GEO-STARIONARY SATELLITE

A geostationary satellite appears stationary for an observation on earth. For a satellite to be Geo-stationary, it must satisfy the following two conditions

1)   Its orbit must lay the equatorial plane of the earth.

2)   Its period and direction of rotation must be same as the period and direction of earth’s rotation about its axis.

The orbit from which the two periods are equal is called a parking orbit or synchronous geostationary orbit or geosynchronous orbit.

                        WEIGHTLESSNESS

Weightlessness: Consider a person getting into a lift to go up a tall building. Suppose the flour is on a weighting scale that displays a weight of the person. Before the lift starts, the scale should read the true weight. But as the lift accelerates upward the scale will displays excess weight corresponding to the value m (g+a). Any time the lift stops and attain a constant upward speed, the scale will give true weight. After taking a view of the city, as the person accelerates downwards, the scale will read reduced weight corresponding to W= m (g-a). So the scale basically measures the relative acceleration due to gravity and due to lift. For a=g, as in free fall, W=0, and the sense of weightlessness arises. Spacecraft in circular orbit around the earth are also in free fall, so everything is weightless. In fact, if the cabin in the spacecraft is accelerating in free space with acceleration g, there is no experiment which can determine whether the experimenter is in such an accelerating spaceship or on the surface of planet of gravitational acceleration g. This is a manifestation of the” principal of equivalence” between gravitational and inertial mass that led Einstein to formulate his gravitational theory of general relativity.

When the weight of a body becomes zero, it is said to be in the state of weightlessness. That a person in a freely falling lifts feels weightlessness has already been discussed in chapter 4. Here we will discuss the same phenomenon in an orbiting spacecraft.

FREE FALL

If a body falling freely under the action of gravity alone negligence of air resistance, the motion is called free fall.

In fact, a body falling in a vacuum or in space is the free fall. One of the examples of free fall could be the body falling on the surface of the moon. This is because the moon has no atmosphere around it. The acceleration of a body in the free fall is equal to acceleration due to gravity “g”. In this condition, the body is in weightlessness. This is because the body feels zero reaction force.

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ESCAPE VELOCITY AND THE SIZE OF BLAC HOLE

The process of formation of stars and their evolution will be discussed in some detail in part 2 of the book. Here, we will use the concept of escape velocity to calculate some features of black hole.

In very massive stars (m greater than 3 solar masses) the gravity may become so strong that even light emitted from its surface will not escape and will be pooled back by the gravitational force. In other words escape velocity from such a star is greater than the speed of light in vacuum. Light or radiation of any kinds does not escape from such stars. Nobody can observe it directly. It is completely black, hence the name” black hole” The existence of black hole is inferred by depletion suffered by another body. Any body includes light, coming close enough is swallowed by the black hole. It is suggested that there is a giant black hole at the center of our Milky Way galaxies and its mass is several million times the solar mass. Many galaxies may have black hole at their center.

SATELLITE

A body circling a planet is called satellite. Moon is a natural satellite of the earth. A man made satellite is also called an artificial satellite.

APPLICATION OF ARTIFICIAL SATELLITE

Artificial satellites have found a wide variety of application. Some of them are listed below:

1)   They are used for scientific investigation on the condition in the upper atmosphere, weather study, ecology, remote sensing etc.

2)   They are used for taking photographs of vital installation for intelligence gathering activities.

3)   They are used to study the radiation coming from outer space and from out space and for intelligence gathering activities.

4)   Geostationary satellite are used mostly for communication, transmit TV programs from one part of the world to another, internet and electronic communication.

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ACCELERATION DUE TO GRAVITY

 

All bodies near the earth’s surface are attracted by earth towards its centre. This property is called gravity. Gravity is the force of attraction exerted by the earth on the bodies lying on or near its surface and the term is reserved for bodies on the earth’s surface only. For bodies on the surface of other planets or satellite, one uses the term gravitation.

If the body is free to move, earth’s gravity will produce an acceleration. This acceleration is called acceleration due to gravity and is denoted by g. Its magnitude is same for all bodies irrespective of their masses. Besides earths, all other heavenly bodies also possesses gravitation and hence acceleration due to it. The acceleration due to gravitation on the lunar surface is g/6 where as gravitational acceleration on the sun is 27g.

