CBSE Class 7 Science Advanced Physics Our Universe Notes Set 01

Our Universe

Introduction

People have long wondered how the heavenly bodies move. Galileo, Copernicus and Kepler each offered explanations, but it was the English scientist Sir Isaac Newton who finally discovered the exact principle behind their motion.

The Law of Gravitation

Newton found that every two material bodies in the universe pull each other with a force called gravitation. The same force keeps the heavenly bodies in motion and makes objects fall towards the earth. It is universal because it acts everywhere in the universe and is not changed by heat, pressure, or electric and magnetic fields.

Law of gravitation: any two material bodies in the universe attract each other with a force that (i) is directly proportional to the product of their masses and (ii) is inversely proportional to the square of the distance between them. The force acts along the line joining the centres of mass of the bodies.

Directly proportional: if one quantity becomes a number of times larger (or smaller), the other becomes that many times larger (or smaller). Example: if you buy twice as many books of one kind, you pay twice as much, so N ∝ P (N is the number of books and P the price).

Inversely proportional: if one quantity becomes a number of times larger, the other becomes that many times smaller. Example: if the number of workers N doubles, the time T needed for the same job halves, so \( N \propto \frac{1}{T} \).

The force is mutual: if body 1 pulls body 2 with some force, body 2 pulls body 1 with the same force. The sun pulls the earth, and the earth pulls the sun equally. Consider two bodies of masses M and m separated by a distance d.

The force F between them satisfies F ∝ Mm (8.1) and \( F \propto \frac{1}{d^2} \) (8.2). Combining the two,

\[ F = G\,\frac{Mm}{d^2} \]

G is a constant of proportionality called the universal gravitational constant. It is the same for all bodies; it does not depend on the masses, on the medium around the bodies, or on heat, pressure, and electric and magnetic fields.

G = 6.67 × 10⁻⁸ dyne cm² g⁻² in the CGS system and G = 6.67 × 10⁻¹¹ N m² kg⁻² in the SI system.

Dependence of Gravitational Force on Mass and Distance

Because F is proportional to the product of the masses, larger masses give a larger force. The pull between the earth and a 10 kg body is much greater than that between two 10 kg bodies. If the distance between two bodies is halved, the force becomes four times; if the distance is doubled, the force falls to one-fourth.

Gravity

When one of the two bodies is the earth, gravitation is called gravity. Gravity is the force of attraction between the earth and any body on or near it. The weight of a body is this pull of the earth on it. The body pulls the earth equally, but the earth is so huge that it does not move; the body, if free, moves towards the earth. Its speed grows as it falls, so it has a constant acceleration, called the acceleration due to gravity, g. In the CGS system g = 980 cm s⁻² and in SI g = 9.8 m s⁻².

g differs on different heavenly bodies, because it depends on both the mass and the radius of the body. In the solar system it is largest on the Sun (274.1 m s⁻²) and smallest on Pluto (0.610 m s⁻²). On the moon g = 1.625 m s⁻².

Weight of a body = mass of the body × acceleration due to gravity (W = mg). g also changes from place to place on the earth, so weight does too. It is largest at the poles (9.831 m s⁻²) and smallest at the equator (9.781 m s⁻²).

The weight of a 1 kg mass is written 1 kilogram weight (1 kgwt), and that of a 1 g mass is 1 gram weight (1 gwt).

When different bodies are dropped from the same height, a light body such as a piece of paper takes longer to reach the ground than a heavy one such as a stone. The reason is air resistance: for the paper it is large compared with its own weight, while for the stone it is small compared with its weight.

A freely falling body is one on which no force other than gravity acts. Such a body is weightless. For the same reason we feel lighter in a lift that goes down with uniform acceleration.

Galileo’s laws of freely falling bodies:

1. In vacuum, all bodies fall with equal rapidity.
2. The velocity acquired by a falling body is directly proportional to the time of fall.
3. The distance covered is directly proportional to the square of the time.

Newton’s guinea and feather experiment proved the first law. A guinea (coin) and a feather were released together in a long glass tube. With air in the tube the guinea fell faster and reached the bottom first. After the air was removed and the tube turned over, both reached the bottom together. So, when no opposing force acts, gravity makes all bodies, light or heavy, fall together if they start from rest.

Escape Velocity

A body thrown straight up usually comes back to the earth. But the earth’s gravity becomes weak far away, so a body thrown fast enough can overcome it and never return. The escape velocity is the minimum velocity a body must have to escape the gravity of the earth. For the earth it is about 11.2 km s⁻¹ (the book takes 11.27 km s⁻¹).

