Keeping Time With The Skies

Namaste, dear students! Welcome to today's science lesson. I am so happy to see you all here, ready to learn something fascinating about the sky above us. Today, we are going to study Chapter 11 from your science textbook – "Keeping Time with the Skies". This is a wonderful chapter that connects the things we see in the sky every day – the Sun, the Moon, and the stars – with how we measure time. Isn't it amazing that ancient people, thousands of years ago, could figure out how to measure days, months, and years just by watching the sky carefully? Let's begin our journey into the sky and discover these secrets together.

So students, let's start with a story. Imagine it is Makar Sankranti, and you are in Ahmedabad for the Patang Mahotsav, the International Kite Festival. You look up at the sky filled with colorful kites, and suddenly you notice something surprising – the Moon is shining during the daytime! You might think this is strange because we usually see the Moon at night, right? But wait, there's more. The Moon does not appear as a full circle – it looks like a curved shape, maybe like a banana or a boat. Now, you might already know that the Moon is spherical and it shines by reflecting sunlight. But then why isn't the whole Moon visible every night? Could it be a lunar eclipse? No, eclipses are rare and last only for a short time. So what causes the Moon's changing shape? This is exactly what we are going to learn in the first part of our chapter.

Let us carefully watch the Moon to understand how its appearance changes over a month. You may have done a similar activity before, but let us do it in more detail now. The best way to start this activity is from the sunrise after a full Moon day, because that is when it is easiest to spot the Moon in the sky.

Here is what you need to do for Activity 11.1. First, spot the Moon at sunrise in the western direction on the first day after the full Moon. Make a table in your notebook similar to Table 11.1. You need to document the date, when you saw the Moon (at sunrise or sunset), and shade a circle with pencil to show the bright portion of the Moon. From the second day onwards, also document whether the size of the bright portion of the Moon is increasing or decreasing from the previous day, and whether the Moon appears closer to or farther from the Sun in the sky than the day before. After about 15 days, you may not be able to see the Moon at sunrise or sunset. For the next 15 days, carry out this activity at sunset instead.

Now, let us analyse the data you recorded. Did the Moon appear different each day? Was the Moon visible on all days? Did the Moon appear at the same position in the sky as on the previous day? These are important questions that will help us understand the Moon's behavior.

Now, let us discuss what we observed. You may have noticed that the bright portion of the Moon decreases from a full circle to a half circle in about a week. The bright portion continues to shrink for another week until it is no longer visible. This two-week period is called the waning period of the Moon. Different names are given to the Moon's visible shapes during this cycle. The day when the Moon appears as a full bright circle is called the full Moon day, which we call Purnima in India. And the day when it is not visible is called the new Moon day, which we call Amavasya.

After the new Moon, its bright side grows to a half circle in about a week and to a full circle (full Moon) in another week. The period when the bright part of the Moon increases is called the waxing period. In India, the waning period of the Moon is generally called the Krishna Paksha, while the waxing period is called the Shukla Paksha. The Moon goes through a waning period followed by a waxing period in a cyclical manner. The cycle from one full Moon to the next takes about a month.

So students, the changing shapes of the bright portion of the Moon from one day to another as seen from the Earth are called the phases of the Moon. This is a very important definition to remember.

Now, let us understand something about locating the Moon. When you checked the Moon at the same time on successive days, for example at sunrise, did you see it in a different part of the sky? On a full Moon day, the Moon is nearly opposite the Sun. When the Sun rises in the East, the Moon is almost setting in the West. On subsequent mornings at sunrise, as its bright part continues to decrease, the Moon appears to move closer in the sky to the Sun. When the bright part of the Moon decreases to a half circle shape, the Moon is overhead at sunrise. A few days later, the crescent Moon appears even closer to the Sun. Knowing the phase of the Moon and whether it is waxing or waning can thus help us find out where and when to look for the Moon on any given day. A waxing Moon is easiest to spot at sunset, and a waning Moon at sunrise. Because of these shifts, the Moon always rises and sets at different times than the Sun.

Let me tell you something interesting here. Many people believe the Moon rises when the Sun sets, but that is not always true. If you look in a local newspaper or on the Positional Astronomy Centre website, you can find the moonrise time in your area. Check these times for several days in a row and you will see that the Moon rises about 50 minutes later each day. Sometimes moonrise happens in the afternoon, around 2:00 to 4:00 p.m., so you can spot the Moon in the eastern sky during daylight. You may need to wait about 30 minutes past the listed moonrise time for the Moon to climb high enough for it to be seen. The time and position of moonrise changes from one day to the next.

Now, let us understand why this happens. The shape of the Moon itself does not change – only what we see changes. You may recall learning earlier that the Moon does not emit light of its own, but shines because it reflects sunlight that falls on it. The half of the Moon that faces the Sun receives sunlight and becomes illuminated. The other half facing away from the Sun does not receive sunlight and remains non-illuminated.

The Moon revolves around the Earth, and only one half of the Moon always faces the Earth. However, the portion of the Moon facing the Earth is not always its illuminated part. We can only see the illuminated portion of the Moon from Earth. Sometimes, the entire illuminated portion of the Moon faces the Earth, and at other times only a part of it. At such times the illuminated portion of the Moon that we see is not a full circle. On new Moon day, we do not see the illuminated portion of the Moon at all, as only the non-illuminated portion of the Moon faces the Earth. Therefore, the Moon appears different on different days.

