Overview
This chapter places the earth where it belongs, as one planet among eight going round an ordinary star at the edge of a galaxy. It begins with the universe, the galaxies and the solar system, describing the sun and the planets in their order, the difference between the inner rocky planets and the outer gas giants, and the smaller members of the family such as satellites, asteroids, comets and meteors. It then turns to the earth itself and asks the oldest question of geography: what is its shape? The chapter reviews the ancient beliefs of a flat earth, the reasoning of the Greeks, the voyages that went round the world, the evidence of ships on the horizon, the round shadow on the moon during a lunar eclipse, the changing altitude of the Pole Star and the photographs taken from space, and arrives at the modern answer that the earth is an oblate spheroid, flattened at the poles and bulging at the equator, and in fine detail a geoid, a shape of its own. The size of the earth, its equatorial and polar diameters, its circumference and Eratosthenes' first measurement follow. The chapter ends by explaining why the earth alone among the planets carries life, through its distance from the sun, its atmosphere, water and magnetic field. It matters because everything else in geography rests on this foundation.
Learning Objectives
- Describe the universe, the Milky Way galaxy and the position of the solar system within it.
- Name the members of the solar system in order and distinguish the inner and outer planets.
- Trace the history of ideas about the shape of the earth from the flat earth to the geoid.
- State and explain the evidence that proves the earth is spherical.
- Explain why the earth is called an oblate spheroid and a geoid rather than a perfect sphere.
- State the dimensions of the earth and describe how Eratosthenes measured its circumference.
- Explain the conditions that make the earth the only planet known to support life.
- Describe the moon as the earth's satellite and its relationship with the earth.
Topics in this chapter
12 topics · tap a topic title to jump straight to it.
The universe and the galaxies
Everything that exists — all matter, all energy, all space and all time — is the universe. It is unimaginably large: light, travelling at about 3 lakh kilometres every second, takes more than 13,000 crore years to cross the part of it we can observe. Within this vastness matter is not spread evenly but gathered into enormous islands of stars called galaxies, each holding thousands of crores of stars bound together by gravity, with gas and dust between them. There are perhaps 200,000 crore galaxies in the observable universe.
The origin of the universe. The accepted scientific account is the Big Bang theory, proposed by Georges Lemaître in 1927 and supported by Edwin Hubble's discovery in 1929 that all galaxies are moving away from one another, so that the universe is expanding. About 1,380 crore (13.8 billion) years ago the entire universe was concentrated in a point of unimaginable density and temperature; it expanded suddenly and has been expanding and cooling ever since. Within the first minutes the lightest elements, hydrogen and helium, formed; after some crores of years the gas gathered under gravity into the first stars and galaxies. Heavier elements such as carbon, oxygen and iron — the stuff of planets and of our bodies — were made inside stars and scattered when the stars exploded. The faint glow of the Big Bang, the cosmic microwave background radiation, was detected in 1965 and is its strongest proof.
Our galaxy, the Milky Way. The sun belongs to a spiral galaxy called the Milky Way or Akash Ganga, which appears on a clear dark night as a hazy band of light across the sky — the light of thousands of crores of distant stars in the plane of the galaxy. The Milky Way is a flattened disc about one lakh light years across and about 1,000 light years thick, with a bulge at the centre and spiral arms winding outward. It contains 10,000 to 40,000 crore stars. The sun lies in one of the spiral arms (the Orion arm) about 26,000 light years from the centre, and it goes round the centre once in about 22.5 crore years at a speed of about 220 km per second. Our nearest neighbour galaxy of similar size is Andromeda, 25 lakh light years away, visible to the naked eye as a faint smudge.
Units of distance. Because the distances are so great, astronomers use the light year, the distance light travels in one year, about 9.46 lakh crore kilometres (9.46 × 1012 km), and for the solar system the astronomical unit, the average distance between the earth and the sun, about 15 crore kilometres. The nearest star after the sun, Proxima Centauri, is 4.2 light years away; its light left it four years before we see it.
Stars. A star is a huge ball of hot gas, mainly hydrogen, which shines by nuclear fusion in its core, where hydrogen is converted into helium with the release of enormous energy. Stars are born in clouds of gas and dust called nebulae, live for crores or thousands of crores of years, and die as white dwarfs, neutron stars or black holes according to their mass. Groups of stars that seem to form patterns are called constellations: Ursa Major (Saptarshi), Orion (Kalpurush), Scorpius; the Pole Star (Dhruva tara) stands almost exactly above the north pole of the earth and has guided travellers for thousands of years.
- Light from the sun takes about 8 minutes 20 seconds to reach the earth; from Proxima Centauri 4.2 years; from the Andromeda galaxy 25 lakh years — when we look at Andromeda we see it as it was before humans existed.
- The Milky Way is about 1,00,000 light years across; if it were shrunk to the size of India, the solar system would be smaller than a coin.
- Hubble found in 1929 that the farther a galaxy is, the faster it moves away from us — the observation that led to the Big Bang theory of an expanding universe.
- 1 light year = distance light travels in one year ≈ 9.46 × 10¹² km; 1 astronomical unit (AU) ≈ 15 crore km (149.6 million km).
- Age of the universe ≈ 1,380 crore (13.8 billion) years; age of the solar system ≈ 460 crore (4.6 billion) years.
The solar system: the sun and its family
The solar system is the family of the sun: the eight planets, their satellites, the dwarf planets, and the crores of asteroids, comets and meteoroids that all revolve round the sun under its gravity. It formed about 460 crore years ago, according to the nebular hypothesis first suggested by Kant and Laplace, from a rotating cloud of gas and dust; the centre collapsed into the sun and the surrounding disc gathered into planets.
The sun. The sun is a medium-sized yellow star, a ball of glowing gas — about 71 per cent hydrogen and 27 per cent helium — with a diameter of about 13.9 lakh km, 109 times that of the earth, and a mass 3.3 lakh times the earth's, holding 99.8 per cent of all the mass in the solar system. Its surface temperature is about 5,500 °C and its core about 1.5 crore °C, where hydrogen fuses into helium and releases the energy that reaches us as light and heat. The visible surface is the photosphere; above it lie the chromosphere and the corona, seen during a total eclipse. Dark, cooler patches called sunspots come and go in an 11-year cycle. The sun rotates once in about 25 days at its equator. Its light takes 8 minutes 20 seconds to reach the earth, 15 crore km away.
The planets. A planet is a body that revolves round the sun, is large enough for its gravity to make it round, and has cleared its orbit of other objects. There are eight, in order from the sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune — remembered by the phrase My Very Educated Mother Just Served Us Noodles. They all revolve in the same direction, anticlockwise seen from above the north pole, in nearly circular orbits that lie almost in one plane, the ecliptic. Pluto, counted as the ninth planet from 1930, was reclassified in 2006 as a dwarf planet because it has not cleared its orbit; Ceres in the asteroid belt, Eris, Haumea and Makemake are other dwarf planets.
Two groups. The four inner or terrestrial planets — Mercury, Venus, Earth, Mars — are small, dense and rocky, with solid surfaces, few or no satellites and thin or no rings. They lie within 23 crore km of the sun. The four outer or Jovian planets — Jupiter, Saturn, Uranus, Neptune — are giants made mostly of hydrogen, helium, methane and ammonia, with no solid surface, many satellites and rings, and they lie far out beyond the asteroid belt. Between the two groups, between Mars and Jupiter, lies the asteroid belt of rocky fragments that never formed a planet.
Other members. Satellites or moons revolve round planets; the earth has one, Mars two, Jupiter more than 90, Saturn more than 140. Comets are balls of ice and dust from the outer solar system that grow a glowing tail pointing away from the sun as they approach it; Halley's comet returns every 76 years, last in 1986. Meteoroids are small rocks; when they enter the atmosphere and burn they are seen as meteors or shooting stars, and any piece that reaches the ground is a meteorite, such as the one that made the Lonar crater in Maharashtra. Beyond Neptune lie the Kuiper belt of icy bodies and, far beyond, the Oort cloud from which comets come.
- The sun's diameter, 13.9 lakh km, is 109 times the earth's; about 13 lakh earths would fit inside it, and it holds 99.8 per cent of the mass of the solar system.
- Order of planets: Mercury, Venus, Earth, Mars (rocky), asteroid belt, Jupiter, Saturn, Uranus, Neptune (gas giants); Pluto has been a dwarf planet since 2006.
- Halley's comet, seen in 1910 and 1986, will return in 2061; its tail always points away from the sun because the solar wind pushes the gas and dust outward.
- Members of the solar system: Sun + 8 planets + their satellites + 5 dwarf planets + asteroids + comets + meteoroids.
- Inner planets (Mercury, Venus, Earth, Mars): small, rocky, dense, few moons. Outer planets (Jupiter, Saturn, Uranus, Neptune): large, gaseous, light, many moons, rings.
The planets one by one
Each planet has a character of its own, and the examination often asks for their special features.
Mercury is the nearest to the sun (5.8 crore km) and the smallest planet, only slightly larger than our moon, with a diameter of 4,880 km. It has almost no atmosphere, so its day side reaches 430 °C and its night side falls to −180 °C. It goes round the sun fastest, in 88 days, but rotates slowly, once in 59 days. It has no satellite and its surface is cratered like the moon.
Venus, the second planet, is nearly the earth's twin in size (12,104 km) and mass, and is the brightest object in the sky after the sun and moon — the morning star and the evening star (Shukra). It is wrapped in thick clouds of carbon dioxide and sulphuric acid that trap heat in a runaway greenhouse effect, making it the hottest planet at about 465 °C, hotter than Mercury. It rotates backward (clockwise) and so slowly, in 243 days, that its day is longer than its year of 225 days. It has no satellite.
