Class 8 Science Chapter 11: Keeping Time with the Skies

A Moon in the Afternoon

At the kite festival in Ahmedabad on Makar Sankranti, Meera looked up past the kites and saw the Moon - in broad daylight, with the Sun still up. She had always taken the Moon for a night-time object. It was not a full circle either, though that part did not surprise her, since she knew its shape changes from night to night.

The Question Underneath

She remembered two facts: the Moon is a sphere, and it shines by reflecting sunlight. Put those together and the whole lit sphere ought to be visible every night. She wondered for a moment whether an eclipse was to blame, but eclipses are rare and over quickly, and this happens every month. So what does change the Moon’s shape?

Watch It for a Month

The honest way to answer is to look. Starting the morning after a full Moon, find the Moon at sunrise, in the west, and draw the bright part. Do it every day, noting whether the bright part has grown or shrunk and whether the Moon looks nearer the Sun in the sky than it did yesterday.

What the First Fortnight Shows

The bright part shrinks. From a full circle it falls to a half circle within a week or so, keeps shrinking for a second week, and then cannot be seen at all. Those two weeks of shrinking are called the waning period.

And the Second Fortnight

Then it reverses. From not being visible at all, the bright side grows back to a half circle within a week or so and to a full circle in another week. Those two weeks of growing are the waxing period, and the whole journey from one full Moon round to the next lasts about a month.

Two Days With Names

The day the Moon is a full bright circle is the full Moon day, or Purnima. The day it cannot be seen at all is the new Moon day, or Amavasya. Everything else in the cycle lies between those two.

Paksha

In India the fortnight of shrinking is generally called Krishna Paksha and the fortnight of growing Shukla Paksha. Paksha means a fortnight, so the two names divide the month in half at Purnima and at Amavasya.

Gibbous and Crescent

Two more words for the shapes in between. When more than half of the lit side is visible the Moon is gibbous. When less than half is visible it is a crescent. Both occur twice in a cycle, once while waning and once while waxing.

The Order Round the Cycle

Follow it from the full Moon: full, gibbous, half, crescent, new - that is the waning fortnight. Then crescent, half, gibbous, full - the waxing fortnight. The same shapes, in reverse order, on the way back up.

What a Phase Actually Is

The changing shapes of the bright part of the Moon, as seen from Earth, are what we call its phases. Notice the words "as seen from Earth": the phase is a description of our view, which is the hint the next topic follows.

The Shape Is Not the Moon

It is worth saying plainly, because the drawing can mislead. Nothing is being cut off the Moon and nothing is being added. The Moon is the same sphere all month. What changes over the month is how much of its lit half happens to be pointing our way.

A Cycle You Can Rely On

Because the cycle repeats in about a month, every time, it can be used to count time. That is not a small observation. It is the reason the Moon turns up in calendars all over the world, which is where this chapter goes after the explanation.

Why the Daytime Moon Is Not Strange

Meera’s surprise came from a habit rather than from a fact. The Moon rises and sets at its own times, which drift through the day across the month, so a daytime Moon is ordinary rather than remarkable. The next topic works out exactly when and where to expect it.

Not an Eclipse

Her first guess is worth keeping in mind as the thing the phases are not. An eclipse is rare, brief, and not the same event twice a month. A phase cycle is regular, month after month, and nothing is blocking the light.

What to Carry Forward

The bright part grows for a fortnight and shrinks for a fortnight, and the whole cycle takes about a month. Purnima is the full circle and Amavasya the day nothing shows. Krishna Paksha shrinks and Shukla Paksha grows. Gibbous is more than half and crescent is less. And the Moon itself has not changed at all.

Scenario:

A class is asked to draw the Moon every day for a month. One pupil, Ravi, starts on the day after a full Moon and gets a clean run of drawings for a fortnight. A full circle, then shapes that shrink night after night, then a day on which he writes "not visible". After that his page is blank for eleven days, and then there are three drawings of a fat Moon again. He concludes that the Moon disappears for eleven days every month and then comes back nearly full. His teacher asks what time of day he went out to look. And he says he looked at sunrise every single time, as he had been told to at the start.