Now, here is a question for you to think about. Why does the illuminated portion of the Moon seen from the Earth decrease when it appears closer to the Sun? Let us do an activity to understand this better.

For Activity 11.2, take a small soft ball and insert a stick into it. This represents the Moon. Go to a dark open place at night, and ask a teacher or guardian to shine a torchlight towards you from about 3 meters to represent light coming from the Sun, or you can stand near an electric lamp. Your head represents the Earth.

Now, hold the ball at arm's length in one hand such that it is slightly above your head. Keep the ball at position E towards the direction of the lamp. Does the portion of the ball facing you appear to be illuminated or not? It should appear dark because you are looking at the side that is away from the lamp.

Now, turn around slowly in the anti-clockwise direction with your arm outstretched and keep looking at the ball. Does the shape of the illuminated portion change? Is the line separating the illuminated and non-illuminated portions of the ball curved? Yes, it is curved, just like what we see in the Moon.

Was your observation similar to the changing shape of the illuminated portion of the ball shown in the figure? The shape of the illuminated portion of the ball, as seen by you, changes depending on where the ball is with respect to the lamp.

When the ball is held opposite to the direction of the lamp, you are facing the entire illuminated portion of the ball, just like the full Moon day. On the other hand, when the ball is held towards the direction of the lamp, you are facing the non-illuminated portion of the ball, and cannot see the illuminated portion of the ball at all. This is similar to the new Moon day. Notice how in other cases, the line separating the illuminated and non-illuminated portions of the ball appears curved, similar to the shape of the illuminated portion of the Moon viewed from the Earth on other days.

Using our observations of Activity 11.2, let us now try to understand the phases of the Moon. The Moon revolves once around the Earth from one position to another and back to the starting position in about one month. The side of the Moon that faces the Sun is illuminated. The portion of the Moon that faces the Earth is marked, and the illuminated portion of only this part of the Moon can be seen from the Earth.

At some positions, more than half of the illuminated portion can be seen. This is called the gibbous phase. At other positions, less than half of the illuminated portion can be seen. This is called the crescent phase. The change in the fraction of the illuminated portion of the Moon seen from Earth causes phases of the Moon.

From one position to another, we see the waning phase, and from another set of positions back to the starting point, we see the waxing phase. Since the rotation period of the Earth of one day is much smaller compared to the revolution period of the Moon which is nearly a month, on a given day, people on different parts of the Earth see nearly the same phase.

As we can see, on the new Moon day, the Moon appears closest to the Sun, and it appears farthest on the full Moon day. Is this not what we also observed in Activity 11.1?

In Activity 11.1, we also observed that the position of the Moon at sunrise or sunset appeared to be shifted on successive days. This happens because the Moon moves ahead in its orbit while the Earth completes one rotation about its axis in 24 hours. Earth needs to rotate some more for the Moon to appear in nearly the same spot in the sky. The Moon takes about 50 minutes longer to come back to nearly the same position in the sky.

Now, let me clarify something important here. The Moon phases do not happen due to Earth's shadow. It is an incorrect explanation for the Moon's phases that Earth's shadow falls on it. As we have learnt, the phases of the Moon occur due to the relative change in orientation of the Sun, Moon, and Earth as the Moon revolves around the Earth. The Earth's shadow on the Moon causes a lunar eclipse, not the Moon's phases. Lunar eclipses can only happen on a full Moon day and solar eclipses can only happen on a new Moon day. But they do not occur every month because of the small tilt of the Moon's orbit with respect to the Earth's orbit around the Sun.

So, the changing phases of the Moon is a natural periodic event, with a cycle of almost a month, which can also be used for time keeping. Yes, along with the natural periodic events of day and night and the changing seasons. But how are these periodic events used for keeping time? This is what we are going to learn next.

Now, let us move to the second part of our chapter – how calendars came into existence.

We have learnt earlier that when viewed from the Earth, the Sun appears to rise in the eastward direction, set in the westward direction every day, and rise again the next day. This apparent periodic motion of the Sun seen by us is primarily due to the rotation of the Earth around its own axis. This natural cycle of the Sun due to the rotation of the Earth is the foundation of the day, a unit to measure time.

The average time that the Sun takes to go from its highest position in the sky on one day to the highest position in the sky the next day is 24 hours, and is called the mean solar day. The highest position of the Sun in the sky can be found by measuring the length of the shadows cast by an object during the day. The shadow is shortest when the Sun is at the highest point in the sky.

Let us do Activity 11.3 to measure a day. Find a small flat area in a ground which receives sunlight during the day. Fix a 1 meter stick vertically in it. Start observing at 11:00 a.m. Every minute, mark a dot on the ground at the tip of the stick's shadow. Keep marking dots until around 1:10 p.m. Identify when the shadow was shortest and find out its time by counting the number of dots. Record this time in Table 11.2. Repeat this exercise for the next few days. Find the duration of the solar day by finding a difference in time on two consecutive days. Find the average duration of the day. Is it nearly equal to 24 hours? Yes, it should be approximately 24 hours.

