Keeping Time with the Skies

1. The opening puzzle — a Moon in daytime

The chapter opens at Makar Sankranti during the Patang Mahotsav (kite festival) in Ahmedabad. Meera spots the Moon shining during the day, and notices it is not a full circle. This puzzles her, because she always thought the Moon comes out only at night and is always round. Two questions drive the chapter:

• Why does the Moon's shape seem to change from night to night?
• Why can the Moon sometimes be seen in daytime, and rise/set at different times?

She remembers the Moon is spherical and shines by reflecting sunlight. It is not a lunar eclipse (those are rare and brief). The real reason is the topic of the chapter — the phases of the Moon.

2. How the Moon's appearance changes (11.1)

If you watch the Moon at the same time (say sunrise) for several days starting after a full Moon, you see a clear pattern recorded in Activity 11.1 / Table 11.1:

• The bright (illuminated) part shrinks from a full circle to a half circle in about a week, then keeps shrinking for another week until the Moon is not visible at all.
• This two-week shrinking period is the waning period.
• After the Moon disappears, its bright part grows back to a half circle in a week and to a full circle in another week — this growing period is the waxing period.

The full bright circle is the full Moon day (Purnima); the day it is not visible at all is the new Moon day (Amavasya). The full cycle — full → new → full — takes about a month.

3. The names of the shapes — phases of the Moon (11.1.1)

The changing shapes of the bright portion of the Moon as seen from Earth are called the phases of the Moon. The main shapes, in order, are:

• New Moon — bright part not visible at all.
• Crescent — less than half the bright part is seen (a thin sliver).
• Half (first/last quarter) — exactly half the bright part is seen.
• Gibbous — more than half (but not full) the bright part is seen.
• Full Moon — the entire bright circle is seen.

During waxing the order is new → crescent → half → gibbous → full; during waning it runs in reverse: full → gibbous → half → crescent → new.

4. Locating the Moon in the sky (11.1.2)

At the same time on successive days the Moon is seen in a different part of the sky:

• On full Moon day the Moon is nearly opposite the Sun — when the Sun rises in the East, the full Moon is almost setting in the West.
• As the bright part shrinks (waning), at sunrise the Moon appears to move closer to the Sun in the sky. When it is a half circle, the Moon is overhead at sunrise; a few days later the crescent is even closer to the Sun.
• A waxing Moon is easiest to spot at sunset; a waning Moon at sunrise. Because of these shifts, the Moon rises and sets at different times than the Sun.

5. Making sense of it — why phases happen (11.1.3)

The shape of the Moon itself does not change — only what we see changes. The reasoning, step by step:

• The Moon does not emit its own light; it reflects sunlight. The half facing the Sun is illuminated; the other half is non-illuminated (dark).
• The Moon revolves around the Earth, and the same side of the Moon always faces Earth. But the side facing Earth is not always the lit side.
• We can only see the illuminated part that faces Earth. Depending on the Moon's position, this lit part we see is a full circle, part of a circle, or nothing.
• On new Moon, the lit side faces away from Earth, so we see nothing. On full Moon, the entire lit side faces Earth.

6. Two common myths cleared up

• Myth: Earth's shadow on the Moon causes the phases. WRONG. Phases come from the changing orientation of Sun, Moon and Earth as the Moon revolves. Earth's shadow on the Moon causes a lunar eclipse — a different, rare event.
• Myth: the Moon rises only when the Sun sets. WRONG. The Moon rises ~50 minutes later each day and can be seen in daytime.

Why eclipses are not monthly: a lunar eclipse can happen only on a full Moon day and a solar eclipse only on a new Moon day — but they don't happen every month because the Moon's orbit is slightly tilted relative to Earth's orbit around the Sun. So the three bodies line up only sometimes.

Why the Moon takes ~50 min longer to return to the same spot (Fig. 11.6): Earth rotates once in 24 hours, but in that time the Moon has moved ahead a little in its own orbit. So Earth must rotate a bit more for the Moon to return to nearly the same place in the sky — taking about 50 extra minutes each day.

7. The phases as a clock — the month (11.2)

The changing phases are a natural periodic event with a cycle of almost a month. Anything that repeats regularly in nature can be used to keep time. There are three natural sky-cycles that gave us our three main units of time:

• Day: the Sun appears to rise in the East and set in the West because the Earth rotates on its axis. The average time from the Sun's highest point one day to its highest point the next is 24 hours — the mean solar day.
• The Sun is at its highest when the shadow of an object is shortest. This is how a sundial works, and is the basis of Activity 11.3 (mark the tip of a vertical stick's shadow every minute; the shortest shadow marks the Sun's highest point).
• Month: the Moon takes about 29.5 days to go through all its phases — the basis of a month.
• Year: the Earth revolves around the Sun in nearly 365¼ days, completing one full cycle of seasons — this defines a solar year.