Earth, the third planet at about 15 crore km, is the largest of the inner planets (12,756 km), the only one with liquid water on its surface, an oxygen-rich atmosphere and life. Seen from space it is the blue planet, because 71 per cent of its surface is ocean. It rotates in 24 hours, revolves in 365¼ days and has one satellite, the moon.
Mars, the fourth planet, is the red planet (Mangal), its colour due to iron oxide in its soil. It is half the earth's size (6,792 km), has a thin carbon dioxide atmosphere, polar ice caps that grow and shrink with the seasons, the largest volcano in the solar system (Olympus Mons, 22 km high) and a great canyon, Valles Marineris. Its day is 24½ hours, its year 687 days, and it has two tiny moons, Phobos and Deimos. Dry river beds show that water once flowed on it, and it is the planet most explored by spacecraft; India's Mangalyaan reached its orbit in 2014.
Jupiter is the largest planet (Brihaspati), with a diameter of 1,42,984 km, eleven times the earth's, and a mass two and a half times all the other planets together. It is a ball of hydrogen and helium with bands of coloured cloud and the Great Red Spot, a storm larger than the earth that has raged for at least 300 years. It rotates fastest of all, in under 10 hours, and takes 12 years to go round the sun. It has more than 90 moons; the four big ones — Io, Europa, Ganymede, Callisto — were discovered by Galileo in 1610, and Ganymede is the largest moon in the solar system.
Saturn (Shani), the second largest (1,20,536 km), is famous for its bright rings of ice and rock, 2.8 lakh km across but only about a kilometre thick. It is the least dense planet — it would float on water. Its year is 29½ years, its day 10½ hours, and it has more than 140 moons; Titan, the largest, has a thick atmosphere.
Uranus, discovered by William Herschel in 1781, is a blue-green ice giant (51,118 km) that rotates on its side, its axis tilted 98°, so that it rolls along its orbit; its year is 84 years. It has faint rings and 27 known moons.
Neptune, the outermost planet, was found in 1846 by calculation before it was seen. It is deep blue, with the fastest winds in the solar system (2,000 km per hour), a diameter of 49,528 km, a year of 165 years and 14 moons, of which Triton orbits backward. It lies about 450 crore km from the sun, and sunlight takes over four hours to reach it.
- Venus is hotter (465 °C) than Mercury although it is farther from the sun, because its thick carbon dioxide atmosphere traps heat — the runaway greenhouse effect.
- Jupiter is so large that 1,300 earths would fit inside it, and its Great Red Spot alone is wider than the earth.
- Mars has seasons and polar ice caps like the earth, a day of 24½ hours, and Olympus Mons, a volcano 22 km high — two and a half times the height of Everest.
- Diameters (km): Mercury 4,880; Venus 12,104; Earth 12,756; Mars 6,792; Jupiter 1,42,984; Saturn 1,20,536; Uranus 51,118; Neptune 49,528.
- Periods of revolution: Mercury 88 days; Venus 225 days; Earth 365¼ days; Mars 687 days; Jupiter 12 years; Saturn 29½ years; Uranus 84 years; Neptune 165 years.
Early ideas about the shape of the earth
To someone standing in a field the earth looks flat, and for most of human history people believed it was. The earliest civilisations pictured it as a flat disc or square floating on water and covered by the dome of the sky. The Babylonians drew the world as a flat circle surrounded by a river; the ancient Egyptians thought of it as a flat plate; in Indian mythology the earth rested on the backs of elephants standing on a tortoise; the Norse peoples imagined a flat disc with a great tree at its centre; and the Chinese thought of a square earth under a round heaven. Sailors feared that a ship going too far would fall off the edge.
The Greek revolution. The Greeks were the first to argue from observation that the earth is a sphere. Pythagoras (about 500 BCE) is credited with suggesting a spherical earth, perhaps because the sphere was thought the perfect shape. Aristotle (about 350 BCE) gave the first real proofs: the earth's shadow on the moon during a lunar eclipse is always circular, and only a sphere throws a circular shadow in every position; travellers going south see new stars rise above the horizon and familiar ones sink, which could not happen on a flat earth; and elephants were found both in India in the east and in Africa in the west, so, he reasoned, the two must be closer round the back than the flat map suggested. Eratosthenes (about 240 BCE), librarian at Alexandria, not only accepted the sphere but measured its circumference, a story told in a later topic. Ptolemy (about 150 CE) built his geography and his star maps on a spherical earth, and his book passed to the Arabs and back to medieval Europe.
India. The astronomer Aryabhata (476–550 CE) stated in his Aryabhatiya that the earth is a sphere that rotates on its axis, and that the apparent movement of the stars is caused by this rotation — a thousand years before Copernicus. Varahamihira and Brahmagupta in the sixth and seventh centuries also held the earth to be round, and Brahmagupta described gravity as an attraction towards the earth's centre.
The Middle Ages and after. Arab geographers such as Al-Biruni, who visited India in the eleventh century and computed the earth's radius from the dip of the horizon seen from a mountain, kept the knowledge alive. In Europe, though educated people knew the earth was round, the idea was not proved by experience until Magellan's expedition (1519–1522) sailed westward from Spain and returned from the east, going right round the earth. Since then no serious doubt has remained, and in the twentieth century photographs from rockets and satellites, and the sight of the whole blue globe from the moon in 1968, made the sphere visible to all.
The story shows how science works: an idea from reasoning (Pythagoras), tested by observation (Aristotle), measured (Eratosthenes), confirmed by experience (Magellan) and finally seen directly (space photographs). The next topic sets out the evidence in order.
- In Indian mythology the flat earth rested on four elephants standing on a tortoise; in Babylon it was a disc floating on the ocean; in China a square under a round sky.
- Aristotle argued in about 350 BCE that the earth must be a sphere because its shadow on the moon in every lunar eclipse is a circle, and because new stars appear as one travels south.
- Aryabhata wrote in 499 CE that the earth is a sphere spinning on its axis, so that the stars only appear to move, as trees on the bank seem to move to a person in a boat.
Evidence for the spherical shape of the earth
The following proofs, taken together, leave no doubt that the earth is round like a ball and not flat.
1. Circumnavigation. Magellan's ships sailed west from Spain in 1519 and, after his death in the Philippines, Elcano brought the Victoria home from the east in 1522: they had gone right round the world. Since then countless ships, aircraft and satellites have done the same. On a flat earth a traveller going always in one direction would reach an edge; on a sphere he returns to where he started.
2. Ships on the horizon. When a ship sails away from a port it does not simply grow smaller; first the hull disappears, then the deck, then the funnel and finally the mast top, as if it were going down a hill. A ship approaching appears mast first. This can only happen if the surface of the sea curves away from the observer. On a flat sea the whole ship would shrink evenly and vanish as a dot.
3. The lunar eclipse. A lunar eclipse occurs when the earth comes between the sun and the moon and its shadow falls on the moon. The edge of the shadow is always an arc of a circle, whatever the position of the earth. Only a sphere throws a circular shadow from every direction; a flat disc would sometimes throw an oval or a line.
4. The rising and setting of the sun at different times. When it is sunrise in Kolkata it is still night in Mumbai and midday in Japan; the sun rises about four minutes earlier for every degree of longitude one goes east. On a flat earth the sun would rise and set for everyone at the same moment. The time difference across the earth is explained only by a curved surface turning on its axis.
5. The altitude of the Pole Star. The Pole Star stands above the north pole. At the equator it is seen on the horizon; as one travels north it rises higher in the sky, and at the north pole it is overhead; south of the equator it cannot be seen at all. The angle of the Pole Star above the horizon equals the observer's latitude, which is possible only on a sphere.
6. The circular horizon. From a ship at sea or a high tower the horizon is always a circle, and it widens as one climbs higher: from a height of 10 m the horizon is about 11 km away, from 100 m about 36 km. On a flat earth the horizon would be the same from every height, and only a sphere shows a circular edge in every direction.
7. Sunrise seen first from a height. The top of a tall building or a mountain peak catches the first rays of the rising sun before the plain below, and keeps the last rays of the setting sun. This is because the curved surface hides the sun from the lower ground first.
8. Aerial and space photographs. The most direct proof: photographs from high-flying aircraft show the curve of the horizon, and photographs from satellites and from the Apollo spacecraft of 1968–72 show the whole earth as a blue ball.
9. Analogy with other heavenly bodies. The sun, the moon and all the planets seen through a telescope are spheres; it would be strange if the earth alone were flat.
10. Surveying and the Bedford Level. Surveyors find that the surface falls away from a straight line of sight by about 8 cm in the first kilometre and four times that in two kilometres; long bridges and canals must be built with this curvature allowed for.
- A ship leaving Haldia is seen from the shore to lose its hull first and its mast last — because the sea surface curves down and away from the observer.
- In every lunar eclipse the edge of the earth's shadow on the moon is a circular arc; a flat earth turned edge-on would throw a straight-line shadow, which has never been seen.
- The Pole Star is 22° above the horizon at Kolkata (22° N), 28° at Delhi (28° N) and on the horizon at Singapore (1° N); the angle equals the latitude, which only a sphere allows.
- Altitude of the Pole Star above the horizon = latitude of the observer (northern hemisphere).
- Distance to the horizon (km) ≈ 3.57 × √(height in metres): from 10 m ≈ 11 km, from 100 m ≈ 36 km.
The true shape: oblate spheroid and geoid
The earth is round, but it is not a perfect sphere. Careful measurement shows two departures from the sphere, and the chapter gives the earth two more exact names.