Analysis:

Ravi’s eleven blank days are an observing error, not a fact about the Moon, and the instruction he followed is where it came from. The watching is meant to begin at sunrise for the first fortnight, because a waning Moon is easiest to find then. And to SWITCH to sunset for the second fortnight, because a waxing Moon is easiest to find at sunset. He kept looking at sunrise, so once the Moon had passed Amavasya it was simply not in the sunrise sky any more. The three fat Moons at the end of his page are the waxing gibbous phase, which had grown large enough to be visible even at the wrong hour. So the cycle in his notebook is correct and complete for half of the month. The bright part shrank from Purnima to Amavasya over a fortnight, which is Krishna Paksha. The missing fortnight is Shukla Paksha, and it was in the evening sky all along.

Activity:

Check a newspaper or a moonrise table for the next ten days and work out which hour you would need to be outside to see the Moon each day.

Title:

Try it at home: draw the Moon for a fortnight

Safety:

Go out with an adult, never look directly at the Sun, and stay where you can be seen from the house.

What You Notice:

Your circles show the bright part shrinking from a full circle to nothing across one fortnight - the waning period, or Krishna Paksha. Your notes should also show the Moon getting closer to the Sun in the sky as the bright part shrinks, which is the clue the next topic picks up.

A daytime Moon is perfectly ordinary. The Moon keeps its own hours of rising and setting, and those hours drift through the day over the course of a month.

Paksha means a fortnight, so naming the two halves of the month Krishna Paksha and Shukla Paksha is simply naming the shrinking half and the growing half.

The best time to start watching the Moon for a month is the morning after a full Moon, because that is the point at which it is easiest to find in the sky.

Waning goes down, waxing goes up — Wane and shrink both have a falling sense; wax is to grow, as in a candle built up of wax. The fortnight that shrinks is Krishna Paksha and the one that grows is Shukla Paksha.

Gibbous is generous — A gibbous Moon gives you more than half of the lit side. A crescent gives you less than half. Both turn up twice in every cycle.

Start From What Does Not Change

The Moon is a sphere, and it stays one. It also makes no light of its own and shines only by reflecting sunlight that falls on it. Hold those two facts still and the explanation of the phases has to come from somewhere else.

Half Lit, Half Dark, Always

Sunlight arrives from one direction, so at any moment the half of the Moon turned towards the Sun is lit and the half turned away is not. That is true every day of the month without exception. The Moon is never half dark because of a shadow; it is half dark because light comes from one side.

The Half That Faces Us

Here is the second fact, and it is the one people miss. The Moon goes round the Earth, and the same half of it always faces us. But the half facing us is not the same as the half that is lit, and the two only line up occasionally.

Putting the Two Together

So there are two halves to keep track of: the lit half, which is set by where the Sun is, and the near half, which is set by where the Moon is in its orbit. We can see only the part that is both lit and facing us. That overlap is what changes through the month.

Full Moon

When the Moon is on the far side of the Earth from the Sun, the half facing us is also the half that is lit. The overlap is complete and we see a full circle. That is Purnima.

New Moon

When the Moon is on the same side as the Sun, the half facing us is the half turned away from the light. The overlap is nothing at all and we see no bright part. That is Amavasya.

Everything In Between

At other positions the overlap is partial. Sometimes more than half of the lit side can be seen, which is the gibbous phase, and sometimes less than half, which is the crescent. The boundary between the lit and unlit parts looks curved rather than straight, and that curve is the giveaway.

Try It With a Ball and a Lamp

The model is easy to build. Push a stick into a small soft ball to make a Moon, stand in a dark room with a lamp or a torch shining from a few metres away to be the Sun, and let your own head be the Earth. Hold the ball out at arm’s length, slightly above your head.

