1. GRAVITATION

2. SECTION 1

3. OVERVIEW
• Gravitation
• Geocentric model
• Heliocentric model
• Newton’s law of Gravitation
• Characteristics of Gravitational force
• Principle of Superposition
• Inertial and gravitational Mass
• Kepler’s law of planetary motion
- I law
- II law
- III law
• Other points to remember

4. GRAVITATION
• It is a natural phenomenon by which objects in
the universe, attract each other due to their
masses
• Force of attraction is called Gravitational force,
which is one of the fundamental forces of nature
• Gravitational interaction between any pair of
bodies in the universe is governed by “Newtons’
Universal Law of Gravitation”
• Ptolemy proposed the geocentric model
• Copernicus proposed the heliocentric model

5. GEOCENTRIC MODEL
• Geocentric model, any
theory of the structure of
the solar system (or the
universe) in which Earth is
assumed to be at the centre
of it all.
• The most highly developed
geocentric model was that
of Ptolemy of
Alexandria (2nd century CE).

6. HELIOCENTRIC MODEL
• In the heliocentric (Sun-
centered) model, the
Earth is just one out of
many planets, all of
which orbit the Sun in
elliptical orbits.

7. HELIOCENTRIC MODEL
• The Coperican model introduced several
innovative ideas:
– The Earth is one of several planets revolving around a
stationary Sun in different orbits.
– The Earth has three motions: daily rotation, annual
revolution, and annual tilting of its axis.
– Retrograde motion of the planets is explained by the
Earth's motion.
– The distance from the Earth to the Sun is small
compared to the distance from the Sun to the stars.

8. NEWTON’S LAW OF GRAVITATION
• Newton’s Law of Universal Gravitation states that every
particle attracts every other particle in the universe with
force directly proportional to the product of the masses and
inversely proportional to the square of the distance between
them.

9. NEWTON’S LAW OF GRAVITATION
• Particle 1 exerts force on Particle 2
• Similarly Particle 2 exerts force on Particle 1

10. Universal Gravitational Constant
• The universal gravitational constant is the
gravitational force acting between two bodies
of unit mass, kept at a unit distance from each
other. Its value is 6.67×10−11 Nm2kg-2.
• The gravitational constant G was first
measured in 1797–98 by the English
scientist Henry Cavendish.

11. Universal Gravitational Constant

12. CHARATERISTICS OF GRAVITATIONAL
FORCE
• The gravitational force acting between two
masses are equal in magnitude and opposite
in direction, which forms an action and
reaction pair.
• The gravitational force is always attractive.
EXPLANATION: Masses always attract each
other. So, the gravitational force is always
attractive. If there were repulsive gravitation
forces, it means an object has a negative mass.

13. CHARATERISTICS OF GRAVITATIONAL
FORCE
• The force does not depend on the presence or
absence of other bodies.
• It is a central force, acting along the line
joining the two interacting particles
• Gravitational constant is independent of the
intervening medium separating the bodies
• Gravitational Force is the weakest force
because of the Gravitational constant.

14. CHARATERISTICS OF GRAVITATIONAL
FORCE
• It is negligibly small in case of light bodies but
becomes quite significant in case of massive
bodies like planets, satellites and stars
• It is a long-range force i.e., it is effective even
if distance between the interacting particles is
very large.
• It is a conservative force. Hence potential
energies are associated with gravitational
forces.

15. PRINCIPLE OF SUPERPOSITION

16. INERTIAL AND GRAVITATIONAL MASS

17. Kepler’s law of planetary motion –
First Law

18. Kepler’s law of planetary motion –
Second Law

19. Kepler’s law of planetary motion –
Second Law

20. Kepler’s law of planetary motion –
Second Law

21. Kepler’s law of planetary motion –
Third Law

22. Other points to remember

23. Other points to remember

24. Other points to remember

25. SECTION 2

26. OVERVIEW
• Acceleration due to gravity
• Variation of acceleration due to gravity
- Effect of Altitude (Height from the surface)
- Effect of Depth below the surface of the
Earth
- Effect of the shape of the Earth
- Effect of Rotation of the Earth