Oblate spheroid. Because the earth spins on its axis once a day, every part of it is pulled outward by the centrifugal effect of the rotation, and the pull is greatest at the equator, where the speed of rotation is highest (about 1,670 km per hour), and zero at the poles. Over the ages this has made the earth bulge at the equator and flatten at the poles. Isaac Newton predicted this in 1687 from his theory of gravitation, and the French Academy sent expeditions in 1735 to Lapland near the Arctic and to Peru near the equator to measure a degree of latitude at each; the degree was longer near the pole, proving that the earth is flattened there. Such a shape, a sphere slightly squashed along its axis, is an oblate spheroid or oblate ellipsoid. The figures are: equatorial diameter 12,756 km, polar diameter 12,714 km, a difference of about 42 km. The equatorial circumference is 40,075 km and the polar (meridional) circumference 40,008 km, a difference of about 67 km. The flattening is only 1 part in 298, so a globe 1 m across would be flattened by about 3 mm — invisible to the eye, which is why the earth looks a perfect sphere from space.
Geoid. Even the oblate spheroid is an idealisation. Measurements by satellites since 1958 show that the earth's surface — more exactly the surface of mean sea level extended under the continents — has small irregularities of its own: the northern hemisphere is very slightly more pointed and the southern very slightly flatter, and there are bumps and hollows of a few tens of metres where the crust and mantle are denser or lighter. For this reason the exact shape is called simply a geoid, from the Greek for earth-shaped, meaning the shape the earth actually has and nothing else. The geoid is defined as the surface of equal gravitational potential that coincides with mean sea level; it is the reference from which heights are measured. Some writers have described the geoid as slightly pear-shaped, but the pear is an exaggeration of differences of only a few metres.
Why the difference matters. For everyday purposes the earth is a sphere: a globe is made round, distances on maps are calculated on a sphere, and the difference is far smaller than the height of Mount Everest. But for satellites, for the Global Positioning System, for measuring gravity and for the exact survey of a country the oblate spheroid and the geoid must be used; the Survey of India uses a reference ellipsoid (the Everest spheroid, named after George Everest) fitted to India.
Summary of shapes. Sphere — the first approximation, a perfect ball. Oblate spheroid — flattened at the poles and bulging at the equator because of rotation, 42 km shorter through the poles. Geoid — the actual irregular shape given by the surface of mean sea level, the earth's own shape.
- Equatorial diameter 12,756 km against polar diameter 12,714 km: the earth is 42 km fatter across the equator than through the poles, a flattening of about 1 in 298.
- The French expeditions of 1735–44 measured one degree of latitude as about 111.9 km in Lapland and about 110.6 km in Peru; the longer degree near the pole proved the earth is flattened there, as Newton had predicted.
- Mount Chimborazo in Ecuador, near the equator, is only 6,263 m above sea level, but because of the equatorial bulge its summit is about 2 km farther from the earth's centre than the top of Everest.
- Equatorial diameter = 12,756 km; polar diameter = 12,714 km; difference ≈ 42 km; flattening ≈ 1/298.
- Equatorial circumference = 40,075 km; polar circumference = 40,008 km; mean radius ≈ 6,371 km.
- Geoid = the surface of mean sea level extended under the continents; the earth's own shape.
Size of the earth and the measurement of Eratosthenes
The dimensions of the earth. The earth is the fifth largest planet and the largest of the four rocky ones. Its main measurements are:
| Equatorial diameter | 12,756 km |
| Polar diameter | 12,714 km |
| Mean radius | 6,371 km |
| Equatorial circumference | 40,075 km |
| Polar circumference | 40,008 km |
| Surface area | 51 crore sq km (510 million sq km) |
| Land area | 14.9 crore sq km (29 per cent) |
| Water area | 36.1 crore sq km (71 per cent) |
| Mass | 5.97 × 1024 kg |
| Average density | 5.52 g per cubic cm |
| Mean distance from the sun | 14.96 crore km (1 AU) |
| Highest point | Mount Everest, 8,849 m |
| Deepest point | Mariana Trench, about 11,034 m |
The difference between the highest mountain and the deepest trench is about 20 km, which on a globe 1 m across would be 1.5 mm — the earth is smoother than a billiard ball in proportion.
Eratosthenes' measurement (about 240 BCE). The first and one of the most elegant measurements of the earth was made by Eratosthenes, the Greek scholar in charge of the library at Alexandria in Egypt. He knew that at Syene (modern Aswan), far to the south, the sun at noon on the day of the summer solstice shone straight down a deep well and a vertical stick cast no shadow: the sun was directly overhead. At Alexandria on the same day at noon a vertical stick did cast a shadow, and he measured the angle between the stick and the sun's rays as about 7.2°, one-fiftieth of a full circle of 360°. Since the sun is so far away that its rays reach the earth parallel, this angle must equal the angle at the centre of the earth between Alexandria and Syene, that is, the difference in their latitudes. The distance between the two cities, he estimated from the time taken by camel caravans, was 5,000 stadia. Then the whole circumference, being 50 times the arc between them, was 50 × 5,000 = 2,50,000 stadia. Taking the stadion at about 157 m, this is about 39,250 km — within a few per cent of the true 40,008 km. The reasoning is the same as that used today: circumference = (360 ÷ angle between the two places) × distance between them.
Later measurements. The Indian astronomer Aryabhata gave the earth's circumference as 4,967 yojanas, which on one reading of the yojana is close to the true value. Al-Biruni in about 1030 CE, standing on a hill in Punjab, measured the dip of the horizon and calculated the radius of the earth as about 6,340 km, only 0.5 per cent low. The French geodesists of the eighteenth century measured arcs of meridian with surveying chains, the Great Trigonometrical Survey of India under Lambton and Everest measured the great arc from Cape Comorin to the Himalaya between 1802 and 1841, and today satellites and laser ranging give the figures to a few centimetres.
- Eratosthenes: shadow angle at Alexandria 7.2° = 1/50 of 360°; distance Alexandria–Syene 5,000 stadia; circumference = 50 × 5,000 = 2,50,000 stadia ≈ 39,250 km, about 2 per cent below the true value.
- The same method today: Kolkata (22.6° N) and Delhi (28.6° N) differ by 6° of latitude and are about 667 km apart along the meridian; circumference ≈ (360 ÷ 6) × 667 = 40,020 km.
- The earth's surface is 51 crore sq km, of which water covers 71 per cent and land only 29 per cent; India's 32.9 lakh sq km is 2.4 per cent of the land.
- Circumference of the earth = (360° ÷ difference in latitude between two places on the same meridian) × distance between them.
- Surface area of a sphere = 4πr²; with r = 6,371 km, area ≈ 51 crore sq km. 1° of latitude ≈ 111 km.
The earth as the living planet
Of the eight planets, and of the thousands of planets now known round other stars, the earth is the only one on which life is known to exist. Seen from space it is unmistakable — a blue-and-white marble with brown and green continents — and astronauts call it the blue planet. Several conditions combine to make it habitable, and the absence of any one of them elsewhere makes those planets dead.
1. The right distance from the sun. The earth lies about 15 crore km from the sun, in the narrow band that astronomers call the habitable zone or Goldilocks zone — neither too hot nor too cold, but just right for water to remain liquid. Venus, 30 per cent nearer, is a furnace; Mars, 50 per cent farther, is frozen. The average surface temperature of the earth is about 15 °C.
2. Liquid water. Water covers 71 per cent of the surface in oceans, seas, lakes and rivers, and is present as vapour in the air and as ice at the poles. Every living thing is mostly water and every life process happens in it. The earth is the only planet where water exists in all three states at the surface; the hydrological cycle — evaporation, condensation, rain, rivers, back to the sea — keeps it moving and fresh.
3. The atmosphere. The earth is wrapped in a blanket of air about 78 per cent nitrogen, 21 per cent oxygen, with argon, carbon dioxide and water vapour. Oxygen, produced by plants over 200 crore years, lets animals breathe; carbon dioxide feeds plants; the ozone layer in the stratosphere screens out the sun's harmful ultraviolet rays; and the greenhouse effect of water vapour and carbon dioxide keeps the surface about 33 °C warmer than it would otherwise be, while not running away as on Venus. The atmosphere also burns up most meteors, spreads heat by winds and carries the rain.
4. The right size and gravity. The earth is massive enough for its gravity to hold on to its atmosphere and water — the moon and Mercury are too small and have lost theirs — but not so massive as to keep a crushing hydrogen atmosphere like Jupiter.
5. The magnetic field. The earth's liquid iron outer core, spinning, produces a magnetic field that reaches far into space and deflects the solar wind, the stream of charged particles from the sun that would otherwise strip away the atmosphere and bathe the surface in radiation. Mars, which has no such field, lost most of its air. The field also gives us the compass and the aurora.
6. Rotation and the tilt of the axis. The earth turns once in 24 hours, a period short enough to keep day and night from becoming extremes of heat and cold, and its axis is tilted at 23½°, giving the seasons that spread warmth over both hemispheres in turn.
7. Geological activity and the moon. The moving plates of the crust recycle carbon and nutrients and build the continents; the large moon steadies the tilt of the axis and drives the tides that helped life move from the sea to the land.
The biosphere. The thin zone where land, water and air meet, a few kilometres deep, is the biosphere, the home of all life from bacteria to blue whales. It is very small in relation to the planet — on a globe 1 m across it would be a film thinner than a coat of paint — and it is now being changed by human activity faster than at any time in its history. Protecting it is the practical reason for studying this chapter.
- Venus at 10.8 crore km from the sun has a surface of 465 °C; Mars at 22.8 crore km averages −60 °C; the earth at 15 crore km averages 15 °C — only the earth sits in the zone where water stays liquid.