What the Ball Shows

Point the ball towards the lamp and the side facing you is dark. Turn slowly anticlockwise, watching the ball, and the lit part you can see grows, becomes a full circle when the ball is opposite the lamp, and shrinks again. You have just produced every phase, with nothing eclipsing anything.

Eight Positions

Mark the orbit with eight positions and the whole month falls out. At one of them the Moon is opposite the Sun and full. At the one opposite that, it is new. At two of them more than half shows, giving the gibbous phases, and at two others less than half shows, giving the crescents.

Going Round Takes a Month

The Moon travels once round the Earth, from a position back to that same position, in about a month. That is why the phase cycle is a month long. The orbit sets the clock, which is a better way to remember it than the list of shapes.

Why Everyone Sees the Same Phase

The Earth spins once a day and the Moon takes a month to go round, so the Moon’s position barely shifts while the Earth turns. People on opposite sides of the world on the same night therefore see very nearly the same phase, even though they see it at different hours.

Near the Sun, and Far From It

The model also explains something the month of watching showed. At the new Moon the Moon lies in the same direction as the Sun, so it appears closest to the Sun in the sky; at the full Moon it is opposite the Sun and appears farthest from it. The shrinking bright part and the shrinking separation go together.

It Is Not Earth’s Shadow

The commonest wrong explanation is that the Earth’s shadow falls on the Moon. It does not, except rarely. The phases come from the changing relative positions of Sun, the Moon and the Earth while the Moon goes round, and nothing is being blocked.

What Earth’s Shadow Really Does

Earth’s shadow on the Moon gives a lunar eclipse, which can only happen at a full Moon; a solar eclipse can only happen at a new Moon. They do not happen every month because the Moon’s orbit is slightly tilted against Earth’s orbit round the Sun, so the three usually miss the straight line.

Scenario:

A school science fair has two groups demonstrating the phases of the Moon. The first group uses a ball on a stick, a torch and a pupil’s head, and turns the ball slowly round the head. The second group has built a neater exhibit. A large ball for the Earth with a small ball beside it. And a cardboard disc on a wire which they slide between the torch and the small ball to darken part of it. Their poster says "the Earth blocks the sunlight, and the part it blocks is the dark part of the Moon". A judge asks the second group how often their disc passes in front of the small ball in one month, and they say once.

Analysis:

The judge’s question is the one that settles it. The second group has built a model of an eclipse and labelled it a model of the phases. Their own answer gives it away: if the blocking happens once a month, their mechanism predicts one dark event a month rather than a continuous cycle through gibbous, half and crescent shapes. And it predicts a lunar eclipse every month, which does not happen, because the Moon’s orbit is slightly tilted. The first group’s model has no blocker in it at all. The torch lights half the ball at every moment, the pupil’s head sees a different amount of that lit half as the ball goes round. And the lit part visible grows and shrinks smoothly through exactly the shapes the real Moon shows. Both models are useful: one shows why the phases happen and the other shows what an eclipse is. The error is only in the label.

Activity:

Build the ball-and-torch model yourself and try to produce a crescent without letting anything come between the torch and the ball.

Title:

Try it at home: make every phase in a dark room

Safety:

Do this with an adult, keep the lamp away from anything that can catch fire, and do not look straight into the torch.

What You Notice:

Your eight drawings are the eight phases, and you produced them without anything blocking the light at any point. The lamp lit half the ball the whole time; what changed was how much of that lit half was turned towards you. The boundary between lit and unlit looked curved in every drawing, just as it does on the real Moon.

You can produce every phase of the Moon in a dark room with a soft ball on a stick and a torch, and nothing in the model eclipses anything at any point.

Because the Earth spins once a day while the Moon takes a month to go round, two people on opposite sides of the world see nearly the same phase on the same night.

The line dividing the lit and unlit parts of the Moon looks curved rather than straight, which is what you would expect on a sphere and not what a shadow’s edge would give.

Lit half, near half, overlap — Two halves and one question. Which half is lit is set by the Sun; which half faces us is set by the orbit; and what we see is where the two overlap.

