Download, print and study this document offline 
Page 1 133 6.1 Newton’s Law of Gravitation Newton’s law of gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Thus the magnitude of the gravitational force F that two particles of masses m 1 and m 2 separated by a distance r exert on each other is given by or F = Also clear that Which is Newton’s third law of motion. Here G is constant of proportionality which is called ‘Universal gravitational constant’. (i) The value of G is 6.67 × 10 –11 Nm 2 kg –2 in S.I and 6.67 × 10 –8 dyne – cm 2 g –2 in C.G.S. system. (ii) Dimensional formula [M –1 L 3 T –2 ]. (iii) The value of G does not depend upon the nature and size of the bodies. (iv) It does not depend upon the nature of the medium between the two bodies. 6.2 Acceleration Due to Gravity The force of attraction exerted by the earth on a body is called gravitational pull or gravity. The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g. If M = mass of the earth and R = radius of the earth and g is the acceleration Page 2 133 6.1 Newton’s Law of Gravitation Newton’s law of gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Thus the magnitude of the gravitational force F that two particles of masses m 1 and m 2 separated by a distance r exert on each other is given by or F = Also clear that Which is Newton’s third law of motion. Here G is constant of proportionality which is called ‘Universal gravitational constant’. (i) The value of G is 6.67 × 10 –11 Nm 2 kg –2 in S.I and 6.67 × 10 –8 dyne – cm 2 g –2 in C.G.S. system. (ii) Dimensional formula [M –1 L 3 T –2 ]. (iii) The value of G does not depend upon the nature and size of the bodies. (iv) It does not depend upon the nature of the medium between the two bodies. 6.2 Acceleration Due to Gravity The force of attraction exerted by the earth on a body is called gravitational pull or gravity. The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g. If M = mass of the earth and R = radius of the earth and g is the acceleration due to gravity, then ? g = (i) Its value depends upon the mass radius and density of planet and it is independent of mass, shape and density of the body placed on the surface of the planet. (ii) Acceleration due to gravity is a vector quantity and its direction is always towards the centre of the planet. (iii) Dimension [g] = [LT –2 ] (iv) It’s average value is taken to be 9.8 m/s 2 or 981 cm/sec 2 , on the surface of the earth at mean sea level. 6.3 V ariation in g with Height Acceleration due to gravity at height h from the surface of the earth g = Also g' = = [As r = R + h] (i) If h << R g' = (ii) If h << R. Percentage decrease . 6.4 V ariation in g with Depth Acceleration due to gravity at depth d from the surface of the earth g' = also g' = (i) The value of g decreases on going below the surface of the earth. (ii) The acceleration due to gravity at the centre of earth becomes zero. Page 3 133 6.1 Newton’s Law of Gravitation Newton’s law of gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Thus the magnitude of the gravitational force F that two particles of masses m 1 and m 2 separated by a distance r exert on each other is given by or F = Also clear that Which is Newton’s third law of motion. Here G is constant of proportionality which is called ‘Universal gravitational constant’. (i) The value of G is 6.67 × 10 –11 Nm 2 kg –2 in S.I and 6.67 × 10 –8 dyne – cm 2 g –2 in C.G.S. system. (ii) Dimensional formula [M –1 L 3 T –2 ]. (iii) The value of G does not depend upon the nature and size of the bodies. (iv) It does not depend upon the nature of the medium between the two bodies. 6.2 Acceleration Due to Gravity The force of attraction exerted by the earth on a body is called gravitational pull or gravity. The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g. If M = mass of the earth and R = radius of the earth and g is the acceleration due to gravity, then ? g = (i) Its value depends upon the mass radius and density of planet and it is independent of mass, shape and density of the body placed on the surface of the planet. (ii) Acceleration due to gravity is a vector quantity and its direction is always towards the centre of the planet. (iii) Dimension [g] = [LT –2 ] (iv) It’s average value is taken to be 9.8 m/s 2 or 981 cm/sec 2 , on the surface of the earth at mean sea level. 6.3 V ariation in g with Height Acceleration due to gravity at height h from the surface of the earth g = Also g' = = [As r = R + h] (i) If h << R g' = (ii) If h << R. Percentage decrease . 6.4 V ariation in g with Depth Acceleration due to gravity at depth d from the surface of the earth g' = also g' = (i) The value of g decreases on going below the surface of the earth. (ii) The acceleration due to gravity at the centre of earth becomes zero. (iii) Percentage decrease . (iv) The rate of decrease of gravity outside the earth (if h << R) is double to that of inside the earth. 