- Mars once had rivers and lakes but, lacking a magnetic field, lost most of its atmosphere to the solar wind and its water froze or escaped; the earth's magnetic shield saved ours.
- The greenhouse effect of water vapour and carbon dioxide keeps the earth about 33 °C warmer than a bare rock at the same distance would be — without it the average would be −18 °C and the oceans frozen.
- Conditions for life on the earth: right distance from the sun (habitable zone) + liquid water + oxygen-rich atmosphere with ozone layer + moderate greenhouse effect + suitable gravity + magnetic field + 24-hour rotation and 23½° tilt.
- Atmosphere: nitrogen 78 per cent, oxygen 21 per cent, argon 0.93 per cent, carbon dioxide 0.04 per cent, plus water vapour.
The moon, the earth's satellite
The moon (Chandra) is the earth's only natural satellite and its nearest neighbour in space, and it is the only other world on which human beings have walked. It is important to geography for the tides, the calendar, eclipses and as the yardstick of all our ideas about the planets.
Size and distance. The moon has a diameter of 3,476 km, about a quarter of the earth's, and a mass 1/81 of the earth's; its gravity is one-sixth of ours, so a person weighing 60 kg on the earth would weigh 10 kg there. It is about 3,84,400 km from the earth on average — about 30 earth-diameters away, a distance light crosses in 1.3 seconds and the Apollo spacecraft in three days. Because its orbit is elliptical, the distance varies between about 3,56,000 km (perigee) and 4,06,000 km (apogee); a full moon at perigee is a supermoon, appearing about 14 per cent larger.
Movements. The moon revolves round the earth once in 27 days 8 hours (the sidereal month), but because the earth is meanwhile moving round the sun, the interval from one new moon to the next is 29½ days (the synodic month), the basis of the lunar calendar. The moon also rotates on its axis in exactly the same time as it revolves, so it always turns the same face to the earth; the far side was first seen by the Soviet Luna 3 spacecraft in 1959.
Phases. The moon has no light of its own; it shines by reflecting sunlight. As it goes round the earth we see different amounts of its lit half: new moon (amavasya, the moon between earth and sun, dark), crescent, first quarter (half lit), gibbous, full moon (purnima, the earth between sun and moon, fully lit), then waning through gibbous, last quarter and crescent back to new. The bright fortnight is the shukla paksha and the dark fortnight the krishna paksha of the Indian calendar.
Surface and conditions. The moon has no atmosphere and no liquid water, so there is no weather, no sound, no blue sky, and the temperature swings from 127 °C in the day to −173 °C at night. The surface has dark plains of solidified lava called maria (seas, though dry), bright cratered highlands, mountain ranges and millions of craters made by meteorite impacts that no air ever slowed. The largest, Bailly, is 300 km across. In 2008 India's Chandrayaan-1 found water molecules in the lunar soil, and in 2023 Chandrayaan-3 landed near the south pole, the first craft to do so.
Origin. The most accepted theory is that soon after the earth formed, about 450 crore years ago, a Mars-sized body struck it and the debris thrown into orbit gathered into the moon — the giant-impact hypothesis, which explains why the moon's rocks resemble the earth's mantle.
Effects on the earth. The moon's gravity pulls the ocean water into two bulges and causes the tides, two high and two low each day, strongest (spring tides) at new and full moon when sun and moon pull together. The moon steadies the tilt of the earth's axis and so keeps the seasons regular. When it passes between earth and sun it causes a solar eclipse; when the earth's shadow falls on it, a lunar eclipse. Eclipses happen only at new or full moon and only when the moon is near the plane of the earth's orbit, which is why they do not happen every month. Human landings between 1969 and 1972 brought back 382 kg of moon rock, and the moon remains the first step of every plan to explore beyond the earth.
- Moon: diameter 3,476 km (about a quarter of the earth's), distance 3,84,400 km, gravity one-sixth of the earth's, orbit 27⅓ days, new moon to new moon 29½ days.
- A total solar eclipse is possible only because of a coincidence: the sun is 400 times wider than the moon and also 400 times farther away, so the two look the same size in the sky.
- Chandrayaan-3 landed near the moon's south pole on 23 August 2023, making India the fourth country to soft-land on the moon and the first at the south pole.
- Sidereal month (one revolution) = 27 days 8 hours; synodic month (new moon to new moon) = 29 days 12 hours 44 minutes.
- The moon rotates once in exactly the time it revolves once, so the same face always faces the earth.
The earth's motions in brief and the shape of its orbit
This chapter introduces, and the next chapter develops, the two motions of the earth, because they are part of what it means to be a planet and they help to explain the earth's shape.
Rotation. The earth spins on its own axis, an imaginary line through the north and south poles, from west to east, once in 23 hours 56 minutes 4 seconds relative to the stars — the sidereal day — which, allowing for the earth's movement round the sun, gives the 24-hour solar day. The spin causes day and night, the apparent rising of the sun in the east and setting in the west, the deflection of winds and currents, the difference of time between places, and, as the previous topic showed, the equatorial bulge. The speed of rotation at the equator is about 1,670 km per hour, falling to zero at the poles; Kolkata at 22½° N moves at about 1,540 km per hour.
Revolution. At the same time the earth travels round the sun in an orbit that is an ellipse, not a circle, with the sun at one focus, once in 365 days 5 hours 48 minutes 46 seconds — the tropical year, which the calendar makes up with a leap day every fourth year. The speed of revolution is about 30 km per second, or 1,07,000 km per hour, and the orbit is about 94 crore km round. Because the orbit is an ellipse, the earth's distance from the sun varies: it is nearest (perihelion, 14.71 crore km) about 3 January and farthest (aphelion, 15.21 crore km) about 4 July. The difference is only 3 per cent and it is not the cause of the seasons; the northern hemisphere winter comes when the earth is nearest the sun.
The tilt of the axis. The earth's axis is not upright to the plane of its orbit but inclined at 23½° to the vertical, that is at 66½° to the plane of the orbit, and it keeps pointing in the same direction (towards the Pole Star) throughout the year. This tilt, combined with revolution, causes the seasons, the varying length of day and night, and the apparent movement of the sun between the Tropic of Cancer and the Tropic of Capricorn. These are the subjects of the next chapter.
The earth among the planets. All eight planets rotate and revolve, but the earth's combination of a 24-hour day, a nearly circular orbit and a moderate tilt is unusually kind to life: a day of 59 earth-days as on Mercury would roast one side and freeze the other, and a tilt of 98° as on Uranus would give each pole 42 years of darkness. The earth also shares the sun's motion: with the whole solar system it circles the centre of the galaxy at 220 km per second, so that in space nothing stands still.
Why the orbit is an ellipse. Kepler discovered in 1609 that every planet moves in an ellipse with the sun at one focus, and that it moves faster when nearer the sun; Newton in 1687 showed that this follows from gravitation, the same force that makes an apple fall. The earth stays in orbit because its forward motion and the sun's pull are exactly balanced: if the sun's gravity vanished, the earth would fly off in a straight line; if the earth stopped moving, it would fall into the sun.
- The earth rotates once in 23 h 56 min 4 s relative to the stars; its equator moves at about 1,670 km/h, faster than a passenger aircraft, yet we feel nothing because the air moves with us.
- Perihelion on about 3 January (14.71 crore km) and aphelion on about 4 July (15.21 crore km): the earth is nearest the sun in the northern winter, so distance is not what causes seasons.
- The year is 365 days 5 h 48 min 46 s; the extra quarter-day is collected as 29 February every fourth year, and century years are leap only if divisible by 400 (2000 was, 1900 was not).
- Rotation: once in 23 h 56 min 4 s (sidereal) / 24 h (solar), west to east; speed at the equator ≈ 1,670 km/h.
- Revolution: once in 365 d 5 h 48 min 46 s in an ellipse; speed ≈ 30 km/s; perihelion ≈ 3 January, aphelion ≈ 4 July.
- Axis tilted 23½° from the vertical (66½° to the orbital plane), always pointing towards the Pole Star.
Studying the earth from space
For all of history until 1957 the earth could be studied only from its own surface. The launch of the first artificial satellite, Sputnik 1, by the Soviet Union on 4 October 1957 opened the space age, and since then the view from above has transformed geography.
Artificial satellites. A satellite is put into orbit by a rocket that gives it a speed of about 28,000 km per hour; at that speed its fall towards the earth exactly matches the curve of the earth, so it circles endlessly. Satellites are of several kinds. Remote-sensing or earth-observation satellites carry cameras and sensors that photograph the earth in visible light and in infrared and microwave bands, mapping forests, crops, floods, cyclones, glaciers and cities; India's IRS series, Resourcesat and Cartosat, are among the best in the world. Weather satellites such as INSAT and Kalpana-1 watch clouds and track cyclones in the Bay of Bengal, giving the warnings that have cut cyclone deaths so sharply. Communication satellites in geostationary orbit, 35,786 km above the equator, relay television, telephone and internet. Navigation satellites — the American GPS, the Russian GLONASS, the European Galileo and India's own NavIC — let a mobile phone find its position to within a few metres. Scientific satellites measure the earth's gravity, magnetism, shape and the height of the sea.
What space has taught us about the earth. Photographs from Apollo 8 in 1968 and the famous Blue Marble photograph from Apollo 17 in 1972 showed the whole earth as a small blue sphere — the first time humanity saw its home entire. Satellite measurements refined the geoid, revealed the bumps in the earth's shape, and fixed its dimensions to centimetres. Satellites measure the rise of the sea (about 3.3 mm a year), the shrinking of Arctic ice, the loss of forests in the Amazon and the Sundarbans, the movement of the plates (India moves north-east at about 5 cm a year), and the growth of cities at night. They map the ocean floor by measuring the height of the sea surface, which follows the hidden relief below.