8. Lunar calendars (11.2.1)

In one cycle of seasons (~365 days) you can fit nearly 12 cycles of the Moon's phases. So ancient people built lunar calendars: day = shortest unit, month ≈ 29.5 days, and a lunar year = 12 lunar months. The Moon's phases gave an easy, reliable way to track time.

9. Solar calendars (11.2.2)

Farmers needed to know when seasons arrive, so the year had to match the seasons — this led to solar calendars. The Gregorian calendar we use today is a solar calendar. Its months are adjusted to add up to 365 days — that is why some months have 30 days, some 31, and February has 28.

• Earth actually takes about an extra quarter day beyond 365. These quarter-days add up to roughly one full day every 4 years.
• To fix this, a leap year adds one extra day: if a year is divisible by 4, February gets 29 days. This keeps the calendar in step with the seasons.
• Fine correction: a quarter-day is slightly too much, so century years are not leap years (1700, 1800, 1900) — unless divisible by 400 (so 1600 and 2000 are leap years).

Tropical vs sidereal year: the time from one spring equinox to the next is the tropical year (Gregorian is based on this). The time for the same stars to rise again at sunset is the sidereal year, which is longer than the tropical year by about 20 minutes. Astronomers use the sidereal year to track Earth's position in its orbit.

10. Our scientific heritage — the Indian sky (within 11.2)

For thousands of years Indians observed the sky and built calendars without knowing Earth revolves around the Sun and without modern instruments — through careful patient observation.

• The Sun does not always rise exactly in the East. In summer it rises a little north of East; in winter a little south of East. The extremes are the solstices (around June 21 and December 21).
• The Sun's apparent northward movement (December → June) is Uttarayan; its southward movement (June → December) is Dakshinayan. This repeats yearly and is linked to the seasons.
• The Taittirīya Samhitā (verse 6.5.3) records the Sun moving south for six months and north for six months. The Surya Siddhanta noted that the stars of Capricorn (called Makar in India) lay behind the Sun at the winter solstice.

11. Luni-solar calendars and the Indian National Calendar (11.2.3–11.2.4)

Luni-solar calendars primarily use the Moon's phases for days and months, but also adjust to stay in sync with the seasons. Since 12 lunar months (354 days) fall short of the solar year by ~11 days, every 2–3 years an extra month — called Adhika Maasa (intercalary month) — is added. This keeps the lunar cycle and solar year in step. Such calendars are used widely across India.

12. Festivals and astronomy (11.3)

Many Indian festivals are tied to the phases of the Moon, so they follow lunar or luni-solar calendars and fall on different Gregorian dates each year:

• Diwali — new Moon of Kartika.
• Holi — full Moon of Phalguna.
• Buddha Purnima — full Moon of Vaisakha.
• Eid-ul-Fitr — after sighting the crescent Moon at the end of Ramazan (purely lunar, so it shifts ~11 days earlier each year).
• Dussehra — tenth day of Ashwina.

Luni-solar festivals shift by less than a month (the intercalary month corrects the drift); purely lunar festivals like Eid drift much more. A few festivals — Makar Sankranti, Pongal, Bihu, Vaisakhi, Poila Baisakh, Puthandu — follow a solar (sidereal) calendar, so they fall on nearly the same Gregorian date every year. Because of the slow wobble of Earth's axis, Makar Sankranti drifts ahead by about 1 day every 71 years. The Positional Astronomy Centre publishes the Rashtriya Panchang to fix festival dates uniformly across India.

13. Artificial satellites (11.4)

The Moon is Earth's natural satellite. Artificial satellites are human-made and launched into orbit. They appear as tiny specks moving in the night sky; most orbit about 800 km above Earth and complete one orbit in roughly 100 minutes.

• Uses: communication, navigation, weather monitoring, disaster management, and scientific research.
• ISRO missions: the Cartosat series (maps, city planning, disasters — feeding the Bhuvan platform); AstroSat (observing stars); Chandrayaan 1, 2, 3 (Moon); Aditya L1 (Sun); Mangalyaan (Mars). Student satellites include AzaadiSAT, InspireSat-1, Jugnu.
• How to spot one: just before sunrise or after sunset, look for a steady (non-twinkling) point of light moving fast across the sky.
• Space debris: dead satellites and rocket parts become "space junk" that can collide with working satellites — countries now cooperate to remove it.

14. Quick revision checklist

• Moon shines by reflecting sunlight; its shape never changes — only the lit part we see does.
• Phases come from the Moon's changing position as it revolves around Earth — NOT from Earth's shadow.
• Order (waxing): new → crescent → half → gibbous → full. Waning is the reverse.
• Full Moon ⇒ Moon opposite the Sun; new Moon ⇒ Moon closest to the Sun. Cycle ≈ 29.5 days.
• Day = Earth's rotation; month = Moon's phases; year = Earth's revolution.
• Lunar (354 d) vs solar (365 d) vs luni-solar (adds Adhika Maasa every 2–3 years). Leap year fixes the quarter-day.
• Indian National Calendar: solar, 365 days, Shaka era, starts 22 March; Meghnad Saha's committee.