6.5 Gravitational Field The space surrounding a material body in which gravitational force of attraction can be experienced is called its gravitational field. Gravitational Field intensity : The intensity of the gravitational field of a material body at any point in its field is defined as the force experienced by a unit mass (test mass) placed at that point. If a test mass m at a point in a gravitational field experiences a force 6.6 Gravitational Potential At a point in a gravitational field potential V is defined as negative of work done per unit mass in shifting a test mass from some reference point (usually at infinity) to the given point. Negative sign indicates that the direction of intensity is in the direction where the potential decreases. Gravitational potential V = 6.7 Gravitational Potential Energy The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force. W = This work done is stored inside the body as its gravitational potential energy ? U = If r = 8 then it becomes zero (maximum). 6.8 Escape V elocity The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity. I Page 4 133 6.1 Newton’s Law of Gravitation Newton’s law of gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Thus the magnitude of the gravitational force F that two particles of masses m 1 and m 2 separated by a distance r exert on each other is given by or F = Also clear that Which is Newton’s third law of motion. Here G is constant of proportionality which is called ‘Universal gravitational constant’. (i) The value of G is 6.67 × 10 –11 Nm 2 kg –2 in S.I and 6.67 × 10 –8 dyne – cm 2 g –2 in C.G.S. system. (ii) Dimensional formula [M –1 L 3 T –2 ]. (iii) The value of G does not depend upon the nature and size of the bodies. (iv) It does not depend upon the nature of the medium between the two bodies. 6.2 Acceleration Due to Gravity The force of attraction exerted by the earth on a body is called gravitational pull or gravity. The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g. If M = mass of the earth and R = radius of the earth and g is the acceleration due to gravity, then ? g = (i) Its value depends upon the mass radius and density of planet and it is independent of mass, shape and density of the body placed on the surface of the planet. (ii) Acceleration due to gravity is a vector quantity and its direction is always towards the centre of the planet. (iii) Dimension [g] = [LT –2 ] (iv) It’s average value is taken to be 9.8 m/s 2 or 981 cm/sec 2 , on the surface of the earth at mean sea level. 6.3 V ariation in g with Height Acceleration due to gravity at height h from the surface of the earth g = Also g' = = [As r = R + h] (i) If h << R g' = (ii) If h << R. Percentage decrease . 6.4 V ariation in g with Depth Acceleration due to gravity at depth d from the surface of the earth g' = also g' = (i) The value of g decreases on going below the surface of the earth. (ii) The acceleration due to gravity at the centre of earth becomes zero. (iii) Percentage decrease . (iv) The rate of decrease of gravity outside the earth (if h << R) is double to that of inside the earth. 6.5 Gravitational Field The space surrounding a material body in which gravitational force of attraction can be experienced is called its gravitational field. Gravitational Field intensity : The intensity of the gravitational field of a material body at any point in its field is defined as the force experienced by a unit mass (test mass) placed at that point. If a test mass m at a point in a gravitational field experiences a force 6.6 Gravitational Potential At a point in a gravitational field potential V is defined as negative of work done per unit mass in shifting a test mass from some reference point (usually at infinity) to the given point. Negative sign indicates that the direction of intensity is in the direction where the potential decreases. Gravitational potential V = 6.7 Gravitational Potential Energy The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force. W = This work done is stored inside the body as its gravitational potential energy ? U = If r = 8 then it becomes zero (maximum). 6.8 Escape V elocity The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity. I 136 If v e is the required escape velocity, then (i) Escape velocity is independent of the mass and direction of projection of the body. (ii) For the earth, v e = 11.2 km/sec (iii) A planet will have atmosphere if the velocity of molecule in its atmosphere is lesser than escape velocity. This is why earth has atmosphere while moon has no atmosphere. 6.9 Kepler’s laws of Planetary Motion (1) The law of Orbits : Every planet moves around the sun in an elliptical orbit with sun at one of the foci. (2) The law of Area : The line joining the sun to the planet sweeps out equal areas in equal interval of time. i.e., areal velocity is constant. According to this law planet will move slowly when it is farthest from sun and more rapidly when it is nearest to sun. It is similar to law of conservation of angular momentum. Areal velocity = (3) The law of periods : The square of period of revolution (T) of any planet around sun is directly proportional to the cube of the semimajor axis of the orbit. T 2 ? a 3 or T 2 ? where a = semimajor axis r 1 = Shortest distance of planet from sun (perigee). r 2 = Largest distance of planet from sun (apogee). Page 5 133 6.1 Newton’s Law of Gravitation Newton’s law of gravitation states that every body in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Thus the magnitude of the gravitational force F that two particles of masses m 1 and m 2 separated by a distance r exert on each other is given by or F = Also clear that Which is Newton’s third law of motion. Here G is constant of proportionality which is called ‘Universal gravitational constant’. (i) The value of G is 6.67 × 10 –11 Nm 2 kg –2 in S.I and 6.67 × 10 –8 dyne – cm 2 g –2 in C.G.S. system. (ii) Dimensional formula [M –1 L 3 T –2 ]. (iii) The value of G does not depend upon the nature and size of the bodies. (iv) It does not depend upon the nature of the medium between the two bodies. 