India in space. The Indian Space Research Organisation (ISRO), set up in 1969 under Vikram Sarabhai, launched Aryabhata in 1975, the Rohini satellite by its own SLV-3 rocket in 1980, and now flies the PSLV and GSLV launchers from Sriharikota in Andhra Pradesh. Chandrayaan-1 (2008) found water on the moon, Mangalyaan (2014) reached Mars orbit at the first attempt, Chandrayaan-3 (2023) landed near the moon's south pole and Aditya-L1 (2023) studies the sun. Rakesh Sharma flew in space in 1984, and Kalpana Chawla and Sunita Williams, of Indian origin, flew for NASA.
Geographic Information Systems and the modern map. Satellite images, GPS positions and census data are now combined in computers as layered digital maps — Geographic Information Systems — used for planning cities, tracking disease, managing disasters and guiding vehicles. The map on a mobile phone that shows where you are is the descendant of Eratosthenes' stick and shadow: the same earth, measured from above instead of below.
- Sputnik 1, launched on 4 October 1957, circled the earth in 96 minutes and began the space age; its orbit, and those of every satellite since, confirms the earth's curvature and its oblate shape.
- INSAT weather satellites tracked cyclone Amphan for a week before it struck the Sundarbans in May 2020, allowing 20 lakh people to be moved to shelters.
- Chandrayaan-3 soft-landed near the moon's south pole on 23 August 2023; Mangalyaan reached Mars orbit on 24 September 2014 at the first attempt.
- Geostationary orbit: 35,786 km above the equator, period 24 hours, so the satellite stays over one point.
- Orbital speed for a low earth orbit ≈ 28,000 km/h (7.8 km/s); one orbit ≈ 90–96 minutes.
Comparing the earth with its neighbours
A good way to understand the earth is to set it beside the two planets nearest to it, Venus and Mars, and beside the moon. The comparison shows how narrow the conditions for life are.
Earth and Venus. Venus is almost the earth's twin in size (12,104 km against 12,756 km), mass (82 per cent) and density, and it is made of the same rocky materials; astronomers once imagined jungles beneath its clouds. But it lies 30 per cent closer to the sun, and as it warmed its oceans boiled away, the water vapour and carbon dioxide trapped ever more heat, and the greenhouse effect ran away. Today its atmosphere is 96 per cent carbon dioxide at 90 times the earth's pressure, its clouds are sulphuric acid, and its surface is 465 °C, hot enough to melt lead, day and night, pole and equator alike. It rotates backward and very slowly, has no moon and no magnetic field. Venus is the warning of what a greenhouse effect can do.
Earth and Mars. Mars is half the earth's size and a tenth of its mass, and 50 per cent farther from the sun. It has a 24½-hour day, a 25° tilt and seasons, polar ice caps, volcanoes, canyons, dust storms and dry river beds — of all the planets it is the most earth-like, and long ago it had rivers and lakes. But its small size meant weak gravity and a core that cooled and stopped generating a magnetic field; the solar wind stripped away most of its atmosphere, which is now thin carbon dioxide at less than 1 per cent of the earth's pressure, and its water froze into the ground or escaped. The average temperature is −60 °C. Mars shows what happens to a planet too small to hold its air.
Earth and the moon. The moon is a quarter of the earth's diameter, has one-sixth of its gravity, no atmosphere, no water at the surface and no magnetic field; its surface swings through 300 °C between day and night and is pitted by every meteorite that ever struck it, because nothing ever eroded the craters away. The earth has been struck as often, but wind, water and moving plates have erased almost every scar. The moon is the earth without air, water and internal activity — a museum of the early solar system.
What the comparison teaches.
- Distance from the sun sets the temperature range; a small difference tips a planet into furnace or freezer.
- Size sets gravity, and gravity decides whether a planet keeps its atmosphere and water.
- An active interior gives a magnetic field that shields the atmosphere and plates that recycle the crust.
- An atmosphere with the right greenhouse effect keeps water liquid — too little and the world freezes, too much and it boils.
- Water in liquid form is the single condition that all life requires.
The earth passes all these tests, and it is the only body we know that does. The lesson of the chapter is that the earth is not merely a planet among planets: it is a rare and delicately balanced one, and its balance — its atmosphere, its climate, its water — is now partly in human hands. Geography, the study of the earth as the home of humankind, begins with understanding how special that home is.
- Venus and the earth are nearly the same size, yet Venus has a surface of 465 °C under 90 atmospheres of carbon dioxide — the result of a runaway greenhouse effect on a planet a little too close to the sun.
- Mars has a day of 24 h 37 min and a tilt of 25°, so its seasons resemble ours, but with a tenth of the earth's mass it could not keep its atmosphere and its rivers dried up 300 crore years ago.
- Meteor Crater in Arizona and Lonar crater in Maharashtra are among the few impact scars left on the earth; the moon, with no air or water to erase them, keeps every one of its millions of craters.
- Venus: diameter 12,104 km, distance 10.8 crore km, surface 465 °C, day 243 earth-days (retrograde), no moon. Mars: diameter 6,792 km, distance 22.8 crore km, average −60 °C, day 24 h 37 min, two moons. Moon: diameter 3,476 km, gravity 1/6 of the earth's, no atmosphere.
Key Concepts
- Universe
- The totality of all matter, energy, space and time, containing hundreds of thousands of crores of galaxies.
- Galaxy
- A vast system of thousands of crores of stars, gas and dust held together by gravity, such as our Milky Way.
- Big Bang theory
- The theory that the universe began about 1,380 crore years ago from a point of extreme density and has been expanding ever since.
- Light year
- The distance light travels in one year, about 9.46 lakh crore kilometres, used to measure distances between stars.
- Solar system
- The sun together with the eight planets, their satellites, dwarf planets, asteroids, comets and meteoroids that revolve round it.
- Planet
- A body that revolves round the sun, is large enough to be rounded by its own gravity and has cleared its orbit of other objects.
- Inner (terrestrial) planets
- Mercury, Venus, Earth and Mars — small, dense, rocky planets close to the sun with few or no satellites.
- Outer (Jovian) planets
- Jupiter, Saturn, Uranus and Neptune — large gaseous planets far from the sun with many satellites and rings.
- Dwarf planet
- A rounded body orbiting the sun that has not cleared its orbit, such as Pluto or Ceres.
- Asteroid belt
- The zone of rocky fragments between the orbits of Mars and Jupiter that never formed a planet.
- Comet
- A body of ice and dust from the outer solar system that grows a glowing tail pointing away from the sun as it approaches.
- Oblate spheroid
- A sphere flattened at the poles and bulging at the equator, the earth's shape caused by its rotation.
- Geoid
- The earth's own slightly irregular shape, defined by the surface of mean sea level extended under the continents.
- Equatorial and polar diameter
- The earth's width across the equator, 12,756 km, and through the poles, 12,714 km, differing by about 42 km.
- Lunar eclipse
- The passage of the moon through the earth's shadow at full moon, whose always-circular edge proves the earth is a sphere.
- Circumnavigation
- Travelling right round the earth and returning to the starting point, first done by Magellan's expedition in 1519–22.
- Habitable zone
- The band of distances from a star, neither too hot nor too cold, within which water can stay liquid on a planet's surface.
- Biosphere
- The thin zone of land, water and air on the earth where all living things exist.
- Satellite
- A body that revolves round a planet, either natural like the moon or artificial like INSAT.
- Geostationary orbit
- An orbit 35,786 km above the equator in which a satellite takes 24 hours to circle the earth and so stays above one point.
End-of-Chapter Trial Paper & Test Questions
Topic-wise questions to test your understanding of every concept in this chapter.
