Chapter 11: Keeping Time with the Skies (Physics)

1. True.
2. False. The phases happen because, as the Moon goes around the Earth, we see different amounts of its sunlit half. The Earth's shadow falling on the Moon causes a lunar eclipse, not the phases.
3. True.
4. False. The Moon is often seen in the daytime, for example in the afternoon around the first quarter, or in the morning after the full Moon.

(i) True (ii) False (iii) True (iv) False

No. His birthday follows the solar calendar (365 days), but full Moons follow the lunar month of about 29.5 days. Twelve lunar months make only about 354 days, so each year the full Moon comes about 11 days earlier in relation to 6 May.

His birthday will fall on a full Moon only once in a while, roughly every 19 years, when the two cycles line up again.

No: 12 full-Moon cycles take about 354 days, so the full Moon shifts about 11 days earlier each solar year.

1. Stars are drawn inside the dark part of the Moon. The dark part is still the Moon's solid body; it is just not lit by the Sun. It blocks the stars behind it, so no star can be seen through it.
2. The Moon is drawn in front of a cloud. Clouds are only a few kilometres up, while the Moon is about 3,84,000 km away. Clouds can hide the Moon, but the Moon can never be in front of a cloud.

Stars appear inside the Moon's dark part (they would be hidden by it), and the Moon overlaps a cloud as if it were in front (clouds are far nearer to us).

Match by how much of the disc is bright:

(ii) Never seen: F. The line between the bright and dark parts (the terminator) always runs between two opposite points of the Moon's edge. In F, the dark patch has its ends only a quarter of the way round the edge, which never happens.

(The exact tilt of the bright part in the sky depends on the time and place of viewing.)

D: three days after new Moon; E: full Moon; A: three days after full Moon; C: a week after full Moon; B: new Moon. F is never seen.

(i) When the Moon is overhead at sunset, it is a quarter of the way around its orbit from the Sun, so we see a half Moon (first quarter). Its bright half faces the setting Sun in the west.

(ii) Waxing. A Moon seen at sunset, high in the sky, is growing towards the full Moon. A waxing Moon is easiest to see at sunset.

(i) A half Moon, with the bright half towards the west. (ii) Waxing (first quarter).

Kaushalya.

• A Moon rising in the east at sunset is opposite the Sun, so it is a full Moon, not a crescent. A crescent Moon is always close to the Sun in the sky, so it rises and sets close to the Sun.
• A waxing gibbous Moon (a few days before full) rises in the east in the afternoon and can be seen in daylight.

Kaushalya. A crescent is always near the Sun, so it cannot be rising in the east at sunset (only a full Moon does that), while a waxing gibbous Moon does rise in the afternoon.

Less often. If the Moon is slower, each lunar month becomes longer, so 12 lunar months add up to more days. They then fall short of the solar year by fewer days each year.

The gap of about 11 days builds up more slowly, so an extra month needs to be added less often. (This change is extremely slow: it takes millions of years to notice.)

Less often: longer lunar months make 12 of them closer to a solar year, so the gap grows more slowly.

Three years have $3\times 12=36$ calendar months. Put the 37 full Moons into these 36 months like letters into boxes. Even if each month got one full Moon, that would use only 36 of them. So the 37th must go into a month that already has one.

So at least one month has two full Moons. (A second full Moon in the same month is popularly called a "blue moon".)

37 full Moons into 36 months: some month must hold two (the pigeonhole principle).

The full Moon. It is opposite the Sun, so it rises at sunset, stays up all night and sets at sunrise.

Full Moon

A solar year is about $365\frac{1}{4}$ days. Without leap years, our calendar would slip by about $\frac{1}{4}$ day every year against the seasons, so 15 August would come a little earlier in the season each year.

To move from mid-August back to winter (about 6 months, or roughly 180 days):

$$180÷\frac{1}{4}=720\text{ years}$$

In about 700–750 years (about 180 days of drift at ¼ day per year).

Satellites are used for:

• communication: telephone, TV, internet;
• weather forecasting and cyclone warnings;
• navigation, such as GPS and India's NavIC;
• mapping and monitoring forests, crops, water, floods and disasters (remote sensing);
• scientific research on space, the Sun, the Moon and the planets;
• defence and security.

Communication, weather forecasting, navigation, Earth observation (mapping and disasters), scientific research and defence.

1. Day: the Earth's rotation on its axis (sunrise to the next sunrise).
2. Month: the cycle of the Moon's phases as it goes around the Earth (about 29.5 days).
3. Year: the Earth's revolution around the Sun, which also brings the cycle of seasons.

Day: Earth's rotation. Month: the Moon's phases (its revolution around the Earth). Year: Earth's revolution around the Sun.