Phases every month, eclipses hardly ever — Count the frequency and the two cannot be the same event. A full cycle of phases arrives every month; an eclipse is rare and brief.

The Moon Moves Across the Sky Too

A month of watching turns up a second pattern beside the changing shape. If you look at the same hour every day, the Moon is in another part of the sky altogether each time. The phase tells you the shape; the position tells you where to point your eyes.

Full Moon: Opposite the Sun

At the full Moon the Moon stands nearly opposite the Sun. So as the Sun comes up in the east, the Moon is just going down in the west. The two are as far apart in the sky as they ever get, which is no coincidence - it is the same arrangement that makes the Moon look full.

Closing the Gap

Look again at sunrise on the following mornings. The bright part is shrinking, and the Moon has moved nearer the Sun in the sky. The two changes travel together, because both of them follow from the Moon’s position in its orbit.

Overhead at Sunrise

Keep going. When the bright part has shrunk to a half circle, the Moon is directly overhead at sunrise. Some days after that, with only a crescent left, it is closer still to the Sun - low in the east, not far ahead of sunrise.

So You Can Predict Where to Look

That makes the phase useful rather than merely pretty. A waning Moon is easiest at sunrise; a waxing one at sunset. Knowing the shape and which way it is going tells you both where to look and when.

The Moon Keeps Its Own Hours

One consequence worth stating plainly: the Moon does not rise when the Sun sets. It rises and sets at times of its own, which drift steadily, so any rule tying moonrise to sunset is wrong.

Fifty Minutes Later Each Day

The drift is measurable. Moonrise comes about fifty minutes later every day. Over a fortnight that adds up to many hours, which is why moonrise sometimes falls in the afternoon, between about two and four o’clock, and the Moon can be spotted in the eastern sky in daylight.

Where to Check

Moonrise times are published - in local newspapers, and by the Positional Astronomy Centre of the India Meteorological Department. Looking them up for several days running is the quickest way to see the fifty-minute shift for yourself. Allow about half an hour after the listed time for the Moon to rise clear of buildings to see.

Why Fifty Minutes

Here is the reason. The Earth turns once on its axis in twenty-four hours, and in that same twenty-four hours the Moon has moved a little further along its orbit. So when the Earth has completed its turn, the Moon is no longer where it was; the Earth has to turn a bit more to bring it back overhead. That extra bit of turning takes about fifty minutes.

From Patterns to Units

Now change the question. Instead of asking where the Moon will be, ask how we came to measure time at all. Every unit we use rests on something in the sky that repeats.

The Day

The Sun seems to come up in the east and set in the west and rise again, and that apparent motion comes from the Earth turning on its own axis. That cycle is the foundation of the day. Measured properly, the average time from the Sun’s highest point one day to its highest point the next is twenty-four hours, and it is called the mean solar day.

Finding the Sun’s Highest Point

You do not need a clock on the Sun to find it; you need a shadow. The shadow of an upright object shrinks to its shortest with the Sun at its highest. Fix a metre stick upright, mark the tip of its shadow every minute through the middle of the day, and the shortest mark gives you the moment.

Repeat It and You Have Measured a Day

Do that on two days in a row and the gap between the two shortest-shadow moments is one solar day. Do it over several days and the average comes out very close to twenty-four hours. That is the whole of it - a stick, a pencil and some patience.

The Month

The next cycle up is the Moon’s. It needs some 29.5 days, which is nearly a month, to run through all its phases, and that cycle is the basis of the month as a unit of time. Which is why this chapter spent two topics on the phases before arriving at calendars.

The Year

The largest of the three comes from the seasons. The Earth needs about 365 and a quarter days to travel once round the Sun, and in that time it goes through one full cycle of seasons. That cycle defines the solar year. Day, month, year: a spin, an orbit and an orbit, each of them a periodic event in the sky.

Scenario:

A school plans a sky-watching evening and tells families to gather at sunset, promising a bright Moon rising in the east as the Sun goes down. The teacher picks the date from the calendar because it is a Saturday, and checks only that the Moon will be a few days past full. On the night, the sky is clear, the Sun sets, and no Moon appears. Parents begin to leave. One pupil looks up the moonrise time on her phone and finds it listed for twenty to ten at night, almost three hours after sunset.