The phases of the Moon give us another natural cycle with a duration that is longer than a day. The Moon takes about 29.5 days, nearly a month, to cycle through all its phases. The cycle of the phases of the Moon is the basis for a month, another unit to measure time.

The next larger unit to measure time is related to the natural cycle of seasons. Do you remember learning earlier that the Earth revolves around the Sun and takes nearly 365 and a quarter days to complete one revolution around the Sun? The Earth undergoes one cycle of seasons during this time, which can be used to define a solar year.

Now, let us talk about lunar calendars. In ancient times, people had noticed that during one cycle of seasons, one can fit nearly 12 cycles of the phases of the Moon, that is, 12 lunar months. This is how lunar calendars came into being, with the day as the shortest unit, a month of nearly 29.5 days, and a lunar year consisting of 12 lunar months. The phases of the Moon thus gave an easy and a perfectly sound way to track the passage of time.

However, in a lunar calendar the seasons do not remain synchronised to the same lunar months in successive lunar years. The reason is that the seasons repeat in approximately 365 days while the lunar year is 354 days long. There is a difference of about 11 days between the lunar year and the solar year.

Now, let us discuss solar calendars. It was important to know the arrival of seasons for agricultural purposes. This need for a year to synchronise with seasons led to the creation of solar calendars. The Gregorian calendar, widely used today, is a solar calendar. The months in solar calendars are adjusted to add up to 365 days. That is why in Gregorian calendars, some months have 30 days, others 31, and February has only 28 days.

On top of the 365 days, the Earth takes nearly an extra quarter of a day to complete one revolution around the Sun. These extra hours add up to approximately one day every four years. To adjust for this, solar calendars add an extra day every four years using the concept of a leap year. In the Gregorian calendar, if a year is divisible by four, then an extra leap day is added. So in a leap year, February has 29 days, which keeps the calendar well synchronised with the seasons.

Let me tell you something more interesting. The Earth takes slightly less time than 365 and a quarter day to go from one spring equinox to the next spring equinox. Adding a day every four years helps to synchronise with the seasons, but it actually adds a little too much over time. To fix this, leap years are skipped every 100 years, like in 1700, 1800, and 1900. But skipping all of them would make the calendar lag slightly behind. So every 400 years, a leap year is again added back, like in 1600 and 2000. These careful corrections keep the calendar closely matched with the seasons over long periods of time!

As we learnt earlier, seasons are caused by the Earth's revolution around the Sun and its movement from the spring equinox to winter equinox and back. The time between successive spring equinoxes is called the tropical year. The Gregorian calendar is based upon the tropical year.

We have also learnt earlier that the stars that rise at sunset change throughout the year due to the Earth's revolution around the Sun. The time duration required for the same stars to rise again at sunset is called the sidereal year, and it can also be used to define a solar calendar. The sidereal year is longer than the tropical year by a mere 20 minutes, and so it takes a long time before the differences between the two calendars become noticeable. In modern times, astronomers use the sidereal year to keep track of the Earth's position in its orbit around the Sun.

Now, let me tell you about our scientific heritage. For thousands of years, people, including those in India, have been observing the sky and developing calendars. People in ancient times did not know that Earth revolves around the Sun, and lacked modern instruments. Yet through years of careful sky observations, they noticed patterns and cycles in natural events. Hence, they could determine that the length of the year was approximately 365 days, allowing them to create calendars.

For example, careful observation reveals that the Sun does not always rise exactly in the East. In summer, it rises a little northward of East, and in winter a little southward of East. These extremes happen on the solstices, around June 21 and December 21 each year. The Sun's apparent northward movement from December to June is called Uttarayan, and its apparent southward movement from June to December is Dakshinayan. This cycle repeats every year and is closely linked to the changing seasons. The Taittirīya Saṃhitā records it in the verse 6.5.3: "Thus the Sun moves southwards for six months and northwards for six months."

In the past, the equinoxes and solstices were also tracked by identifying the stars that rose at sunset. Ancient Indian texts like the Surya Siddhanta noted that the pattern of stars, Capricorn, called Makar in India, would be in the background of the Sun around the winter solstice during those ancient times. The Surya Siddhanta says: "From the moment of the Sun's entrance into the constellation of Capricorn, six months make up its northward progress (Uttarayana), so likewise from the moment of entrance into the constellation of Cancer, six months are its southward progress (Dakshinayana)."

Over the years, different types of calendars have evolved based on specific needs. A number of these calendars are used in different parts of India to track time and celebrate festivals.

Now, let us discuss luni-solar calendars. There is another kind of calendar which primarily uses the Moon's phases for counting days and months but also makes adjustments to stay in sync with the cycle of seasons.

The 12 lunar months add up to 354 days and thus fall short by nearly 11 days compared to the solar year. Thus every 2–3 years, the accumulated difference becomes close to a full month. Therefore, every few years, an extra month, called Adhika Maasa or intercalary month, is added to the year in some calendars. This keeps the solar year and the lunar cycle in step. Such calendars are called luni-solar calendars. They combine elements from both the solar and the lunar calendars and are used in many parts of India.

You may have heard of the names of the months in various Indian luni-solar calendars – Chaitra, Vaisakha, Jyeshtha, Ashadha, Shravana, Bhadrapada, Ashwin, Kartika, Margashirsha or Agrahayan, Pausha, Magha, and Phalguna. In some communities, the new month starts on the first day after the new Moon and ends on the day of the new Moon. Such calendars are called Amant. In others, the start of the new month corresponds to the day after the full Moon, and the month ends on the full Moon. Such calendars are called Purnimant.