GRAVITATIONAL FIELD

The phenomenon of gravitation has been presented, so far, by using Newton’s law of universal gravitation. Accordingly, a body exerts gravitational force on other body at the distance. This viewpoint is to present the effect of gravitation through fields. Accordingly every point in space around the massive body (mass M) is thought to possess a value for the magnitude of force that would act on a unit mass at that point, and a direction of force. Then, any other masses m brought at that point will experience a force equal to the value of the force acting on a unit mass at that point multiplied by the mass m. We say that the massive body M, also called gravitating body, has created a gravitational field around itself. It interacts with any other mass through this gravitational field.

In this way, by gravitational field, we mean the region around a massive body where a force a gravitational can be experienced.

                          

                        EXCAPE VELOCITY

If we throw a body vertically upwards, it returns to the thrower. If it is thrown turns with a larger velocity, it attains a greater height but again returns back. If we keep increasing the velocity the body would rise too infinitely and may not return to the thrower. This velocity is called escape velocity. In other words, it will escape the gravitational pull of the earth (or planets) and go into outer space.

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SPECIAL FEATURES OF GRAVITATIONAL FORCE

     The gravitational force between two bodies constitute on action and reaction pair. If the force exerted by the mass m1 and mass m2 is called action. Then the force exerted by the mass m2 on the mass m1 is to be called reaction. Clearly, these forces are equal in magnitude but oppositely directed.                                                                      

 

1) The gravitational force between two bodies does not depend upon the nature of the intervening medium. This rule out the possibilities of making gravity screens. The gravitational force between two bodies of masses m1 and mass m2 are same whatever be the medium like air, water, glass etc. between them. That is, we cannot alert the value of gravitational force between two bodies without varying their mass and distance between their centers. Thus, gravitational force between two bodies does not depend upon the or absence of others bodies in between other nearby these bodies

 The gravitational force between light bodies is extremely small and hence such smaller force is not felt in practice. However, it becomes appreciable in the case of massive bodies. This is clear from the following example:

Suppose your friend have the same mass of 40 kg and are standing at the separation of 1 m. The mutual force of attraction between you is given by,

                 =6.67×10ˉˡˡ×40×40/ (1)²

                 = 1.067×10-7N

This is a force of negligible magnitude in our daily life. Thus, the gravitational force between you and you friend does not stick you and your friend standing nearby.

The distance between the sun and the earth is about 1.5×10-7 km. The gravitational force between then is of the order of 10-7 km. The gravitational force between then is of the order of 1027 N, which cannot be ignored. Thus, the earth revolves around the sun due to the gravitational force of such large magnitude.

 

EF       EFFECTS OF GRAVITY

Gravity plays a vital role in our everyday life as well. Some of the effects are as follows:

1)   We are able to stand up, run and perform other activities freely due to gravity of the earth. On the surface of the moon, we cannot push a body as done on the surface of the earth; otherwise the body gets thrown away in space and never returns again to the surface of the moon. This is because of small gravity of moon.

2)   Construction of building and bridges is possible due to the gravity of the earth.

3)   There will be no atmosphere around the earth in the absence of gravity of the earth. Thus, it makes life possible on the earth. There will be no season change without atmosphere .as the gravity of the moon is very small, it does not have atmosphere.

4)   If a body is thrown upwards, its motion is opposed by gravity of the earth. So, it falls back to the earth.

5)   Tides occur by the gravity of the moon on ocean water. As mass of ocean water is grater, there is more force of gravity in between the water and the moon. It results the pull of water due to which ocean level increases and tide occurs. The flowing property of liquid also supports the process.

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CHARACTERTICS OF GRAVITATIONAL FORCE

i)                 It is always attractive

ii)             It is independent of the medium between the bodies. In contrast electric and magnetic forces are medium dependent.

iii)          It holds good over a wide range of distances ranging from interatomic distance to intergalactic distance. Its range is infinitive.

iv)           Gravitational force is conservative.

v)              The presence of solar system and planets revolve round the sun due to the presence of gravitational force.

vi)           The presence of atmosphere on the earth is due to the gravitational force.

vii)       The gravitational force of the earth keeps us firmly on the surface of the earth.

viii)    Tides in seas and oceans are due to the gravitational force of the sun and moon.