Analysis:

The promise was the error, not the weather. Moonrise comes about fifty minutes later every day. So a Moon that rose at sunset on the full Moon night rises nearly three hours after sunset three days later - which is exactly the gap the pupil found. The teacher also had the phase working against the plan in a second way. A few days past full is a WANING Moon, and a waning Moon is easiest to spot at SUNRISE, not at sunset, because it is drawing nearer to the Sun in the morning sky. Two fixes were available and both were cheap. The evening could have been held a few days BEFORE the full Moon, when the waxing Moon is already up as the Sun goes down. Or the gathering could have been held at dawn for the waning Moon. Looking up a published moonrise time, from a newspaper or the Positional Astronomy Centre, would have settled it in a minute.

Activity:

Find the moonrise time for the next five days and work out which evening would suit a sky-watching event.

Title:

Try it at home: measure a day with a stick

Safety:

Do not look at the Sun at any point, wear a hat, and take the stick out of the ground when you have finished.

What You Notice:

The shortest shadow marks the moment the Sun was highest in the sky, and the gap between one such moment and the next is one solar day. Averaged over a few days it comes out very close to twenty-four hours, which is the mean solar day. And you will have measured it with a stick and a pencil.

Moonrise sometimes falls in the middle of the afternoon, between about two and four o’clock, which is one of the ways a Moon ends up visible in broad daylight.

You should allow about half an hour after the listed moonrise time before expecting to see the Moon, because it needs to climb clear of buildings and trees first.

Moonrise times for your area are published in local newspapers and by the Positional Astronomy Centre of the India Meteorological Department.

Waxing at sunset, waning at sunrise — The growing Moon is easiest to find in the evening sky and the shrinking Moon in the morning sky. Knowing the phase tells you which end of the day to go out.

Spin, orbit, orbit — The day comes from the Earth spinning, the month from the Moon orbiting the Earth, and the year from the Earth orbiting the Sun. Three units, three motions.

Twelve Moons in a Year of Seasons

Ancient sky-watchers noticed something convenient: about twelve cycles of the Moon’s phases fit inside one cycle of the seasons. That observation is where calendars begin. Take the day as the smallest unit, a month of about 29.5 days above it, and a year of twelve such months, and you have a working calendar built entirely on the Moon.

And It Works, Up to a Point

A lunar calendar is easy to keep and perfectly sound for counting the passage of time. Anyone can check the date by looking up. The trouble only appears when you ask it to tell you about the seasons.

Where the Lunar Calendar Drifts

Twelve lunar months come to 354 days, and the seasons come back in about 365. So each year the calendar runs eleven days ahead of the seasons, and a month that fell in the cold season will drift into the hot one over the years. The dates stay honest about the Moon and stop being honest about the weather.

Why That Mattered

Farming is the reason. Knowing when a season will arrive decides when to sow, and a calendar that slides eleven days a year is no help at all. The need for a year that keeps step with the seasons is what produced the solar calendars.

The Solar Calendar

A solar calendar fixes the year to the cycle of seasons instead of to the Moon. The Gregorian calendar, which most of the world uses today, is one of these. Its months are adjusted so that they add up to 365 days, which is why some run to 30 days, others to 31, while February only 28.

The Leftover Quarter Day

The Earth does not take a whole number of days to go round the Sun; it takes nearly 365 and a quarter. Those extra quarters add up to about one whole day every four years, so solar calendars insert an extra day - a leap day - every fourth year. In the Gregorian calendar a year divisible by four gets one, and February then has 29 days.

The Correction to the Correction

A quarter is itself slightly too much, so adding a day every four years overshoots a little. The fix is to skip the leap year every hundred years - 1700, 1800 and 1900 had none. But skipping all of them would undershoot, so every four hundred years the leap year is put back, which is why 1600 and 2000 were leap years after all.