Now, let us talk about the Indian National Calendar. A national calendar by the Government of India is used along with the Gregorian calendar for multiple official purposes. It is based on the Shaka Era. The Indian National Calendar is a solar calendar consisting of 365 days in a year. The year begins on 22 March, which is the day after the spring equinox. Unlike the Gregorian calendar, months in the Indian National Calendar have either 30 or 31 days. The names of these months were taken from traditional Indian calendars. In a regular year, the second to sixth months have 31 days and the rest have 30 days. The leap years are matched to the Gregorian calendar by adding a day to Chaitra, the first month of the year. In such years, the new year begins on 21 March of the Gregorian calendar.

In 1952, the Government of India set up a Calendar Reform Committee to examine all existing calendars which were being followed in the country at that time and to recommend an accurate and uniform calendar for the whole of India. The Calendar Reform Committee recommended a Unified National Calendar, which was adopted for use with effect from 21 March 1956 CE, that is, 1 Chaitra 1878 Saka. The Indian National Calendar follows the general principles as that of the Surya Siddhanta.

Now, let us discuss whether festivals are related to astronomical phenomena. Many Indian festivals are tied to the phases of the Moon and hence are based on either lunar or luni-solar calendars. For instance, Diwali falls on the new Moon of the month of Kartika, Holi on the full Moon of Phalguna, Buddha Purnima on the full Moon of Vaisakha, Eid-ul-Fitr is celebrated after sighting the crescent Moon at the end of the month of Ramazan, while Dussehra is celebrated on the tenth day in the month of Ashwina. Hence, they occur on different dates in the Gregorian calendar in successive years.

Why do most Indian festivals fall on different dates every year? For festivals based on luni-solar calendars, the Gregorian calendar dates can shift, but this shift is typically less than a month. This is because the luni-solar calendars add the intercalary month every few years which correct for the difference between the lunar and the solar year. In contrast, purely lunar calendars do not account for this difference. Any festival celebrated according to the phases of the Moon, such as Eid-ul-Fitr, therefore can occur in different months of the Gregorian calendar year after year.

A few festivals in India, like Makar Sankranti, Pongal, Bihu, Vaisakhi, Poila Baisakh, and Puthandu, follow a solar sidereal calendar. These festivals happen on almost the same date every year in the Gregorian calendar which is based on the tropical year.

A long time ago, these festivals were tied to either a solstice or an equinox. Due to the small difference in the sidereal and tropical years, the dates of these festivals slowly shift away from the solstices and equinoxes. This shift is due to slow wobble of the Earth's axis, similar to the movement of the axis of a wobbling top. This causes the dates of festivals based on the sidereal calendar to move ahead in the tropical calendar. For example, Makar Sankranti moves ahead by one day every 71 years.

The dates of many Indian festivals are based on the exact lunar phase at sunrise. As sunrise occurs earlier in Eastern India and later in Western India, these dates can also shift by a day between these regions even in the same year. To maintain uniformity throughout the country, the Positional Astronomy Center of the Government of India annually publishes the Rashtriya panchang, a detailed calculation of the positions of celestial objects, such as the Moon and the Sun for a central location in India. Based on these calculations, it provides an advance intimation on dates of festivals to the Government of India for holiday declaration.

The Moon and moonlight have inspired ragas in Indian classical music. Chandrakauns, Chandranandan, and Shubhapantuvarali are a few ragas that display the moon's imagery in their names and melodic expressions. Similarly, mudras, hand gestures, for example Chandrakala and Ardhachandran relating to the Moon can be found in Indian classical dance Bharatanatyam. The same is true for other dance forms – Kathak, Odissi, and Kuchipudi. Even the traditional painting styles – Madhubani, Warli, and other forms of art, such as sculpture and pottery among Saura, Gond and other tribes invoke depictions of the Moon and the Sun prominently, implying their significance in daily life.

Now, let us discuss why we launch artificial satellites in space. The Moon is Earth's natural satellite, orbiting our planet. Besides the Moon, man-made satellites sent by various countries also orbit the Earth. These artificial satellites appear as tiny specks moving in the night sky. Most orbit about 800 km above Earth's surface and take roughly 100 minutes to complete one orbit.

When you look at the night sky in early evening, you may see some moving stars. What are they? Is their motion also periodic? These are artificial satellites. These satellites help us in many ways like communication, navigation, weather monitoring, disaster management, and scientific research. The Indian Space Research Organisation, ISRO, has launched many satellites that support these activities.

The Cartosat series of satellites, launched by ISRO, capture high-quality images of the Earth to improve maps, plan cities, and handle natural disasters in India. One such mapping platform, Bhuvan, uses these images to show terrain, soil, land use, vegetation, and more. AstroSat, another ISRO mission, makes scientific observations of stars and other celestial objects. India's other space missions include Chandrayaan 1, 2, and 3 to the Moon; Aditya L1 to study the Sun; and Mangalyaan to Mars. ISRO also lets Indian students build and launch small satellites, such as AzaadiSat, InspireSat-1, and Jugnnu.

