2. Flow of chapter
• Introduction of Gravitation
• Kepler’s Law of Planetary motion
• Universal law of gravitation
• Gravitational constant
• Acceleration due to gravity on earth
• Gravitational potential energy
• Escape velocity
• Earth satellites
• Energy of orbiting satellites
• Geostationary and polar satellite
• Weightlessness
3. Introduction
Whenever we throw an object towards the sky, it falls back to the
ground. For example: a ball comes down when thrown up; rain
drops fall towards the ground.
There is a force due to which all bodies are attracted towards the
earth, known as gravitation.
Gravitation is the force of attraction between all massive bodies in
the universe.
In this chapter we will take a look at gravitational force and laws
governing gravitation. We will also study about planetary and
satellite motion.
5. Law of orbits (first law)
Each planet revolves around the sun in an elliptical
sun situated at the one of the two foci.
orbit with the
6. Law of areas (second law)
The radius vector drawn from the sun to a planet sweeps out equal
areas in equal intervals of time i.e the areal velocity ( area covered
per unit time) of a planet around the sun is constant.
7. Law of periods (third law)
• Kepler's third law states that the square of the period is
proportional to the cube of the semi-major axis of the orbital
8. Newton's universal law of gravitation
Gravitational force F ,is always attractive, and it depends only on the
masses involved and the distance between them. Every object in the
universe attracts every other object with a force along a line joining
them.
The equation for Newton’s law of gravitation is:
• Fg is the gravitational force between m1 and m2
• G is the gravitational constant
9. Evidence in support of law of gravitation
• The rotation of the earth around the sun or that of the moon
around earth is explained on the basis of this law.
• The tide are formed in ocean due to the gravitational
force of attraction between earth and the moon.
• The value of g can be used to predict the orbits and time
period of an satellite.
10. Important feature of law of gravitation
• The Gravitation force between two masses is independent of the
intervening medium.
• The mutual gravitational forces between two bodies are equal and
opposite i.e. Gravitational Forces obey Newton’s third law of motion.
• The gravitational force is an conservative force.
• The law of gravitation holds only for point masses.
• The gravitational force between two point masses is a central force.
Its magnitude depends only on r and has no angular dependence .
• The Gravitational force between two bodies is independent of the
presence of other bodies.
11. Acceleration due to gravity
Near the surface of Earth, the acceleration due to gravity is
approximately constant. But, at large distances from the Earth, or
around other planets or moons, it is varying. The acceleration due to
gravity depends on the terms as the following
Suppose a mass ‘m’ is situated outside the earth at a distance ‘r’
from it Centre . The gravitational force on the mass is
As the height (h) is negligibly small compared to the radius of the
earth we re-frame the equation as follows,
f = GmM
r2
Now equating both the expressions,
mg = GmM
r2
⇒ g = GM
r2
By the above equation we can say that Acceleration due to gravity
is independent on mass of object
12. Acceleration at Height from the surface of earth
• Let g be the value of acceleration due to gravity at the surface of
earth and g' at a height h above the surface of earth.
13. Acceleration Variation with depth
• Let g be the value of acceleration due to gravity at the surface of
earth and g' at a depth d below the surface of earth.
• If the earth is considered as a sphere of homogeneous
composition of density ρ
, then g at any point on the surface of the
earth is given by:
14. Gravitational field
Two bodies attract each other by the gravitational force even if
they are not in direct contact. This interaction is called action at
a distance. It can best explained in terms of concept of field.
According to the field concept.
Every mass modifies the space around it . This modified space
is called gravitational field
When any other mass is placed in this field , it feels a
gravitational force of attraction due to its interaction with the
gravitational field
The space surrounding a material body within which its
gravitational force of attraction can be experiences a force of
attraction towards the Centre of earth
15. Gravitational potential energy
Amount of work done in bringing a body from infinity to the given point in
the gravitational field of the other.
Expression for Gravitational potential energy.
W = Fdx
Work down in bringing the body to point B from PointA.
16. Escape velocity
• If we throw a ball into air , it rises to a certain height and falls back.
If we throw it with a greater velocity , it will rise higher before falling
down.If we throw with sufficient velocity , it will never come back
.i.e. It will escape from the gravitational pull of the earth.
• The minimum velocity required to do so is called escape velocity.
• Consider the earth to be a sphere of mass M and radius R with
Centre O.
17.
18. Satellites
• Satellite is an body which continuously revolves on it own around
and a much larger body in a stable orbit.
• Natural satellites : A satellite created by nature is called natural
satellite .
example : moon.
• Artificial satellite : A man made satellite is called an artificial
satellite.
Example Chandrayaan .
• World’s Frist satellite was SPUTNIK-1.
19. Launching a satellite
• Principle for launching a satellite : Consider a high tower
projecting outside the earth’s atmosphere.
• Lets throw a body horizontally from the top of the tower
• with different velocities.
with its top
• As we increase the velocity of horizontal projection , the body will hit the
ground at point farther and farther from the foot of the tower.
• At certain velocity the body will not hit the ground , but always be in a
state of free fall under the influence of the gravity.
• Then the body will follow a stable circular orbit . And that body is called
satellite.
20. Geostationary satellite
A satellite which revolves around the earth in tis equatorial plane with
the same angular speed and in the same direction as the earth rotates
about its own axis is called a geostationary or synchronous satellite.
21. Necessary condition for geostationary satellite
• It should revolve in an orbit concentric and coplanar with
the equatorial plane of the earth.
• Its sense of rotation should be same as that of the earth ,
i.e From west to east.
• Its period of revolution around the earth should be exactly
same as that of the earth about its own axis , i.e 24 hours
• It should revolve at a height of exactly 35930 km.
22. Orbital velocity
Orbital velocity is the velocity required to put the satellite into its
orbit around earth
Centripetal force is also important, as this is the force responsible for
circular motion. For deriving a simple equation for orbital velocity, we
will assume uniform circular motion. In the case of an orbiting body,
the centripetal force is the gravitational force.
23. Total energy of satellite
• Consider a satellite of mass m moving around the earth with velocity
in an orbit of a radius r.
• Because of the gravitation pull of the earth, the satellite
has a potential energy which is given by
24. Binding energy of satellite
The energy required by a satellite to leave its orbit around the earth and
escape to infinity is called binding energy.
Binding energy
Because the total energy of the satellite is
In order to escape into infinity , it must be supplied extra
energy so that its energy E becomes zero.
25. Use of geostationary satellite
• In communicating radio,T
.V and telephone signals across the
world.
• In studying the upper regions of the atmosphere.
• In Forecasting weather.
• In studying meteorites.
• In studying solar radiation and cosmic rays.
• And used in GPS (Global positioning System).
26. Polar satellite
• A satellite that revolves in a polar orbit is called a polar
satellite. Eg IERS (Indian earth resources satellites)
• Uses of Polar satellite
– Polar satellites are used in weather and environment
monitoring.
– Spying
– Study topography of other
celestial bodies
27. Weightlessness
• In case of a satellite that is rotating around the earth, every part of the
satellite has an acceleration which is exactly the value of earth’s
acceleration due to gravity at that position.
• Thus in the satellite everything is in the state of free fall.
• Therefore , weightlessness is experienced by astronauts in satellites.