PROPERTIES OF G

1.   The value of G is independent of the nature and chemical composition of the masses of the bodies, and the medium in which the bodies are occurred.

2.   The value of G is unaffected by temperature and pressure.

VALUE OF G

A scientist henry Cavendish determined the value of G experimentally by using extra sensitive apparatus, The value of G is 6.67×10ˉˡNm²kgˉ².

GRAVITATIONAL CONSTANT G

If m1=m2=1 unit and r=1 unit, then, equation(7.1) reduces to G=F

Universal gravitational constant G is numerically equal to the force of attraction between two unit point masses separated by unit distance. Its value is 6.673×10-ˡˡ Nm²kg² in SI and 6.673×10-8 dyne cm²/g² in CGS system. Its dimensional formulae is mˉˡl³tˉ²

The value of G is same everywhere between all bodies in the universe. All our observation confirm this. Newton’s law of universal gravitation is applicable to bodies as small as electronic and atoms and as big as galaxies and cluster of galaxies.

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GRAVITATION

INTRODUCTION

We are already familiar with the term ‘gravity’ and ‘gravitation’ from chapter 3 and 5, in which kinematics of freely falling objects under gravity and conservation force were discussed. Galileo studied the motion of falling bodies systematically. Newton was the first to realize that the weight of the object on the earth’s surface was due to the force of attraction between the objects and the earth. He also realized that this attraction is universal between any two objects in the universe. In 1660, at the age of 23 he discovered his famous law of universal gravitation and published in his book ‘Principal Mathematica’

In this chapter, we will study Newton’s law of gravitation and apply it to the study of the motion of planets and satellites.

NEWTON’S LAW OF UNIVERSAL GRAVITATION

Historically, in 1665, the college at Cambridge, where Sir Isaac Newton studied, was closed due to plague. So, he went to his home in Lincolnshire. One day, according to a popular story, while sitting under an apple tree he saw an apple falling to the earth. That incident set him to think about gravitation. It occurred to him that the force responsible for a body(or apple) to fall to earth is also responsible for providing centripetal force to keep the moon moving round the earth in a close orbit. Accelerations possessed by the moon and the falling body might have the same origin.

Newton also assumed that both centripetal acceleration and acceleration of free fall are directed towards the centre of the earth acting on the moon and the apple respectively.

The acceleration due to gravity g was known to be equal to 9.8 m/s². Centripetal acceleration was calculated by Newton using expression a=ŵ²r=4Π²r/T² and it was found to be 2.72×10-³m/s². In this calculation T- period of rotation of the moon – was taken as 27.3 days and r-earth-moon distance as 3.84×10^8m.

This expression shows that acceleration, and hence, force is inversely proportional to the square of its distances from the centre of the earth. Newton was able to justify this result only by assuming the mass of the earth to be concerned at centre of the earth.

These ideas generalized by Newton in his well known law of gravitation, are given in the statement below:

“Everybody in the universe attracts every other body which is directly proportional to the product of masses and inversely proportional to the square of  distance between their centre.

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VECTORS

1. Scaler and Vectors

All physical quantities can be divided into two categories: Scaler and vectors.

SCALERS: Physical quantities which have only magnitude but no direction are called scalers. Mass, length, time, volume, speed, density, work, energy, power, temperature, specific heat, entropy, charge, electric current, electric potential, frequency etc. belong to this category.

Scaler quantity can be specified by a numerical value and a unit. For example, if one says that the average speed of a bicycle is 25 km/hr, 25 is the number(numerical value) and km/hr is the unit in which the speed has been expressed. This of course, does not say anything about the direction in which the bicycle is going. Scalers, being numbers, can be added algebraically.

VECTORS: Physical quantities, which has both magnitude as well as direction are called vectors. Velocity, acceleration, displacement, force, current density, electric and magnetic field, intensities etc belong to this category. Vector quantity can be specified by a unit, a numerical value and a statement about its direction. For example, if one says that the average velocity of a bicycle is 25 km/hr towards east, then this physical quantity has a numerical value25. a unit km/hr and a direction as east. Therefore, velocity is a vector.

The rule of ordinary algebra donot apply to vectors. For example, addition of two equal forces each of magnitude 2N can produce any resultant force from zero to 4N depending on direction of forces being added. In this chapter, we will define addition and multiplication rules for vectors and derive expressions for a resultant.

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