27. ACCELERATION DUE TO GRAVITY
• The force of attraction between two bodies
produces acceleration of the bodies towards
each other
• Force of attraction between Earth (mass – M)
and body (mass – m) on the earth’s surface,

28. ACCELERATION DUE TO GRAVITY
(contd.)
• The force gives an acceleration a=g towards
the centre of the earth on the mass m

29. VARIATION OF ACCELERATION DUE TO GRAVITY –
EFFECT OF ALTITUDE (HEIGHT FROM THE SURFACE)

30. EFFECT OF ALTITUDE (HEIGHT FROM
THE SURFACE)

31. EFFECT OF DEPTH BELOW THE
SURFACE OF THE EARTH

32. EFFECT OF DEPTH BELOW THE
SURFACE OF THE EARTH

33. EFFECT OF SHAPE OF THE EARTH

34. EFFECT OF ROTATION OF EARTH

35. IMPORTANT POINTS

36. IMPORTANT POINTS

37. SECTION 3

38. OVERVIEW
• Gravitational field
• Gravitational Field Intensity due to Spherical Mass Distribution
(a) For solid sphere of mass M and Radius R
(b) For a Spherical shell of Mass M and Radius R
• Graphical Representation
(a) Variation of Acceleration due to gravity (g) versus Distance (r)
(b) Variation of Gravitational Field Intensity (E) versus Distance (r)
• Gravitational Field Intensity due to a thin uniform ring at a point on its axis
• Gravitational Field Intensity due to a Uniform Disc at a point on its axis
• Gravitational Potential
• Gravitational potential due to a Solid Sphere
• Gravitational Potential due to a Spherical Shell (Hollow Sphere)
• Gravitational Potential due to a Ring
• Gravitational Potential due to a Disc
• Relation between Gravitation field Intensity and Gravitational Potential

39. Gravitational Field
• The space around a body where its
gravitational influence can be felt is called
Gravitational field of the body

40. Gravitational Field

41. Gravitational Field Intensity due to
Spherical Mass Distribution
(a) For solid sphere of mass M and Radius R

42. Gravitational Field Intensity due to
Spherical Mass Distribution – Solid
sphere

43. Gravitational Field Intensity due to
Spherical Mass Distribution
(b) For a Spherical shell of Mass M and Radius R

44. Variation of Acceleration due to
gravity (g) versus Distance (r)

45. Variation of Gravitational Field
Intensity (E) versus Distance (r) –
Solid sphere

46. Variation of Gravitational Field
Intensity (E) versus Distance (r) –
Spherical Shell

47. Gravitational Field Intensity due to a
thin uniform ring at a point on its axis

48. Gravitational Field Intensity due to a
thin uniform ring at a point on its axis

49. Gravitational Field Intensity due to a
Uniform Disc at a point on its axis

50. GRAVITATIONAL POTENTIAL
• It is equal to the work done by an external
agency in taking a unit mass from infinity to a
point near a body of mass M against its
gravitational force of attraction, without
acceleration.

51. GRAVITATIONAL POTENTIAL

52. GRAVITATIONAL POTENTIAL
DIFFERENCE
• Gravitational potential difference between
two points is the work done by an external
agency to move unit mass from one point to
another point inside the gravitational field
without any acceleration

53. Gravitational potential due to a Solid
Sphere

54. Gravitational Potential due to a
Spherical Shell (Hollow Sphere)

55. Gravitational Potential due to a Ring

56. Gravitational Potential due to a Disc

57. Relation between Gravitation field
Intensity (E) and Gravitational
Potential (V)

58. SECTION 4

59. OVERVIEW
• Gravitational Potential Energy (U)
• Gravitational Potential Energy of a system of two particles
• Gravitational Potential Energy of three particle system
• Change in potential energy (or) Work done to raise a body of mass
m to a height h above the surface of earth
• Velocity required to project a body to a height h from the surface of
earth
• Maximum height attained by a body when it is projected with a
velocity v from the surface of the earth
• ‘Gravitational self energy’ of bodies
• Escape velocity
• Gravitational Binding energy (or) Escape Energy
• Velocity of body at infinity when projected with a velocity of nve
from the surface of Earth or any other planet