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What is the solar system? Name the planets in order from the sun and state the difference between the inner and outer planets. / सौरमंडल क्या है? सूर्य से क्रम में ग्रहों के नाम लिखिए और आंतरिक तथा बाह्य ग्रहों में अंतर बताइए।
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The solar system is the family of the sun: the eight planets, their satellites, the dwarf planets, asteroids, comets and meteoroids that all revolve round the sun under its gravity, formed about 460 crore years ago from a rotating cloud of gas and dust. In order from the sun the planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. The four inner or terrestrial planets — Mercury, Venus, Earth and Mars — are small, dense and rocky with solid surfaces, thin or no atmospheres of heavy gases, few or no satellites and no rings, and lie close to the sun inside the asteroid belt. The four outer or Jovian planets — Jupiter, Saturn, Uranus and Neptune — are huge, light and gaseous, made largely of hydrogen, helium, methane and ammonia with no solid surface, have many satellites and ring systems, rotate quickly and lie far from the sun beyond the asteroid belt, taking from 12 to 165 years for one revolution. / सौरमंडल सूर्य का परिवार है: आठ ग्रह, उनके उपग्रह, बौने ग्रह, क्षुद्रग्रह, धूमकेतु और उल्कापिंड जो सब सूर्य के गुरुत्व में उसकी परिक्रमा करते हैं, और जो लगभग 460 करोड़ वर्ष पहले गैस और धूल के घूमते बादल से बना। सूर्य से क्रम में ग्रह हैं बुध, शुक्र, पृथ्वी, मंगल, बृहस्पति, शनि, अरुण और वरुण। चार आंतरिक या पार्थिव ग्रह — बुध, शुक्र, पृथ्वी और मंगल — छोटे, घने और चट्टानी हैं, जिनकी सतह ठोस है, भारी गैसों का पतला या कोई वायुमंडल नहीं, कम या कोई उपग्रह नहीं और कोई वलय नहीं, और वे क्षुद्रग्रह पट्टी के अंदर सूर्य के पास हैं। चार बाह्य या बृहस्पति-सदृश ग्रह — बृहस्पति, शनि, अरुण और वरुण — विशाल, हल्के और गैसीय हैं, जो मुख्यतः हाइड्रोजन, हीलियम, मीथेन और अमोनिया से बने हैं और जिनकी कोई ठोस सतह नहीं, उनके अनेक उपग्रह और वलय तंत्र हैं, वे तेज़ी से घूमते हैं और क्षुद्रग्रह पट्टी के परे सूर्य से दूर हैं, एक परिक्रमा में 12 से 165 वर्ष लेते हुए।
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Give four proofs that the earth is spherical. / पृथ्वी के गोलाकार होने के चार प्रमाण दीजिए।
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First, circumnavigation: Magellan's expedition sailed west from Spain in 1519 and returned from the east in 1522, and ships, aircraft and satellites have gone round the earth countless times since; on a flat earth a traveller going in one direction would reach an edge. Second, a ship sailing away disappears hull first and mast last, and an approaching ship appears mast first, which is possible only if the sea curves away from the observer. Third, in every lunar eclipse the edge of the earth's shadow on the moon is a circular arc, and only a sphere throws a circular shadow in every position. Fourth, the Pole Star is on the horizon at the equator and rises higher as one goes north until it is overhead at the pole, its altitude equalling the latitude, which can happen only on a curved surface. Further proofs are the different times of sunrise at different longitudes, the widening circular horizon seen from a height, and photographs of the whole earth from space. / पहला, परिभ्रमण: मैगलन का अभियान 1519 में स्पेन से पश्चिम की ओर चला और 1522 में पूर्व से लौटा, और तब से जहाज़, विमान और उपग्रह अनगिनत बार पृथ्वी का चक्कर लगा चुके हैं; चपटी पृथ्वी पर एक दिशा में चलने वाला यात्री किनारे पर पहुँच जाता। दूसरा, दूर जाता जहाज़ पहले अपना ढाँचा और अंत में मस्तूल छिपाता है, और आता जहाज़ पहले मस्तूल दिखाता है, जो तभी संभव है जब समुद्र देखने वाले से दूर मुड़ता हो। तीसरा, हर चंद्रग्रहण में चंद्रमा पर पृथ्वी की छाया का किनारा वृत्ताकार चाप होता है, और केवल गोला ही हर स्थिति में वृत्ताकार छाया डालता है। चौथा, ध्रुव तारा भूमध्य रेखा पर क्षितिज पर होता है और उत्तर जाने पर ऊँचा उठता जाता है जब तक ध्रुव पर सिर के ऊपर न आ जाए, उसका उन्नतांश अक्षांश के बराबर होता है, जो केवल वक्र सतह पर हो सकता है। अन्य प्रमाण हैं भिन्न देशांतरों पर सूर्योदय का भिन्न समय, ऊँचाई से दिखने वाला फैलता वृत्ताकार क्षितिज, और अंतरिक्ष से पूरी पृथ्वी के चित्र।
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Why is the earth called an oblate spheroid? What is a geoid? / पृथ्वी को लध्वक्ष गोलाभ (ओब्लेट स्फेरॉइड) क्यों कहा जाता है? जिओइड क्या है?
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The earth is called an oblate spheroid because it is not a perfect sphere but is flattened at the poles and bulges at the equator. This is caused by its rotation: the centrifugal effect of spinning is greatest at the equator, where the surface moves at about 1,670 km per hour, and zero at the poles, so over the ages the equatorial region has been pushed outward. As a result the equatorial diameter is 12,756 km while the polar diameter is 12,714 km, a difference of about 42 km, and the equatorial circumference of 40,075 km exceeds the polar circumference of 40,008 km by about 67 km. Newton predicted this flattening in 1687 and the French measurements of a degree of latitude in Lapland and Peru in the 1730s confirmed it. A geoid is the name for the earth's actual shape, which satellite measurements show to depart slightly even from the oblate spheroid, with small bumps and hollows of a few tens of metres and a slightly more pointed northern hemisphere; it is defined as the surface of mean sea level extended under the continents, and the word simply means earth-shaped, because no geometrical figure fits the earth exactly. / पृथ्वी को लध्वक्ष गोलाभ इसलिए कहा जाता है क्योंकि यह पूर्ण गोला नहीं है बल्कि ध्रुवों पर चपटी और भूमध्य रेखा पर उभरी हुई है। इसका कारण इसका घूर्णन है: घूमने का अपकेंद्री प्रभाव भूमध्य रेखा पर सबसे अधिक है, जहाँ सतह लगभग 1,670 किमी प्रति घंटे की गति से चलती है, और ध्रुवों पर शून्य, इसलिए युगों में भूमध्यरेखीय क्षेत्र बाहर की ओर धकेला गया है। फलस्वरूप भूमध्यरेखीय व्यास 12,756 किमी है जबकि ध्रुवीय व्यास 12,714 किमी, लगभग 42 किमी का अंतर, और 40,075 किमी की भूमध्यरेखीय परिधि 40,008 किमी की ध्रुवीय परिधि से लगभग 67 किमी अधिक है। न्यूटन ने 1687 में इस चपटेपन की भविष्यवाणी की थी और 1730 के दशक में लैपलैंड और पेरू में अक्षांश के एक अंश के फ्रांसीसी मापन ने इसकी पुष्टि की। जिओइड पृथ्वी की वास्तविक आकृति का नाम है, जो उपग्रह मापनों के अनुसार लध्वक्ष गोलाभ से भी थोड़ी भिन्न है, जिसमें कुछ दसियों मीटर के छोटे उभार और गड्ढे हैं और उत्तरी गोलार्ध थोड़ा अधिक नुकीला है; इसे महाद्वीपों के नीचे विस्तारित माध्य समुद्र तल की सतह के रूप में परिभाषित किया जाता है, और इस शब्द का अर्थ केवल पृथ्वी-आकार है, क्योंकि कोई भी ज्यामितीय आकृति पृथ्वी पर ठीक-ठीक नहीं बैठती।
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How did Eratosthenes measure the circumference of the earth? / एराटोस्थनीज़ ने पृथ्वी की परिधि कैसे मापी?
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Eratosthenes, the Greek librarian of Alexandria, made the first measurement in about 240 BCE. He knew that at Syene, now Aswan, at noon on the summer solstice the sun shone straight down a deep well and a vertical stick cast no shadow, so the sun was directly overhead there. At Alexandria, due north, at noon on the same day he measured the angle between a vertical stick and the sun's rays as about 7.2°, which is one-fiftieth of 360°. Since the sun is so distant that its rays reach the earth parallel, this angle equals the angle at the earth's centre between the two cities, that is the difference in their latitudes. The distance between them, estimated from the journey of camel caravans, was 5,000 stadia. The full circumference was therefore 50 times this arc, 50 × 5,000 = 2,50,000 stadia, which at about 157 m to the stadion is roughly 39,250 km, within two per cent of the true polar circumference of 40,008 km. The principle, circumference = (360 ÷ angle) × distance, is still valid. / अलेक्ज़ांड्रिया के यूनानी पुस्तकालयाध्यक्ष एराटोस्थनीज़ ने लगभग 240 ईसा पूर्व पहला मापन किया। वे जानते थे कि साइनी, अब असवान, में ग्रीष्म संक्रांति की दोपहर को सूर्य एक गहरे कुएँ में सीधा चमकता था और खड़ी छड़ी कोई छाया नहीं डालती थी, अतः वहाँ सूर्य ठीक सिर के ऊपर था। ठीक उत्तर में अलेक्ज़ांड्रिया में उसी दिन दोपहर को उन्होंने खड़ी छड़ी और सूर्य की किरणों के बीच का कोण लगभग 7.2° मापा, जो 360° का पचासवाँ भाग है। चूँकि सूर्य इतना दूर है कि उसकी किरणें पृथ्वी पर समांतर पहुँचती हैं, यह कोण दोनों नगरों के बीच पृथ्वी के केंद्र पर बने कोण, अर्थात उनके अक्षांशों के अंतर, के बराबर है। ऊँट के कारवाँ की यात्रा से अनुमानित उनके बीच की दूरी 5,000 स्टेडिया थी। अतः पूरी परिधि इस चाप की 50 गुनी, 50 × 5,000 = 2,50,000 स्टेडिया थी, जो लगभग 157 मीटर प्रति स्टेडियन के हिसाब से लगभग 39,250 किमी है, जो 40,008 किमी की वास्तविक ध्रुवीय परिधि से दो प्रतिशत के भीतर है। सिद्धांत, परिधि = (360 ÷ कोण) × दूरी, आज भी मान्य है।
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State the equatorial and polar diameters and circumferences of the earth. Why do they differ? / पृथ्वी के भूमध्यरेखीय और ध्रुवीय व्यास तथा परिधियाँ बताइए। वे भिन्न क्यों हैं?