The escape velocity from a planet is \( v_e = \sqrt{\frac{2GM}{R}} \), where M and R are the mass and radius of the planet.

Example. If a planet’s mass and radius are both double those of the earth, find its escape velocity.

Solution: \( v = \sqrt{\frac{2G(2M_e)}{2R_e}} = \sqrt{\frac{2GM_e}{R_e}} \), which is the same as the earth’s escape velocity. So the escape velocity of the planet is about 11.2 km s⁻¹ (11.27 km s⁻¹ using the book’s value).

Moon’s Gravitation

On the moon g is one-sixth of its value on the earth, because the moon’s mass is much smaller. A body weighing 6 kgwt on the earth weighs 1 kgwt on the moon.

The moon has no atmosphere. Since the moon’s mass is small, its escape velocity is small, and the speeds of gas particles exceed it. The gases therefore escape, and the moon keeps no atmosphere.

Tides

The water level of the oceans rises and falls again and again, with a gap of 12 hours 26 minutes. This is called a tide. Tides are caused by the gravitational pulls of the moon and the sun on the earth; the sun’s pull is only about 46% of the moon’s.

The spinning of the earth about its axis also helps. It causes a centrifugal (outward) force on everything on the earth, which tends to throw objects away from the centre. They stay in place because of a centripetal force acting opposite to it, which is supplied by gravity. The water particles tend to move outwards because of the centrifugal force, and this adds to the tides.

There are two kinds of tides: high tides and low tides. High tides may be direct (primary) or antipodal (secondary). Suppose place A faces the moon as in the figure.

The water at A is pulled towards the moon and swells up, giving a direct or primary tide. At the opposite (antipodal) place B the pull of the moon is weak, being farther away. Water there swells up too, because of the centrifugal force and a reaction to the pull at A, giving an antipodal or secondary tide. As the water rises at A and B, it falls at D and E, which have low tides.

The earth turns once in 24 hours, so A and B exchange places after 12 hours, and one might expect the direct tide at A to come back after 12 hours. In fact it comes after 12 hours 26 minutes. The reason is that the moon moves forward in its orbit meanwhile (see the figure), and the earth needs 26 more minutes for the place to face the moon again.

So the gap between two successive primary (or secondary) tides at a place is 2 × (12 h 26 min) = 24 hours 52 minutes.

Different Types of Tides

1. Spring tides: high tides that occur on full moon and new moon days, when the sun, the earth and the moon are in a straight line.

On a full moon day the sun and the moon are on opposite sides of the earth, in a straight line.

The place where the moon makes a primary tide is also given a secondary tide by the sun, and vice versa, so the tides reinforce each other.

On a new moon day the sun and the moon are on the same side of the earth, and both make primary tides at the same place.

Spring tides on a new moon day are much stronger than those on a full moon day, because the water is pulled by the moon and the sun together.

2. Neap tides: they occur when the pulls of the moon and the sun on the earth are at right angles to each other.

Neap tides are low tides, because the net pull on the earth is small. They occur at the first and the last quarter phases of the moon.

Good effects of tides: Tidal water makes rivers navigable and washes away the waste in them, which keeps river water clean. Fishes such as Salmon and Hilsa, which swim up rivers to lay eggs (anadromous fishes), are helped into rivers by tidal water, and fishermen catch them in large numbers. Salt is made from sea water that comes on to the land during high tides. The energy of tidal water is used to generate electricity.

Bad effects of tides: Tides can spoil river water and deposit sediments that make navigation hard. They sometimes make fishing difficult, and rivers may overflow because of tidal water, damaging crops and harming people living on the coast.

Constellations and the Zodiac

The stars of the night sky are grouped into patterns called constellations. Ancient scholars named them after people, animals or objects, and astronomers have since identified many more. They are seen from different parts of the earth and in different seasons, and studying them helps us to identify other stars.

From the earth the sun appears to move across the sky. Our ancestors divided its path into twelve parts and named the constellation in each part after its shape. The twelve constellations together are called the zodiac, and each one is called a sign. The table gives each constellation, its shape and the period when it is visible. (The pictures of the twelve signs are not reproduced here.)

Astrologers and almanac makers use the dates in this table. Astronomers have now identified 88 constellations. The biggest is Hydra, which has at least 78 very big stars.

Rocket

There are two kinds of rockets: those used in war and those used to study the atmosphere and outer space. A rocket works on Newton’s third law of motion: to every action there is an equal and opposite reaction. Fuel burns in the combustion chamber to produce hot gases, which rush out through a nozzle at great speed. The gases leave with a great force (the action). As the reaction, the gases push the rocket with an equal force in the opposite direction, and the rocket speeds off. The parts of a rocket are shown in the figure.