Two Kinds of Year

Astronomers distinguish two. The tropical year is the time from a spring equinox round to the next, and the Gregorian calendar is built on it. The sidereal year is the time until the same stars rise at sunset again. The sidereal year is longer, by only about twenty minutes, so the two take a long while to disagree noticeably.

Reading the Year From the Horizon

Ancient observers in India had neither the knowledge that the Earth goes round the Sun nor modern instruments, and still arrived at a year of about 365 days, by watching patiently. One of the things they watched was where on the horizon the Sun came up.

Uttarayan and Dakshinayan

The rising point of the Sun is not fixed due east. Through the summer it comes up a little to the north of east, and through the winter a little to the south, and the extremes fall on the solstices, around 21 June and 21 December. The apparent northward journey running from December to June, is named Uttarayan and the southward journey from June to December Dakshinayan. The Taittiriya Samhita records the six-months-each pattern, and the Surya Siddhanta notes which star pattern lay behind the Sun at the winter solstice in those times.

The Luni-Solar Compromise

There is a third kind of calendar, and it tries to have both. A luni-solar calendar counts days and months by the Moon’s phases, as a lunar one does, but then adjusts itself to stay in step with the seasons.

The Extra Month

The adjustment is arithmetic. Twelve lunar months fall about eleven days short of the solar year, so every two or three years the shortfall has grown to nearly a whole month. At that point an extra month is inserted - called Adhika Maasa, or an intercalary month - and the calendar is back in step. Many Indian calendars work this way.

Amant and Purnimant

The Indian luni-solar month names will be familiar: Chaitra and Vaisakha; then Jyeshtha, Ashadha, Shravana and Bhadrapada; then Ashwin, Kartika and Margashirsha; and last Pausha, Magha and Phalguna. Where a month begins differs by region. In an Amant calendar it starts the day following the new Moon and closes on a new Moon; in a Purnimant calendar it starts after the full Moon and ends on a full Moon.

The Indian National Calendar

India also has a national calendar, used beside the Gregorian one for official purposes. It is solar, with 365 days. Its year opens on 22 March, the day after the spring equinox, and its months - named from the traditional calendars - have either 30 or 31 days: in an ordinary year the months from the second to the sixth have 31 and the rest 30. In a leap year an extra day goes to Chaitra, the first month, and the year then opens on 21 March.

How It Came About

A Calendar Reform Committee was set up by the government in 1952 to examine the calendars then in use and recommend one accurate, uniform calendar for the whole country. Its unified national calendar came into use on 21 March 1956, which is 1 Chaitra 1878 of the Saka era, and it follows the general principles of the Surya Siddhanta. The committee was chaired by Meghnad Saha, the astrophysicist who studied the temperatures of stars and gave his name to the Saha equation and to the Kolkata institute of nuclear physics that carries his name.

Scenario:

A village keeps a harvest festival on a fixed day of a purely lunar calendar, counted from new Moon to new Moon, twelve months to the year. Three generations ago the festival fell just as the crop came in. The oldest villagers say it used to be a dry, bright day. It now falls in the middle of the monsoon, and the committee is arguing about why. One member says the monsoon itself must have shifted. Another says the calendar must have been miscounted somewhere. A schoolteacher is asked to work out which.

Analysis:

Neither explanation is needed, because the arithmetic of the calendar accounts for it by itself. Twelve lunar months come to 354 days and the seasons return in about 365. So a purely lunar date runs about eleven days ahead of the seasons every year. Over thirty years that is roughly 330 days - nearly a full year. And over three generations the festival will have travelled right round the seasons and begun again. So the monsoon has not moved and nobody has miscounted; the calendar is doing exactly what a lunar calendar does. It is still perfectly accurate about the Moon: the festival falls on the same phase every year, which was the point of fixing it that way. What it cannot do is predict a season, and that is precisely why solar and luni-solar calendars were devised. A luni-solar calendar would keep the lunar date and insert an Adhika Maasa every two or three years, so the festival would stay near the harvest.