Let us do Activity 11.4 to identify artificial satellites. Spotting an artificial satellite is a night sky watching activity like we have done previously. Just before sunrise or after sunset, go to a location, accompanied by an adult, that has a clear view of the sky, without any obstruction of trees or tall buildings. To identify satellites in the sky, look for any moving object in the sky that appears as a point of light with steady or flickering brightness and is moving very fast across the sky. You can see them with the naked eye or with binoculars. You may use mobile apps or websites that provide details of satellites visible in your location and when they will be passing above you in the sky.

A lot of artificial satellites are being sent up in space by many countries. After their useful life, many of them and their rocket parts become space junk or space debris. This debris crowds space and could collide with working satellites. While small debris burns up in the atmosphere when it falls towards the Earth, the larger pieces can crash on ground. Countries are now working together to remove this dangerous debris.

Vikram Ambalal Sarabhai, 1919-1971, was a researcher in space science and nuclear physics and is known as the Father of the Indian Space programme. He pioneered the effort to launch the first artificial satellites. The Vikram Sarabhai Space Centre, VSSC, located in Thiruvananthapuram, the ISRO centre that develops rockets and launch vehicle technology, is named after him.

Now, students, let us go through the questions at the end of the chapter and solve them one by one.

First, let us look at "Keep the curiosity alive" section.

Question 1: State whether the following statements are True or False.

(i) We can only see that part of the Moon which reflects sunlight towards us.

This is TRUE. The Moon does not produce its own light. We can only see the part of the Moon that reflects sunlight towards the Earth.

(ii) The shadow of Earth blocks sunlight from reaching the Moon causing phases.

This is FALSE. This is a common misconception. The phases of the Moon are NOT caused by Earth's shadow. They occur because we see different parts of the illuminated portion of the Moon as it moves around the Earth. Earth's shadow causes lunar eclipses, but only occasionally, not every month.

(iii) Calendars are based on various astronomical cycles which repeat in a predictable manner.

This is TRUE. Calendars are indeed based on astronomical cycles like the Earth's rotation (day), the Moon's phases (month), and the Earth's revolution around the Sun (year).

(iv) The Moon can only be seen at night.

This is FALSE. The Moon can be seen during the day as well. In fact, sometimes you can see the Moon in the afternoon or morning sky. For example, during the waxing phase, the Moon is often visible during the day.

Question 2: Amol was born on 6th of May on a full Moon day. Does his birthday fall on the full Moon day every year? Explain your answer.

No, his birthday will not fall on the full Moon day every year. This is because the Gregorian calendar year has 365 or 366 days, while the lunar cycle (from one full Moon to the next) is about 29.5 days. So the date of full Moon shifts by about 11 days each year in the Gregorian calendar. Therefore, on 6th May of subsequent years, the Moon will be in a different phase. Only if we use a lunar calendar would his birthday fall on the full Moon day every year.

Question 3: Name two things that are incorrect in Fig. 11.10.

Since I cannot see the figure, I will tell you what is commonly incorrect in such diagrams. Usually, the incorrect things could be: the direction of the Sun's rays, the relative positions of the Sun, Earth, and Moon, or the labeling of the phases. Without the actual figure, I cannot specify exactly what is wrong, but typically students should look for: whether the illuminated side of the Moon is facing the Sun (it should always face the Sun), whether the Earth is shown correctly between the Sun and Moon for certain phases, and whether the labels match the positions shown.

Question 4: Look at the pictures of the Moon in Fig. 11.11, and answer the following questions.

(i) Write the correct panel number corresponding to the phases of the Moon shown in the pictures above.

The table asks us to match pictures with phases:

Three days after New Moon – This would be a thin crescent, just a small sliver of the Moon visible.

Full Moon – This would be a complete circle, fully illuminated.

Three days after Full Moon – This would be a gibbous Moon, but now past full, so it would be in the waning phase, showing most of the circle but with a small portion in shadow.

A week after Full Moon – This would be a half Moon, specifically the last quarter or third quarter Moon.

Day of New Moon – This would be completely dark, the Moon is not visible at all.

(ii) List the picture labels of the phases of the Moon that are never seen from Earth. Hint: You can use your observations from Activity 11.1 or Fig. 11.2 as reference.

From Earth, we never see the "back" of the Moon – the side that always faces away from us. We also never see a fully illuminated "back" side. The phases we never see from Earth would be those where the far side of the Moon is fully illuminated but facing Earth, which doesn't happen naturally. Actually, from Earth, we always see the same side of the Moon, so we never see the far side at all. The phases that are never seen are those where the entire near side would be dark (which is new Moon – we don't see it) or where the entire near side would be illuminated (which is full Moon – we do see it). Wait, let me reconsider. The question asks for phases "never seen from Earth." Actually, all the main phases (new Moon, crescent, half, gibbous, full) are visible from Earth at some point. What we never see is the far side of the Moon in any phase. So perhaps the answer refers to specific positions in the orbit that would show us the Moon in a way we cannot observe from Earth.

Question 5: Malini saw the Moon overhead in the sky at sunset.

(i) Draw the phase of the Moon that Malini saw.