Artificial Satellites

Artificial satellites are put into different orbits and do jobs such as communication, radio and TV transmission and weather reporting. They are sent up with a multi-stage launching system in which different rockets are fired in turn. This gives the satellite the least speed needed to reach its orbit and then the proper speed to keep revolving in it. (A picture of a satellite orbiting the earth is not reproduced.)

Artificial satellites orbit the earth, whereas space probes such as Venus 13, Venus 14, Pioneer 10 and Voyager 2 are sent to study other planets.

Travel in Space and on the Moon

People admired the moon for ages and dreamt of walking on it. After years of research, scientists found how to travel in space, and in 1969 American scientists landed on the moon. They sent a spacecraft there, lifted into space by rockets. The table summarises the main space missions, mostly by Russia and the USA with a few other countries.

Uses of space travel

1. Messages, telephone calls and TV programmes can be sent very quickly from one country to another with communication satellites.
2. To explore outer space and study heavenly bodies.
3. To locate water and minerals hidden under the ground and fish in the seas and oceans.
4. To help in navigation and air travel, and in weather forecasting.
5. To study the X-rays and ultraviolet rays in our atmosphere and outer space.
6. To produce electronic goods, alloys, mixtures and vaccines that cannot be made on the earth.
7. To study the causes of cancer.

Space Travel – India

With Russia’s help India put its first artificial satellite, Arya Bhatta, into space, joining the few nations that study space. With Russian help India also set up rocket launching stations at Thumba in Kerala and Sriharikota in Andhra Pradesh.

India has also launched Bhaskara I and II, Rohini, I.R.S, Apple and Insat IA, IB, IC and ID. They are used for telecommunication, radio and TV transmission, weather forecasting, agricultural research and so on. On 22 October 2008 India’s Polar Satellite Launch Vehicle (PSLV-C11) put Chandrayan-1 into its first orbit from Sriharikota, starting the spacecraft’s journey to the moon. This was the first time India sent a spacecraft to the moon.

Winds, Storms and Cyclones

The earth is wrapped in a layer of air extending about 1000 km above the surface, called the atmosphere. It is made of molecules of various gases, and the weight of these gases presses on the earth’s surface, so air exerts pressure.

Activity to show that air exerts pressure: Half fill a metal container with water, heat it for a while, then close it tightly with a cap. When it is cooled strongly, the steam inside condenses and the pressure inside falls, and the container is crushed by the pressure of the air outside.

The pressure of the air is called atmospheric pressure. It is measured with a barometer. Torricelli was the first scientist to design one, so it is called Torricelli’s barometer.

Construction of a Barometer

Take a glass tube about 1 m long, closed at one end, with a narrow uniform bore of 1 cm diameter. Fill it completely with pure, dry mercury, with no air bubbles, and close the open end with your thumb. Invert the tube into a trough of mercury and take the thumb away. Some mercury runs down into the trough and leaves an empty space at the top of the tube, called the Torricellian vacuum. The vertical mercury column that remains exerts a pressure equal to the atmospheric pressure, so its height measures the atmospheric pressure of the place. At sea level the column is usually 76 cm high, so the pressure is 76 cm of mercury. Atmospheric pressure decreases as the altitude increases.

Uses of a barometer

1. It measures the atmospheric pressure at a place.
2. It can be used as an altimeter, to find the height of a place above sea level.
3. Changes in atmospheric pressure shown by it help forecast rain and the coming of storms.

Wind

Moving air is called wind. The air pressure is not the same everywhere, because temperatures at different places differ. Air moves from a region of high pressure to one of low pressure, and the greater the pressure difference, the faster it moves.

Most substances, air included, expand when heated and contract when cooled. When they expand, their volume increases and their density decreases. Warm air is therefore lighter than cold air, so warm air rises and cold air sinks. This is why smoke rises and why exhaust fans are fixed high on walls: warm, exhaled air collects near the top, and the fan pushes it out so that fresh air can enter.

In nature, when warm air rises at a place, the pressure there drops and cooler air from the surroundings rushes in. This sets up convection currents in the air, and wind currents are produced by this uneven heating of the earth.

The equator gets the most heat from the sun, so air there is heated and rises, and cooler air flows in from the belts between 0° and 30° latitude on either side. The warm air at these latitudes also rises, and cold air from the poles moves in. The rotation of the earth affects the movement of these winds.

Monsoon

A monsoon is a seasonal wind that blows for several months. In summer the land near the equator warms faster than the ocean water and is mostly at a higher temperature. Winds carrying water vapour then blow from the ocean towards the land and bring rain; these are the monsoon winds. In winter the direction reverses, from land to ocean. These colder winds carry little moisture and bring little rain.

