasya) or two consecutive full moons (Purnima). This period is approximately 29.5329.53 days.

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A 'Tithi' is a lunar day. It is defined as the time duration in which the angular distance between the Moon and the Sun increases by 12∘12^\circ.

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There are 3030 tithis in a lunar month: 1515 in the 'Shukla Paksha' (waxing phase) and 1515 in the 'Krishna Paksha' (waning phase).

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A lunar year consists of 1212 lunar months, which totals approximately 12×29.5=35412 \times 29.5 = 354 days.

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The solar year is approximately 365.25365.25 days. The difference between a solar year and a lunar year is about 1111 days per year.

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To synchronize the lunar calendar with the seasons (solar calendar), an extra month called 'Adhik Maas' or 'Purushottam Maas' is added to the lunar calendar roughly every 2.72.7 to 33 years.

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The Moon revolves around the Earth in approximately 27.327.3 days (Sidereal month), but because the Earth also moves around the Sun, it takes 29.529.5 days for the Moon to return to the same phase (Synodic month).

📐Formulae

Duration of Lunar Year=12×29.53≈354 days\text{Duration of Lunar Year} = 12 \times 29.53 \approx 354 \text{ days}

Gap per Year=365.25−354.36=10.89 days\text{Gap per Year} = 365.25 - 354.36 = 10.89 \text{ days}

Total Tithis=360∘12∘=30\text{Total Tithis} = \frac{360^\circ}{12^\circ} = 30

Angular separation for nth Tithi=n×12∘\text{Angular separation for } n^{th} \text{ Tithi} = n \times 12^\circ

💡Examples

Problem 1:

Calculate the approximate difference in days between a solar year and a lunar year over a period of 33 years. Use 365365 days for a solar year and 354354 days for a lunar year.

Solution:

Gap for 1 year=365−354=11 days\text{Gap for 1 year} = 365 - 354 = 11 \text{ days} Gap for 3 years=11×3=33 days\text{Gap for 3 years} = 11 \times 3 = 33 \text{ days} Using vertical subtraction for the annual gap: 365−35411\begin{array}{r} 365 \\ - 354 \\ \hline 11 \end{array}

Explanation:

Since the lunar year is shorter than the solar year, the gap accumulates. In 3 years, the gap is approximately 33 days, which is why an intercalary month (Adhik Maas) is added approximately every third year to reset the calendar.

Problem 2:

If the Moon has moved 72∘72^\circ away from the Sun starting from the New Moon, which Tithi is occurring?

Solution:

Number of Tithi=Angular Distance12∘\text{Number of Tithi} = \frac{\text{Angular Distance}}{12^\circ} Tithi=72∘12∘=6\text{Tithi} = \frac{72^\circ}{12^\circ} = 6

Explanation:

Since each Tithi corresponds to a 12∘12^\circ change in angular distance between the Sun and the Moon, an angle of 72∘72^\circ indicates the completion of the 6th6^{th} Tithi (Shashti) of the Shukla Paksha.