If the Moon is overhead at sunset, this means the Moon is in the sky when the Sun is setting. At sunset, the Sun is in the west, going down. If the Moon is overhead, it is directly above. For the Moon to be overhead at sunset, it must be at the full Moon phase or nearly full. Actually, let me think more carefully. At sunset, the Sun is in the west. The Moon overhead means it is in the zenith. For the full Moon, the Moon is opposite the Sun in the sky, so when the Sun sets in the west, the full Moon rises in the east and is overhead around midnight, not at sunset. For the Moon to be overhead at sunset, it must be at the first quarter phase (waxing half Moon). In the first quarter, the Moon is 90 degrees away from the Sun in the sky. So when the Sun sets in the west, the first quarter Moon is overhead. So Malini saw a half Moon, specifically the first quarter or waxing half Moon.

(ii) Is the Moon in the waxing or the waning phase?

Since it is overhead at sunset and we determined it is the first quarter Moon, this is the waxing phase. The waxing half Moon is exactly overhead at sunset.

Question 6: Ravi said, "I saw a crescent Moon, and it was rising in the East, when the Sun was setting." Kaushalya said, "Once I saw the gibbous Moon during the afternoon in the East." Who out of the two is telling the truth?

Let us analyze this. Ravi said he saw a crescent Moon rising in the East when the Sun was setting. When the Sun is setting, it is in the West. For a crescent Moon to rise when the Sun is setting, the Moon must be close to the Sun in the sky. A crescent Moon is indeed close to the Sun. During sunset, the Sun is in the West, and the crescent Moon would be rising in the East. This is possible. So Ravi could be telling the truth.

Kaushalya said she saw the gibbous Moon during the afternoon in the East. The gibbous Moon is more than half illuminated. For it to be in the East during the afternoon, it would need to be rising in the East while the Sun is still up in the afternoon. A gibbous Moon that is waxing would rise in the East in the late afternoon or evening. This is also possible. However, let us think more carefully. During the afternoon, the Sun is in the western part of the sky. A gibbous Moon in the East would mean it has already risen. The gibbous phase occurs when the Moon is more than half illuminated. For a waxing gibbous, it rises in the afternoon and is visible in the evening. For a waning gibbous, it rises late at night and is visible in the morning. So it is possible to see a gibbous Moon in the East during the afternoon, especially if it is waxing gibbous. Both could be telling the truth, but we need to consider which one is more likely. Actually, let me reconsider. A crescent Moon rising at sunset is very plausible. A gibbous Moon in the East during afternoon is also plausible, but less common. Both statements could be true. However, if we have to choose one, Ravi's statement is more typical. But actually, both could be true depending on the specific day. Let me think again about Kaushalya's statement. During the afternoon, the Sun is in the sky. For the Moon to be visible in the East during the afternoon, it must have risen already. A waxing gibbous Moon rises in the afternoon and is visible in the evening sky. So yes, it is possible. So both could be telling the truth. But perhaps the question expects us to say that Ravi is more likely correct. Actually, let me check the positions more carefully. For Ravi: crescent Moon rising in the East at sunset. At sunset, the Sun is in the West. A crescent Moon is close to the Sun in the sky, so it would be in the western part of the sky at sunset, not rising in the East. Wait, that's not right either. Let me think about the geometry. At sunset, the Sun is in the West, going down. The Moon's position depends on its phase. For a new Moon, the Moon is in the same direction as the Sun. For a full Moon, the Moon is opposite the Sun. For a crescent Moon, the Moon is between the new Moon and first quarter positions. At sunset, the Sun is in the West. A waxing crescent Moon would be in the western sky, close to the Sun. It would not be rising in the East at sunset – it would be setting in the West, actually. A waning crescent Moon would rise in the East before sunrise. So Ravi's statement seems incorrect. Let me reconsider Kaushalya. For a gibbous Moon to be in the East during the afternoon: a waxing gibbous Moon would be in the eastern sky in the late afternoon/evening as it rises. A waning gibbous Moon would be in the eastern sky in the early morning. So Kaushalya could be correct if it was a waxing gibbous. So Kaushalya is more likely telling the truth.

Actually, let me reconsider Ravi's statement more carefully. "I saw a crescent Moon, and it was rising in the East, when the Sun was setting." If the Sun is setting, it is evening. A crescent Moon rising in the East in the evening – is this possible? A waxing crescent Moon rises in the East in the morning and sets in the West in the evening, but it is close to the Sun, so it sets shortly after the Sun. Actually, a waxing crescent is visible in the evening sky after sunset, not rising at sunset. A waning crescent rises in the East before sunrise. So neither waxing nor waning crescent rises at sunset. Ravi's statement seems incorrect. Kaushalya's statement: "Once I saw the gibbous Moon during the afternoon in the East." A waxing gibbous Moon rises in the East in the afternoon and is visible in the evening. So this is possible. So Kaushalya is telling the truth.

Question 7: Scientific studies show that the Moon is getting farther away from the Earth and slower in its revolution. Will luni-solar calendars need an intercalary month more often or less often?