Thunderstorms and Cyclones

A storm with heavy rain, lightning, thunder and wind, sometimes with hail, is a thunderstorm. Thunderstorms are very common in hot, humid tropical regions. The high temperature there produces strong upward winds that carry water droplets up. When the droplets freeze and fall, their swift motion together with the rising air produces lightning and thunder.

Precautions during a thunderstorm with lightning

1. Do not take shelter under tall, isolated trees.
2. A vehicle with closed windows is a safe shelter.
3. Avoid sitting near a window.
4. An umbrella with a metal tip, open garages and metal sheds are not safe.
5. Do not stay in water during lightning. Come out of the water and stay inside a building.

Cyclone is a violent rotating storm. When water vapour in the air condenses into raindrops, it gives out heat and warms the air around. This warm air rises and the pressure falls, and more and more cool air rushes in towards the centre of the storm. At times the process ends in a very low-pressure system with extremely fast winds spinning around it, which is a cyclone. Wind speed, wind direction, temperature and humidity affect its development.

The centre of a cyclone is called the eye. It is a calm region 10 to 30 km across with no clouds and light winds. A large cyclone has a violently rotating mass of air 10 to 15 km high. Around the eye there is a cloudy region about 150 km wide with high winds, thick clouds and heavy rain.

Destruction: Cyclones cause immense damage. The very low pressure in the eye can raise the sea surface by 3 to 12 m, flooding low coastal areas. Continuous heavy rain and strong winds cause great loss of life and property.

Weak roofs can be lifted and blown off in high winds. When fast wind blows over a roof, the air pressure above the roof falls, while the pressure inside the building is much higher, and this difference lifts the roof. In general, higher wind speed goes with lower air pressure. Two simple activities show this: (1) blow air along the top of a sheet of paper lying on a table, and the paper rises; (2) hang two ping pong balls 10 to 12 cm apart from a stick and blow between them, and they move closer together. So fast moving air has low pressure.

Tornadoes

A tornado is a dark funnel-shaped cloud reaching from the sky to the ground. Its diameter ranges from about 1 m to 1 km. Most are weak, but a violent tornado can move at about 300 km h⁻¹. Because of the low pressure, the funnel sucks dust, debris and anything near its base and throws it out near the top.

Storms and cyclones are low-pressure systems, and wind speed is important in forming them. An anemometer measures wind speed. The meteorological department uses satellites and radar to forecast cyclones and warn people. A cyclone alert (watch) is issued 48 hours in advance and a cyclone warning 24 hours in advance, which helps the government and people to take safety measures.

People in cyclone-prone areas must not ignore warnings and should be well prepared. In a cyclone-hit area, do not drink contaminated water, touch wet switches or power lines, or go out for fun. Cooperate fully with neighbours and the authorities.

Floatation and Density

The density of water is 1 g cm⁻³. Wood, cork, petrol, kerosene, vegetable oil and the like are less dense than water, while iron, gold, silver, stone and glass are denser. Substances denser than water sink in it, and those less dense than water float.

A solid less dense than the liquid floats on it, and it sinks in more in a liquid of smaller density and less and less as the liquid’s density rises.

The density of sea water changes with temperature at different places and when fresh water mixes in, and sea water is denser than fresh water. A ship moving from a denser to a less dense region of the sea may therefore sink. For safety, every ship carries marks on its hull showing how deep it may be immersed at a given place.

Points to Remember

1. Any two material bodies in the universe attract each other with the gravitational force.
2. Newton’s universal law of gravitation: \( F \propto \frac{M_1 M_2}{d^2} \) and \( F = G\,\frac{M_1 M_2}{d^2} \), where G is the universal gravitational constant.
3. The weight of a body is the force of attraction of the earth on it, W = m × g. The value of g on the earth’s surface is 980 cm s⁻² or 9.8 m s⁻².
4. g varies from place to place on the earth: maximum at the poles (9.831 m s⁻²) and minimum at the equator (9.781 m s⁻²).
5. Substances denser than water sink in water, and substances less dense than water float.
6. Bodies falling freely from rest fall with equal rapidity in vacuum; the velocity gained is proportional to the time of fall; the distance travelled is proportional to the square of the time.
7. Escape velocity is the minimum velocity a body needs to escape the earth’s gravity. On the earth it is about 11.2 km s⁻¹ (11.27 km s⁻¹ in the book).
8. g on the moon is 1/6 of g on the earth.
9. Density = mass ÷ volume, and the density of water is 1 g cm⁻³.
10. A barometer measures atmospheric pressure, and near sea level the mercury column is 76 cm high.