Chapter 11 Solutions — Keeping Time with the Skies

A solar (Gregorian) calendar year is approximately 365.25 days, while the Moon completes one full cycle of phases (synodic month) in approximately 29.53 days.

Number of synodic months in one solar year = 365.25 ÷ 29.53 ≈ 12.37

Since 12.37 is not a whole number, 12 complete lunar months (≈ 354.4 days) fall short of one solar year by about 11 days. The full Moon therefore shifts approximately 11 days earlier each year relative to the Gregorian calendar.

This means the full Moon day moves to a different calendar date each year. Only after about 19 years (the Metonic cycle — 19 solar years ≈ 235 lunar months) does the full Moon nearly coincide with the same calendar date again, and even then it may differ by a day.

Therefore, Amol's birthday (6th May) does NOT fall on a full Moon day every year.

Analysing Ravi's claim:

A crescent Moon (waxing or waning) is always close to the Sun in the sky — separated by only a small angle.

At sunset, the Sun is on the western horizon. For the Moon to be RISING in the EAST at the same moment, the Moon would need to be roughly 180° away from the Sun — near the Full Moon position, not a crescent.

A waxing crescent sets in the West shortly after the Sun; a waning crescent rises in the East just before sunrise.

A crescent Moon rising in the East at sunset is geometrically impossible.

Ravi is NOT telling the truth.

Analysing Kaushalya's claim:

A waxing gibbous Moon is more than half lit and is between First Quarter and Full Moon in its orbit.

The waxing gibbous Moon rises around midday, well before sunset, and is visible in the afternoon sky.

In the afternoon, when the Sun is in the South or South-West, a waxing gibbous Moon would indeed be in the Eastern part of the sky — this is consistent with its orbital position.

Kaushalya's observation is physically possible.

Kaushalya is telling the truth.

Currently, a lunar month is approximately 29.53 days, giving a lunar year of 12 × 29.53 ≈ 354.4 days.

A solar year is approximately 365.25 days.

The difference is about 10.9 days per year, which is why luni-solar calendars add an intercalary (extra) month roughly every 3 years to keep the lunar calendar aligned with the seasons.

If the Moon gets farther from Earth and slows in its revolution:

A slower Moon means each orbit takes longer → the synodic (lunar) month becomes longer.

A longer lunar month means 12 lunar months would add up to more days — closer to the length of a solar year.

The gap between 12 lunar months and one solar year would shrink.

The lunar calendar would drift less from the solar calendar each year.

Therefore, an intercalary month would be needed LESS OFTEN.