If the Moon is getting farther away and slower in its revolution, the lunar month would become longer. Currently, the lunar month is about 29.5 days. If it becomes longer, then the difference between the lunar year (12 lunar months) and the solar year would become smaller or larger? Let me calculate. Currently, 12 lunar months = 12 × 29.5 = 354 days. The solar year is 365 days. The difference is 11 days. If the lunar month becomes longer, say 30 days, then 12 × 30 = 360 days. The difference would be 5 days, which is smaller. Wait, that's the opposite. If the Moon is slower, it takes longer to complete one revolution, so the lunar month becomes longer. A longer lunar month means the lunar year becomes longer (more days in a year). If the lunar year becomes longer, it gets closer to the solar year, so the difference becomes smaller. If the difference is smaller, we would need the intercalary month less often. Currently, we add an extra month every 2-3 years. With a longer lunar month, the difference between lunar and solar year decreases, so we would need to add the intercalary month less frequently. So the answer is: luni-solar calendars will need an intercalary month less often.

Question 8: A total of 37 full Moons happen during 3 years in a solar calendar. Show that at least two of the 37 full moons must happen during the same month of the solar calendar.

We need to prove that in 3 years, with 37 full Moons, at least two must fall in the same month. There are 12 months in a year, so in 3 years, there are 36 months. We have 37 full Moons but only 36 months. If each full Moon fell in a different month, we could have at most 36 full Moons in 36 different months. But we have 37 full Moons. Therefore, by the pigeonhole principle, at least two full Moons must happen during the same month of the solar calendar. This is a mathematical certainty.

Question 9: On a particular night, Vaishali saw the Moon in the sky from sunset to sunrise. What phase of the Moon would she have noticed?

If Vaishali saw the Moon in the sky from sunset to sunrise, this means the Moon was visible all night long. For the Moon to be visible all night, it must be opposite the Sun in the sky. When the Sun sets in the West, the Moon must be rising in the East. When the Sun rises in the East, the Moon must be setting in the West. This happens when the Moon is at the full Moon phase. At full Moon, the Moon is opposite the Sun, so it rises when the Sun sets and sets when the Sun rises. So Vaishali would have noticed a full Moon.

Question 10: If we stopped having leap years, in approximately how many years would the Indian Independence day happen in winter?

Indian Independence Day is celebrated on August 15. Currently, it is in the monsoon season, not winter. If we stopped having leap years, the calendar would gradually drift relative to the seasons. Without leap years, we would not add the extra day every four years. This means the calendar year would be 365 days instead of 365.25 days. Over time, the calendar would fall behind the actual solar year by about 0.25 days per year. In 100 years, the drift would be about 25 days. So in about 400 years, the drift would be about 100 days, or roughly three months. If August 15 drifts back by three months, it would become around mid-May. That's still not winter. Wait, let me think about this differently. Actually, if we go forward in time, the seasons would shift forward in the calendar. So August 15 would gradually move into earlier seasons. Actually, without leap years, the calendar would not account for the extra quarter day per year. So the calendar would be shorter than the actual year. This means the calendar dates would gradually occur earlier in the actual solar year. So after many years, August 15 would occur earlier and earlier in the actual year. Let me calculate: each year, the calendar is short by 0.25 days. After 1 year, the calendar is 0.25 days behind. After 10 years, 2.5 days behind. After 100 years, 25 days behind. After 400 years, 100 days behind. So after about 400 years, August 15 would be about 100 days earlier in the solar year than it is now. Currently, August 15 is about mid-August. 100 days earlier would be around early May. That's still not winter. Actually, wait. I think I need to think about this in terms of seasons. The seasons are determined by the Earth's position in its orbit. If the calendar doesn't account for leap years, the dates would gradually shift through the seasons. Actually, let me reconsider. The question asks: "in approximately how many years would the Indian Independence day happen in winter?" Winter in India is generally December-January. Currently, Independence Day is August 15. The difference is about 4-5 months. If we lose 0.25 days per year, how long to shift 4-5 months (about 120-150 days)? 120 days divided by 0.25 days per year = 480 years. 150 divided by 0.25 = 600 years. So approximately 500-600 years. But wait, that's if we go forward. Actually, without leap years, the calendar would be shorter than the actual year, so the calendar dates would happen earlier in the actual year over time. So August 15 would gradually move to earlier in the year in terms of the solar year. Actually, I think I'm confusing myself. Let me think simply. The calendar year is getting shorter by not adding leap days. This means the calendar is advancing faster than the actual seasons. So the dates are moving forward through the seasons. Actually, no. If we have a 365-day calendar instead of 365.25, then each year we are "losing" 0.25 days relative to the solar year. This means after one year, our calendar date is 0.25 days "behind" where it should be in the solar year. After 10 years, 2.5 days behind. After 100 years, 25 days behind. After 400 years, 100 days behind. So August 15, which is currently in late summer, would occur 100 days earlier in the solar year after 400 years. 100 days before August 15 is approximately May 8. That's spring/early summer, not winter. Actually, wait. The seasons in India are: Summer (April-June), Monsoon (July-August), Autumn (September-October), Winter (November-March). August 15 is currently in the monsoon. If it shifts 100 days earlier, it would be in early May, which is summer. That's not winter either. Let me think about the other direction. Actually, I think I have the direction wrong. Let me reconsider. If we don't have leap years, the calendar year is 365 days. The solar year is 365.25 days. So each year, the calendar falls behind by 0.25 days. This means that the same calendar date occurs later in the actual solar year over time. Wait, that's the opposite. Let me think carefully. The solar year is the actual time for Earth to complete one revolution. The calendar year is our artificial division of time. If the calendar year is shorter than the solar year, then each year, when the calendar says the year has ended, the Earth hasn't quite completed its revolution yet. So the calendar is ahead of the solar year. Actually, no. If the calendar year is 365 days and the solar year is 365.25 days, then after one calendar year, the solar year is 0.25 days from completion. So the calendar date for, say, the start of the year, would occur 0.25 days earlier in the solar year each year. So after 100 years, the start of the calendar year would occur 25 days earlier in the solar year. So August 15 would occur 25 days earlier in the solar year after 100 years. After 400 years, 100 days earlier. So August 15 would move from August 15 to around May 8. That's still not winter. Actually, wait. Maybe the question is thinking about the reverse. If we stopped having leap years, the calendar would gradually become out of sync with the seasons. But actually, without leap years, the calendar would drift such that the seasons would occur later in the calendar year over time. Let me think again. Actually, I think I had it backwards. If we have a 365-day calendar and the actual year is 365.25 days, then each year, the calendar is "missing" 0.25 days. This means that after one year, when the calendar says it's the same date as last year, the Earth has actually gone 0.25 days further in its orbit. So the seasons would shift to later calendar dates. Actually, this is confusing. Let me use an example. Suppose the summer solstice is on June 21 in a leap year. Without adding leap days, the next year, the solstice would be on June 21.25, which is June 21 plus 0.25 days, which is June 21 and 6 hours. In calendar terms, we would say it's still June 21, but actually it's later in the day. But over years, the solstice would drift to later calendar dates. Actually, no. The calendar date stays the same, but the actual event shifts. Wait, I'm getting confused. Let me think about it this way. The Gregorian calendar adds a day every 4 years to keep in sync with the solar year. If we stop adding that day, the calendar would gradually fall behind the solar year. This means that the same calendar date would correspond to an earlier point in the solar year over time. Actually, that's what I thought initially. So August 15 would gradually move to earlier in the solar year. After enough time, it would move from August (monsoon) to May (summer), then to February (winter). How long for August 15 to become winter? Winter in India is roughly December to February. August is about 4 months before December. That's about 120 days. At 0.25 days per year, it would take 120/0.25 = 480 years. So approximately 500 years. That seems reasonable. So the answer is approximately 500 years.