Activity:

Work out how many days a purely lunar date drifts in ten years, and how many years it takes to go right round the seasons.

Title:

Try it at home: track where the Sun rises

Safety:

Never look directly at the Sun - glance at the horizon as it first appears and look away - and go out with an adult.

What You Notice:

The arrows do not sit on top of one another: the sunrise point creeps along the horizon week by week. Between December and June it moves northward, which is Uttarayan, and between June and December southward, which is Dakshinayan. The extremes fall at the solstices, around 21 June and 21 December. And the Sun rises exactly in the east on the equinoxes - which is how the length of the year was measured long before anyone had an instrument.

1900 was not a leap year and 2000 was, because leap years are skipped every hundred years and then restored every four hundred.

The sidereal year exceeds the tropical year by only about twenty minutes, so the two take a very long time to drift noticeably apart.

Meghnad Saha, who chaired the Calendar Reform Committee, was an astrophysicist best known for studying the temperatures of stars and for the equation that bears his name.

354, 365, and eleven short — Twelve lunar months make 354 days and the seasons take about 365. The eleven-day gap is the whole reason the other two kinds of calendar exist.

Uttar is north, Dakshin is south — Uttarayan is the Sun’s apparent northward journey from December to June, and Dakshinayan the southward one from June to December. The names say the direction.

Why Festival Dates Move

Most festivals in India are set by the phases of the Moon, which means they are fixed by a lunar or a luni-solar calendar rather than by the Gregorian one. Their dates in the Gregorian calendar therefore change from year to year - not because anyone shifts them, but because two different calendars are being read at once.

Five Examples

Diwali is kept at the new Moon of Kartika. Holi falls on the full Moon of Phalguna, and Buddha Purnima at the Vaisakha full Moon. Dussehra is kept on the tenth day of Ashwina. Eid-ul-Fitr is celebrated after the crescent Moon is sighted at the end of Ramazan.

Why Some Shift a Little and Some a Lot

The size of the shift tells you which kind of calendar is behind a festival. A luni-solar calendar inserts an extra month every few years, which corrects for the gap between the lunar year and the solar one, so its festivals move about within a window of less than a month.

And the Lunar Ones Travel Right Round

A purely lunar calendar makes no such correction. A festival fixed by one, such as Eid-ul-Fitr, therefore drifts steadily and can fall in a different Gregorian month from one year to the next - which over enough years takes it right round the seasons.

The Festivals That Hardly Move

A few Indian festivals barely shift at all: Pongal, Puthandu, Bihu, Poila Baisakh, Vaisakhi and Makar Sankranti. These follow a solar sidereal calendar, and because the Gregorian calendar is solar too, the two keep close company and the dates stay nearly fixed.

Even Those Creep

Long ago these festivals were tied to a solstice or an equinox. The sidereal year is slightly longer than the tropical year the Gregorian calendar uses, so their dates creep away from the solstices and equinoxes very slowly. The cause is a slow wobble of the Earth’s axis, rather like the axis of a spinning top that is beginning to wobble.

One Day in Seventy-One Years

The rate is small enough to be worth stating: Makar Sankranti moves ahead by about one day every seventy-one years. Nobody notices it in a lifetime, and over centuries it adds up.

Why Even One Year Can Have Two Dates

Many festival dates depend on the exact phase of the Moon at sunrise. Sunrise comes earlier in the east of India and later in the west, so the same festival can fall on different days in different parts of the country in the same year.

The Rashtriya Panchang

To keep one date for the whole country, the Positional Astronomy Centre of the Government of India publishes the Rashtriya Panchang every year. It is a careful working-out of where to find the Sun, the Moon and other bodies for one central location in India, and the festival dates it gives are used by the government to declare holidays in advance.

From Natural to Artificial

The Moon is Earth’s natural satellite: a body that orbits our planet. It is not the only thing up there any more. Many countries have put artificial satellites into orbit, and on a clear evening they appear as tiny specks of light moving steadily across the sky.

