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Keep the Curiosity Alive (Page 187-189)

(i) True. We see the Moon because it reflects sunlight.
(ii) False. Phases are caused by our changing viewing angle of the lit side, not Earth’s shadow. (Earth’s shadow causes eclipses).
(iii) True. Calendars are based on periodic astronomical cycles.
(iv) False. The Moon is often visible during the day, but it is fainter than the Sun.

Question: Amol was born on 6th May on a Full Moon day. Will his birthday fall on a Full Moon every year? Answer: No.

The Gregorian calendar (May 6th) is based on the Sun.
The Full Moon cycle (Lunar month) is ~29.5 days.
These two cycles do not match perfectly. Next year, on May 6th, the Moon phase will be about 11 days different. It will likely be a waning gibbous or quarter moon, not a Full Moon.

Observation of Figure 11.10 (implied context): usually depicts stars inside the crescent or incorrect shadows.

Stars inside the Crescent: We cannot see stars through the Moon. The dark part of the Moon is solid rock blocking the view.
Incorrect Illumination: The lit side of the Moon must always face the Sun. If the Sun is below the horizon, the bottom of the Moon should be lit.

Matching:

Day of New Moon: E (Completely Dark)
Three days after New Moon: D (Waxing Crescent)
A week after Full Moon: F (Waning Gibbous/Last Quarter approach - Note: Actually, a week after Full Moon is Last Quarter, represented by a half moon, but looking at options, F is the waning gibbous/quarter shape).
Full Moon: B (Fully Lit)

Scenario: Moon overhead at Sunset.

Logic:
- Sun is setting in the West.
- Moon is Overhead (90 degrees away).
- This geometry corresponds to the First Quarter (Half Moon).
Waxing or Waning? Since it follows the New Moon and is visible at sunset, it is the Waxing phase.

Ravi: “Crescent Moon rising in the East when Sun was setting.” $\rightarrow$ $\to$ False.
- A crescent moon is close to the Sun. If the Sun is setting (West), the Crescent moon must also be in the West. It cannot rise in the East at that time.
Kaushalya: “Gibbous Moon during afternoon in the East.” $\rightarrow$ $\to$ True.
- A Waxing Gibbous moon rises in the afternoon (around 3 PM) in the East and is visible while the Sun is still up in the West.

Question: Moon is getting farther away and slower. Will we need Adhika Maasa more or less often? Answer:

If the Moon moves slower, the Lunar Month (currently 29.5 days) becomes longer.
The gap between the Lunar year ( $12 \times \text{Month}$ ) and Solar year (365 days) will decrease.
Currently, gap is $365 - 354 = 11$ days. If Lunar month becomes 30 days, Lunar year = 360 days. Gap = 5 days.
Since the gap is smaller, it will take longer to accumulate enough days for an extra month.
Conclusion: We will need the intercalary month less often.

Proof:

A solar year is 365 days.
A lunar cycle is 29.5 days.
Total Lunar cycles in a year: $365 / 29.5 \approx 12.37$ .
This means there are usually 12 Full Moons, but sometimes 13.
If there are 13 Full Moons in 12 Solar Months, one solar month must have two Full Moons. (This second Full Moon is often popularly called a “Blue Moon”).

Question: If we stopped leap years, when would Independence Day (Aug 15) happen in Winter? Calculation:

Without leap years, the calendar loses 0.25 days every year (stays behind Earth’s orbit).
The calendar date “August 15” will happen earlier and earlier relative to the seasons.
Shift required: From Summer/Monsoon (Aug) to Winter (Jan) is approximately 7 months backwards.
7 months $\approx 210$ days.
Years needed = $\frac{\text{Total Days Shift}}{\text{Error per Year}} = \frac{210}{0.25} = 840$ years.
Answer: In approximately 700-800 years, August 15th would occur during the winter season.