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The equatorial diameter of the earth is 12,756 km and the polar diameter 12,714 km, so the earth is about 42 km wider across the equator than through the poles. The equatorial circumference is 40,075 km and the polar or meridional circumference 40,008 km, a difference of about 67 km. They differ because the earth rotates on its axis once a day, and the centrifugal effect of this spin, which is greatest at the equator where the surface moves fastest and nil at the poles, has pushed the equatorial region outward and flattened the polar regions, giving the earth the shape of an oblate spheroid. The flattening is only about one part in 298, so small that the earth looks a perfect sphere from space, but large enough to be measured by surveys and to matter for satellites and precise maps. / पृथ्वी का भूमध्यरेखीय व्यास 12,756 किमी और ध्रुवीय व्यास 12,714 किमी है, अतः पृथ्वी भूमध्य रेखा के आर-पार ध्रुवों की अपेक्षा लगभग 42 किमी अधिक चौड़ी है। भूमध्यरेखीय परिधि 40,075 किमी और ध्रुवीय या याम्योत्तर परिधि 40,008 किमी है, लगभग 67 किमी का अंतर। वे इसलिए भिन्न हैं क्योंकि पृथ्वी प्रतिदिन एक बार अपनी धुरी पर घूमती है, और इस घूर्णन का अपकेंद्री प्रभाव, जो भूमध्य रेखा पर सबसे अधिक है जहाँ सतह सबसे तेज़ चलती है और ध्रुवों पर शून्य, ने भूमध्यरेखीय क्षेत्र को बाहर धकेला और ध्रुवीय क्षेत्रों को चपटा कर दिया है, जिससे पृथ्वी को लध्वक्ष गोलाभ का आकार मिला है। चपटापन केवल लगभग 298 में एक भाग है, इतना छोटा कि अंतरिक्ष से पृथ्वी पूर्ण गोला दिखती है, पर इतना बड़ा कि सर्वेक्षणों से मापा जा सके और उपग्रहों तथा सटीक मानचित्रों के लिए महत्व रखे।
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Why is the earth the only planet with life? / पृथ्वी ही जीवन वाला एकमात्र ग्रह क्यों है?
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The earth supports life because several conditions occur together on it and nowhere else in the solar system. It lies at the right distance from the sun, about 15 crore km, in the habitable zone where the average temperature of 15 °C keeps water liquid, whereas Venus is a furnace and Mars is frozen. It has abundant liquid water covering 71 per cent of its surface, the medium of every life process, circulating through the hydrological cycle. It has an atmosphere of nitrogen and oxygen that animals breathe, with carbon dioxide for plants, an ozone layer that screens harmful ultraviolet rays, and a moderate greenhouse effect that keeps the surface about 33 °C warmer than it would otherwise be. Its size gives a gravity strong enough to hold the atmosphere and water, unlike the small moon and Mars. Its liquid iron core generates a magnetic field that deflects the solar wind, which stripped Mars of its air. Its 24-hour rotation and 23½° tilt prevent extremes of heat and cold and give seasons, and its active crust and large moon steady the climate. Together these make the thin biosphere the only known home of life. / पृथ्वी पर जीवन इसलिए है क्योंकि कई दशाएँ इस पर एक साथ मिलती हैं और सौरमंडल में और कहीं नहीं। यह सूर्य से सही दूरी पर, लगभग 15 करोड़ किमी, रहने योग्य क्षेत्र में है जहाँ 15 °C का औसत तापमान पानी को द्रव रखता है, जबकि शुक्र भट्टी है और मंगल जमा हुआ। इस पर प्रचुर द्रव जल है जो सतह के 71 प्रतिशत को ढकता है, हर जीवन-प्रक्रिया का माध्यम, जो जल-चक्र से घूमता रहता है। इसका नाइट्रोजन और ऑक्सीजन का वायुमंडल है जिसमें जंतु साँस लेते हैं, पौधों के लिए कार्बन डाइऑक्साइड, हानिकारक पराबैंगनी किरणों को रोकने वाली ओज़ोन परत, और संतुलित ग्रीनहाउस प्रभाव जो सतह को अन्यथा की अपेक्षा लगभग 33 °C गर्म रखता है। इसका आकार इतना गुरुत्व देता है कि वायुमंडल और जल को थामे रखे, छोटे चंद्रमा और मंगल के विपरीत। इसका द्रव लोहे का क्रोड चुंबकीय क्षेत्र बनाता है जो सौर पवन को मोड़ देता है, जिसने मंगल की हवा छीन ली थी। इसका 24 घंटे का घूर्णन और 23½° का झुकाव गर्मी-सर्दी की चरम सीमाएँ रोकते और ऋतुएँ देते हैं, और इसकी सक्रिय भूपर्पटी तथा बड़ा चंद्रमा जलवायु को स्थिर रखते हैं। ये सब मिलकर पतले जैवमंडल को जीवन का एकमात्र ज्ञात घर बनाते हैं।
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Write short notes on: (a) the Milky Way, (b) comets and meteors. / संक्षिप्त टिप्पणियाँ लिखिए: (क) आकाशगंगा, (ख) धूमकेतु और उल्काएँ।
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(a) The Milky Way or Akash Ganga is the galaxy to which the sun belongs. It is a spiral galaxy shaped like a flat disc with a central bulge and winding arms, about one lakh light years across and a thousand light years thick, containing 10,000 to 40,000 crore stars with gas and dust between them. The sun lies in the Orion arm about 26,000 light years from the centre and circles the centre once in about 22.5 crore years. On a clear dark night the galaxy appears as a hazy band of light across the sky, which is the combined light of its distant stars seen edge-on from inside the disc. (b) Comets are bodies of ice, dust and rock from the cold outer solar system that travel in long elliptical orbits; when one nears the sun its ice turns to gas and forms a glowing head and a long tail that always points away from the sun because the solar wind pushes it. Halley's comet returns every 76 years, last in 1986. Meteoroids are small pieces of rock or metal moving in space; when one enters the atmosphere at high speed, friction makes it glow and burn, and we see a meteor or shooting star; a piece that survives to reach the ground is a meteorite, such as the one that formed the Lonar crater in Maharashtra. / (क) आकाशगंगा या मिल्की वे वह गैलेक्सी है जिसका सूर्य सदस्य है। यह सर्पिल गैलेक्सी है जिसका आकार केंद्रीय उभार और घुमावदार भुजाओं वाली चपटी तश्तरी जैसा है, लगभग एक लाख प्रकाश वर्ष चौड़ी और एक हज़ार प्रकाश वर्ष मोटी, जिसमें 10,000 से 40,000 करोड़ तारे और उनके बीच गैस तथा धूल है। सूर्य केंद्र से लगभग 26,000 प्रकाश वर्ष दूर ओरायन भुजा में है और लगभग 22.5 करोड़ वर्ष में केंद्र का एक चक्कर लगाता है। साफ़ अँधेरी रात में गैलेक्सी आकाश के आर-पार प्रकाश की धुँधली पट्टी के रूप में दिखती है, जो तश्तरी के भीतर से किनारे की ओर देखे गए उसके दूर के तारों का सम्मिलित प्रकाश है। (ख) धूमकेतु ठंडे बाह्य सौरमंडल से आए बर्फ, धूल और चट्टान के पिंड हैं जो लंबी दीर्घवृत्ताकार कक्षाओं में चलते हैं; जब कोई सूर्य के पास आता है तो उसकी बर्फ गैस बनकर चमकता सिर और लंबी पूँछ बनाती है जो सदा सूर्य से दूर की ओर होती है क्योंकि सौर पवन उसे धकेलती है। हैली धूमकेतु हर 76 वर्ष में लौटता है, अंतिम बार 1986 में। उल्कापिंड अंतरिक्ष में चलते चट्टान या धातु के छोटे टुकड़े हैं; जब कोई तेज़ गति से वायुमंडल में प्रवेश करता है तो घर्षण से वह चमककर जल उठता है, और हमें उल्का या टूटता तारा दिखता है; जो टुकड़ा बचकर ज़मीन तक पहुँचता है वह उल्कापिंड कहलाता है, जैसे वह जिसने महाराष्ट्र का लोनार गड्ढा बनाया।
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Describe the moon as a satellite of the earth. Why do we always see the same face of the moon? / पृथ्वी के उपग्रह के रूप में चंद्रमा का वर्णन कीजिए। हमें सदा चंद्रमा का एक ही पक्ष क्यों दिखता है?