Actually, wait. Let me reconsider the direction one more time. The leap year adds a day to make up for the fact that the solar year is longer than 365 days. If we don't add that day, the calendar year is shorter than the solar year. This means the calendar progresses faster than the solar year. So the calendar dates would correspond to earlier and earlier points in the solar year over time. So August 15 would gradually occur earlier in the solar year. Currently it's mid-August. Earlier in the solar year would be... wait, earlier in the solar year means it's closer to the beginning of the year. So August 15 would move to July, then June, then May, then April... Eventually it would be in winter. How long to go from August to winter (December/January)? That's about 4-5 months, or 120-150 days. At 0.25 days per year, that's 480-600 years. So approximately 500 years. Yes, that seems right.

Question 11: What is the purpose of launching artificial satellites?

Artificial satellites are launched for many purposes. They help us in communication, navigation, weather monitoring, disaster management, and scientific research. They can be used for telephone, television, internet communication, GPS navigation, forecasting weather, monitoring climate change, studying the Earth and other planets, and many other applications.

Question 12: On which periodic phenomenon are the following measures of time based: (i) day (ii) month (iii) year?

(i) Day – based on the rotation of the Earth on its own axis. One complete rotation of the Earth relative to the Sun gives us one day.

(ii) Month – based on the phases of the Moon, specifically the cycle of the Moon's phases, which takes about 29.5 days.

(iii) Year – based on the revolution of the Earth around the Sun, which takes about 365.25 days, giving us the cycle of seasons.

Now, students, we have covered all the questions in the chapter. Let me now give you a comprehensive summary of everything we have learned in this chapter.

Summary:

In this chapter, we learned about the Moon and how its appearance changes. We learned that the Moon does not produce its own light but reflects sunlight. As the Moon revolves around the Earth, we see different portions of its illuminated side, which gives us the phases of the Moon – new Moon, crescent, half Moon, gibbous, and full Moon. The cycle takes about 29.5 days. We learned about waxing (increasing) and waning (decreasing) phases, and about Krishna Paksha and Shukla Paksha in the Indian context.

We then learned how calendars came into existence. The day is based on the Earth's rotation, the month is based on the Moon's phases, and the year is based on the Earth's revolution around the Sun. We learned about lunar calendars, solar calendars, and luni-solar calendars. We learned about the Gregorian calendar and its leap year system, and about the Indian National Calendar. We also learned about how festivals in India are related to astronomical phenomena, with some based on lunar calendars and others on solar calendars.

Finally, we learned about artificial satellites – human-made objects that orbit the Earth. We learned about their uses in communication, navigation, weather monitoring, and scientific research, and about ISRO's contributions to space science.

This brings us to the end of our lesson. I hope you all now have a clear understanding of the chapter. Remember, the sky has been a clock for humanity for thousands of years, and by watching the sky carefully, we can tell time just like our ancestors did. Keep looking up at the sky, keep asking questions, and keep exploring. Thank you for your attention, and goodbye for now!