60. Gravitational Potential Energy (U)
• It is the work done by an external agency in
moving a mass from infinity to a point inside
the gravitational field of another mass against
the force of attraction of the second mass
without any acceleration

61. Gravitational Potential Energy (U)

62. Gravitational Potential Energy (U)

63. Gravitational Potential Energy of a
system of two particles
• Potential energy of the system
• Work done in separating the masses to infinite distance
• Work done in reassembling the
system

64. Gravitational Potential Energy of
Three particle system

65. Change in potential energy (or) Work done to
raise a body of mass m to a height h above the
surface of earth

66. Change in potential energy (or) Work
done to raise a body of mass m to a
height h above the surface of earth

67. Velocity required to project a body to
a height h from the surface of earth
• It is also the velocity with which a body will hit the ground
when it is dropped from a height h.

68. Maximum height attained by a body
when it is projected with a velocity v
from the surface of the earth

69. Gravitational Self Energy of Bodies
• Energy possessed by a body due to interaction
of particles inside the body is called self
energy of the body
• Self energy of the body is the negative of the
work done by the gravitational forces on
assembling together its infinitesimally
particles from infinity to their corresponding
configuration in order to make the desired
body.

70. Gravitational Self Energy of Bodies

71. ESCAPE VELOCITY
• It is the minimum velocity required to escape
from the gravitational field of a celestial body
such as a planet.
• The magnitude of escape velocity depends on
the mass of the planet and distance from it.

72. ESCAPE VELOCITY (contd.)

73. ESCAPE VELOCITY (contd.)
• Escape velocity does not depend on
(i) mass of the body
(ii) angle of projection

74. Gravitational Binding Energy (or)
Escape Energy
• Binding energy is the negative of the total
energy possessed by a satellite.
• Binding energy or escape energy of a satellite
is defined as the minimum amount of energy
required to be supplied to it in the form of
kinetic energy to free the satellite from
gravitational influence of the planet.

75. Gravitational Binding Energy (or)
Escape Energy

76. Velocity of body at infinity when projected with
a velocity of nve from the surface of Earth or
any other planet

77. SECTION 5

78. OVERVIEW
• Satellites in Circular orbits
• Expression for orbital velocity
• Angular velocity and time period of a Orbiting satellite
• First and second Cosmic velocities
• Energy of an Orbiting Satellite
• Geostationary Satellites
• Polar Satellites
• Angular Momentum of a satellite
• Nature of trajectory
• Weightlessness

79. Satellites in Circular orbits
• Satellites are launched in circular orbits.
Consider a satellite in an orbit of radius r=R+h
where R is the radius of the earth and h is the
height above the Earth at which the satellite is
orbiting.

80. EXPRESSION FOR ORBITAL VELOCITY

81. ANGULAR VELOCITY AND TIME
PERIOD OF A ORBITING SATELLITE

82. FIRST AND SECOND COSMIC
VELOCITIES

83. Energy of an Orbiting Satellite

84. Geostationary Satellites
• These satellites have time period same as that
of the earth so that their position in the orbit
is stationary with respect to the earth.

85. Geostationary Satellites

86. POLAR SATELLITES

87. Angular Momentum of a satellite

88. NATURE OF TRAJECTORY
• Let a satellite be projected
from certain height from
earth’s surface with a velocity v
along the x-direction as shown
in the figure

89. NATURE OF TRAJECTORY (Contd.)

90. WEIGHTLESSNESS
• A body in a satellite orbiting around earth
experiences apparent weightlessness. This is
because its weight W is used to provide the
required centripetal force for circular motion
around the earth.
• Apparent weight of a free falling body is zero.
Hence a body in a orbiting satellite is
equivalent to a free falling body.

91. WEIGHTLESSNESS (Contd.)

92. WEIGHTLESSNESS (Contd.)