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The moon is the earth's only natural satellite, a rocky ball 3,476 km in diameter, about a quarter of the earth's, with one-eightieth of its mass and one-sixth of its gravity, at an average distance of 3,84,400 km. It has no atmosphere or surface water, so its temperature swings from 127 °C by day to −173 °C at night and its surface is covered with impact craters, dark lava plains called maria and bright highlands. It revolves round the earth once in 27⅓ days, and the interval from one new moon to the next is 29½ days, the basis of the lunar month; it shines by reflected sunlight, showing phases from new moon to full moon as different parts of its lit half face us. Its gravity causes the tides and its shadow causes solar eclipses. We always see the same face because the moon rotates on its axis in exactly the same time as it revolves round the earth, 27⅓ days — a condition called synchronous rotation, produced over ages by the earth's tidal pull — so the same hemisphere is always turned toward us and the far side was unseen until a spacecraft photographed it in 1959. / चंद्रमा पृथ्वी का एकमात्र प्राकृतिक उपग्रह है, 3,476 किमी व्यास का चट्टानी गोला, पृथ्वी के लगभग एक चौथाई, जिसका द्रव्यमान पृथ्वी का अस्सीवाँ भाग और गुरुत्व छठा भाग है, औसतन 3,84,400 किमी की दूरी पर। इस पर वायुमंडल या सतही जल नहीं है, इसलिए इसका तापमान दिन में 127 °C से रात में −173 °C तक झूलता है और इसकी सतह टकराव के गड्ढों, मारिया कहलाने वाले काले लावा मैदानों और चमकीली उच्चभूमियों से ढकी है। यह 27⅓ दिन में पृथ्वी की एक परिक्रमा करता है, और एक अमावस्या से अगली तक का अंतराल 29½ दिन है, जो चंद्र मास का आधार है; यह परावर्तित सूर्यप्रकाश से चमकता है और अमावस्या से पूर्णिमा तक कलाएँ दिखाता है क्योंकि इसके प्रकाशित आधे भाग के भिन्न-भिन्न अंश हमारी ओर होते हैं। इसका गुरुत्व ज्वार-भाटा और इसकी छाया सूर्यग्रहण उत्पन्न करती है। हमें सदा एक ही पक्ष इसलिए दिखता है क्योंकि चंद्रमा अपनी धुरी पर ठीक उतने ही समय में घूमता है जितने में पृथ्वी की परिक्रमा करता है, 27⅓ दिन — इसे समकालिक घूर्णन कहते हैं, जो युगों में पृथ्वी के ज्वारीय खिंचाव से बना — अतः वही गोलार्ध सदा हमारी ओर रहता है और दूसरा पक्ष 1959 में अंतरिक्ष यान के चित्र लेने तक अदेखा रहा।
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Explain the Big Bang theory of the origin of the universe. / ब्रह्मांड की उत्पत्ति के महाविस्फोट (बिग बैंग) सिद्धांत की व्याख्या कीजिए।
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The Big Bang theory, proposed by Georges Lemaître in 1927, holds that the whole universe began about 1,380 crore years ago from a single point of unimaginable density and temperature, which expanded suddenly and has been expanding and cooling ever since; space itself grew, carrying matter with it. Within the first minutes the lightest elements, hydrogen and helium, were formed; after some crores of years the gas gathered under gravity into the first stars and galaxies, and heavier elements such as carbon, oxygen and iron were later made inside stars and scattered when they exploded. The theory rests on two chief pieces of evidence: Edwin Hubble's discovery in 1929 that every galaxy is moving away from every other, the farther ones faster, which means the universe is expanding from an earlier smaller state; and the cosmic microwave background radiation discovered in 1965, a faint glow filling all space that is the cooled remnant of the original fireball. The observed proportions of hydrogen and helium also match the theory's predictions. / 1927 में जॉर्ज लेमैत्र द्वारा प्रस्तावित महाविस्फोट सिद्धांत के अनुसार पूरा ब्रह्मांड लगभग 1,380 करोड़ वर्ष पहले अकल्पनीय घनत्व और तापमान के एक बिंदु से शुरू हुआ, जो अचानक फैला और तब से फैलता तथा ठंडा होता जा रहा है; अंतरिक्ष स्वयं बढ़ा और पदार्थ को साथ ले गया। पहले कुछ मिनटों में सबसे हल्के तत्व, हाइड्रोजन और हीलियम, बने; कुछ करोड़ वर्षों बाद गैस गुरुत्व से इकट्ठी होकर पहले तारे और गैलेक्सियाँ बनी, और कार्बन, ऑक्सीजन तथा लोहे जैसे भारी तत्व बाद में तारों के भीतर बने और उनके विस्फोट में बिखर गए। सिद्धांत दो मुख्य प्रमाणों पर टिका है: एडविन हबल की 1929 की खोज कि हर गैलेक्सी हर दूसरी से दूर जा रही है, दूर वाली और तेज़ी से, जिसका अर्थ है कि ब्रह्मांड पहले की छोटी अवस्था से फैल रहा है; और 1965 में खोजा गया ब्रह्मांडीय सूक्ष्मतरंग पृष्ठभूमि विकिरण, समूचे अंतरिक्ष में भरी धुँधली चमक जो मूल अग्निपिंड का ठंडा अवशेष है। हाइड्रोजन और हीलियम के प्रेक्षित अनुपात भी सिद्धांत की भविष्यवाणियों से मेल खाते हैं।
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Write the special features of Venus, Mars, Jupiter and Saturn. / शुक्र, मंगल, बृहस्पति और शनि की विशेषताएँ लिखिए।
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Venus, the second planet, is nearly the earth's twin in size but is wrapped in thick clouds of carbon dioxide and sulphuric acid that trap heat, making it the hottest planet at about 465 °C; it is the brightest object after the sun and moon, seen as the morning and evening star, rotates backward so slowly that its day of 243 earth-days is longer than its year of 225 days, and has no moon. Mars, the fourth planet, is the red planet, coloured by iron oxide, half the earth's size with a thin carbon dioxide atmosphere, polar ice caps, seasons, a day of 24½ hours, a year of 687 days, the highest volcano in the solar system, Olympus Mons, dry river beds showing it once had water, and two small moons, Phobos and Deimos. Jupiter, the fifth, is the largest planet, eleven times the earth's diameter, a ball of hydrogen and helium with coloured cloud bands and the Great Red Spot, a storm bigger than the earth; it rotates fastest, in under ten hours, takes twelve years to orbit the sun and has more than ninety moons including Ganymede, the largest in the solar system. Saturn, the sixth, is the second largest and is famous for its bright rings of ice and rock; it is the least dense planet and would float on water, takes 29½ years to orbit the sun and has more than 140 moons, of which Titan has a thick atmosphere. / शुक्र, दूसरा ग्रह, आकार में लगभग पृथ्वी का जुड़वाँ है पर कार्बन डाइऑक्साइड और सल्फ्यूरिक अम्ल के घने बादलों में लिपटा है जो ऊष्मा को रोक लेते हैं, जिससे यह लगभग 465 °C पर सबसे गर्म ग्रह है; यह सूर्य और चंद्रमा के बाद सबसे चमकीला पिंड है, जो भोर और साँझ के तारे के रूप में दिखता है, इतनी धीमी उल्टी दिशा में घूमता है कि 243 पृथ्वी-दिनों का इसका दिन 225 दिनों के इसके वर्ष से लंबा है, और इसका कोई चंद्रमा नहीं है। मंगल, चौथा ग्रह, लाल ग्रह है, जिसका रंग लौह ऑक्साइड से है, पृथ्वी का आधा आकार, कार्बन डाइऑक्साइड का पतला वायुमंडल, ध्रुवीय हिम टोपियाँ, ऋतुएँ, 24½ घंटे का दिन, 687 दिनों का वर्ष, सौरमंडल का सबसे ऊँचा ज्वालामुखी ओलंपस मॉन्स, सूखी नदी-घाटियाँ जो दिखाती हैं कि कभी इस पर पानी था, और दो छोटे चंद्रमा, फोबोस और डीमोस। बृहस्पति, पाँचवाँ, सबसे बड़ा ग्रह है, पृथ्वी के व्यास का ग्यारह गुना, हाइड्रोजन और हीलियम का गोला जिस पर रंगीन बादलों की पट्टियाँ और पृथ्वी से बड़ा तूफान महान लाल धब्बा है; यह सबसे तेज़, दस घंटे से कम में, घूमता है, सूर्य की परिक्रमा में बारह वर्ष लेता है और इसके नब्बे से अधिक चंद्रमा हैं जिनमें सौरमंडल का सबसे बड़ा गैनिमीड शामिल है। शनि, छठा, दूसरा सबसे बड़ा है और बर्फ तथा चट्टान के चमकीले वलयों के लिए प्रसिद्ध है; यह सबसे कम घना ग्रह है और पानी पर तैर जाएगा, सूर्य की परिक्रमा में 29½ वर्ष लेता है और इसके 140 से अधिक चंद्रमा हैं, जिनमें टाइटन का घना वायुमंडल है।
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How does the changing altitude of the Pole Star prove that the earth is round? / ध्रुव तारे का बदलता उन्नतांश कैसे सिद्ध करता है कि पृथ्वी गोल है?
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The Pole Star lies almost exactly in line with the earth's axis above the north pole, so its position in the sky depends on where the observer stands. At the equator it appears on the northern horizon; as the observer travels north it rises higher and higher, being 22° above the horizon at Kolkata, 28° at Delhi and 34° at Srinagar, until at the north pole it is directly overhead; and from anywhere south of the equator it cannot be seen at all. The angle of the Pole Star above the horizon is always equal to the latitude of the observer. On a flat earth every observer would see the star at the same angle, because all would be facing it from the same plane. Only if the surface curves — so that the observer's horizon tilts more and more away from the star as he goes north — can the altitude change steadily with distance travelled. The regular change, one degree of altitude for every 111 km travelled north, is exactly what a sphere of the earth's size would produce, and it is the method by which sailors found their latitude for centuries. / ध्रुव तारा उत्तरी ध्रुव के ऊपर पृथ्वी की धुरी की लगभग ठीक सीध में है, इसलिए आकाश में उसकी स्थिति इस पर निर्भर करती है कि देखने वाला कहाँ खड़ा है। भूमध्य रेखा पर वह उत्तरी क्षितिज पर दिखता है; जैसे-जैसे देखने वाला उत्तर की ओर जाता है वह ऊँचा उठता जाता है, कोलकाता में क्षितिज से 22° ऊपर, दिल्ली में 28° और श्रीनगर में 34°, जब तक उत्तरी ध्रुव पर वह ठीक सिर के ऊपर न आ जाए; और भूमध्य रेखा के दक्षिण में कहीं से भी वह दिखाई नहीं देता। क्षितिज से ऊपर ध्रुव तारे का कोण सदा देखने वाले के अक्षांश के बराबर होता है। चपटी पृथ्वी पर हर देखने वाला तारे को एक ही कोण पर देखता, क्योंकि सब एक ही तल से उसकी ओर देख रहे होते। केवल तभी जब सतह मुड़ी हो — ताकि उत्तर जाने पर देखने वाले का क्षितिज तारे से अधिकाधिक झुकता जाए — उन्नतांश तय की गई दूरी के साथ नियमित रूप से बदल सकता है। यह नियमित परिवर्तन, उत्तर की ओर हर 111 किमी पर एक अंश उन्नतांश, ठीक वही है जो पृथ्वी के आकार का गोला उत्पन्न करेगा, और यही वह विधि है जिससे नाविक सदियों तक अपना अक्षांश ज्ञात करते रहे।
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