6.2 Acceleration Due to Gravity The force of attraction exerted by the earth on a body is called gravitational pull or gravity. The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g. If M = mass of the earth and R = radius of the earth and g is the acceleration due to gravity, then ? g = (i) Its value depends upon the mass radius and density of planet and it is independent of mass, shape and density of the body placed on the surface of the planet. (ii) Acceleration due to gravity is a vector quantity and its direction is always towards the centre of the planet. (iii) Dimension [g] = [LT –2 ] (iv) It’s average value is taken to be 9.8 m/s 2 or 981 cm/sec 2 , on the surface of the earth at mean sea level. 6.3 V ariation in g with Height Acceleration due to gravity at height h from the surface of the earth g = Also g' = = [As r = R + h] (i) If h << R g' = (ii) If h << R. Percentage decrease . 6.4 V ariation in g with Depth Acceleration due to gravity at depth d from the surface of the earth g' = also g' = (i) The value of g decreases on going below the surface of the earth. (ii) The acceleration due to gravity at the centre of earth becomes zero. (iii) Percentage decrease . (iv) The rate of decrease of gravity outside the earth (if h << R) is double to that of inside the earth. 6.5 Gravitational Field The space surrounding a material body in which gravitational force of attraction can be experienced is called its gravitational field. Gravitational Field intensity : The intensity of the gravitational field of a material body at any point in its field is defined as the force experienced by a unit mass (test mass) placed at that point. If a test mass m at a point in a gravitational field experiences a force 6.6 Gravitational Potential At a point in a gravitational field potential V is defined as negative of work done per unit mass in shifting a test mass from some reference point (usually at infinity) to the given point. Negative sign indicates that the direction of intensity is in the direction where the potential decreases. Gravitational potential V = 6.7 Gravitational Potential Energy The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force. W = This work done is stored inside the body as its gravitational potential energy ? U = If r = 8 then it becomes zero (maximum). 6.8 Escape V elocity The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity. I 136 If v e is the required escape velocity, then (i) Escape velocity is independent of the mass and direction of projection of the body. (ii) For the earth, v e = 11.2 km/sec (iii) A planet will have atmosphere if the velocity of molecule in its atmosphere is lesser than escape velocity. This is why earth has atmosphere while moon has no atmosphere. 6.9 Kepler’s laws of Planetary Motion (1) The law of Orbits : Every planet moves around the sun in an elliptical orbit with sun at one of the foci. (2) The law of Area : The line joining the sun to the planet sweeps out equal areas in equal interval of time. i.e., areal velocity is constant. According to this law planet will move slowly when it is farthest from sun and more rapidly when it is nearest to sun. It is similar to law of conservation of angular momentum. Areal velocity = (3) The law of periods : The square of period of revolution (T) of any planet around sun is directly proportional to the cube of the semimajor axis of the orbit. T 2 ? a 3 or T 2 ? where a = semimajor axis r 1 = Shortest distance of planet from sun (perigee). r 2 = Largest distance of planet from sun (apogee). 137 • Kepler’s laws are valid for satellites also. 6.10 Orbital Velocity of Satellite ? v = [r = R + h] (i) Orbital velocity is independent of the mass of the orbiting body. (ii) Orbital velocity depends on the mass of planet and radius of orbit. (iii) Orbital velocity of the satellite when it revolves very close to the surface of the planet. v = 6.11 Time Period of Satellite T = = [As r = R + h] (i) Time period is independent of the mass of orbiting body (ii) T 2 ? r 3 (Kepler’s third law) (iii) Time period of nearby satellite, T = For earth T = 84.6 minute ˜ 1.4 hr. 6.12 Height of Satellite h = 6.13 Geostationary Satellite The satellite which appears stationary relative to earth is called geostationary or geosynchronous satellite, communication satellite. A geostationary satellite always stays over the same place above the earth. The orbit of a geostationary satellite is known as the parking orbit. (i) It should revolve in an orbit concentric and coplanar with the equatorial plane. (ii) It sense of rotation should be same as that of earth. (iii) Its period of revolution around the earth should be same as that of earth.Read More
102 videos416 docs121 tests

1. What is gravitation and how does it work? 
2. What is the difference between weight and mass? 
3. How does the value of gravitational acceleration change with height? 
4. What is the significance of Newton's Universal Law of Gravitation? 
5. Can the force of gravity be completely eliminated? 

Explore Courses for NEET exam