Eight Hundred Kilometres, A Hundred Minutes

Most artificial satellites orbit about 800 kilometres above the surface and take roughly a hundred minutes to go once round. That is a useful pair of figures to hold: far above the air we breathe, and round the Earth about fourteen times while we sleep once.

What They Are For

Five jobs between them: weather monitoring, scientific research, navigation, disaster management and communication. The Indian Space Research Organisation has launched many satellites that do this work, so the list is not abstract.

Cartosat, Bhuvan and AstroSat

The Cartosat satellites take high-quality pictures of the Earth, which are used to handle natural disasters, plan cities and improve maps. The mapping platform Bhuvan uses those images to show land use, soil, terrain and vegetation. AstroSat does something different - it observes stars and other bodies.

India Beyond Orbit

India has also sent missions further out: Aditya L1 to the Sun, Mangalyaan to Mars, and the three Chandrayaan missions to the Moon. ISRO also allows students in India to build and launch small satellites, among them AzaadiSat, InspireSat-1 and Jugnu.

The Problem Left Behind

When a satellite’s working life ends, it and its rocket parts stay in orbit as space junk. The debris crowds space and could strike a working satellite. Small pieces burn up in the atmosphere on the way down, but larger ones can reach the ground, and countries are now working together to clear it. The first Indian satellites were pioneered by Vikram Sarabhai, called the father of India’s space programme, after whom the Vikram Sarabhai Space Centre in Thiruvananthapuram is named.

Scenario:

A district office prints a wall calendar each year and marks the holidays on it. The clerk who prepares it notices three things while comparing this year’s print with the one from five years ago. Makar Sankranti is on almost the same date in both. Diwali has moved by about three weeks. And a festival that was in April five years ago is now in March. He concludes that the printers have made a mistake with the third one, since a festival cannot change its month. He also asks why the office cannot simply fix the dates itself and save the trouble.

Analysis:

All three observations are correct and none is a misprint. The three festivals are simply on three different kinds of calendar. Makar Sankranti follows a solar sidereal calendar. And because the Gregorian calendar is solar too the two agree closely - it creeps by about one day every seventy-one years, which will not show across five. Diwali is fixed to the new Moon of Kartika on a luni-solar calendar, which inserts an extra month every two or three years to correct the gap to the solar year. So its Gregorian date moves about inside a window of less than a month - three weeks fits that exactly. The third festival must be on a purely lunar calendar, which makes no such correction, so it drifts about eleven days every year and does change its Gregorian month. As for fixing the dates locally. It cannot be done, because many dates depend on the exact phase of the Moon at sunrise and sunrise comes earlier in eastern India. That is why the Positional Astronomy Centre publishes the Rashtriya Panchang for one central location, and the government declares holidays from it.

Activity:

Compare this year’s and last year’s calendars and sort five festivals by how far each has moved.

Title:

Try it at home: spot a satellite after sunset

Safety:

Go with an adult, stay in a safe place you know, and do not use binoculars anywhere near the Sun.

What You Notice:

A satellite crosses the sky in a few minutes in a straight, steady line, which is what tells it apart from an aircraft or a star. The reason you see it just after sunset or before sunrise is that it is still catching sunlight 800 kilometres up while the ground below you is already dark. And at that height it is going round the Earth in about a hundred minutes.

Makar Sankranti moves ahead by about one day every seventy-one years, which is slow enough that nobody notices it within a single lifetime.

ISRO allows students in India to build and launch small satellites, among them AzaadiSat, InspireSat-1 and Jugnu.

The same festival can fall on different days in eastern and western India in one year, because the date depends on the exact phase of the Moon at sunrise and sunrise comes earlier in the east.

Luni-solar wobbles, lunar wanders — A luni-solar festival moves inside a window of less than a month, because an extra month is added every few years. A purely lunar one drifts right through the Gregorian months.

Eight hundred up, a hundred round — Most artificial satellites orbit about 800 kilometres above the surface and take roughly a hundred minutes to go once round the Earth.