This PPT is according to class 11 physics CH-8 Gravitation (NCERT).

1. Gravitation
Made by- Balaji Kaushik

2. More about Gravitation
⋆ As far as we know, humans have always been
interested in the motions of objects in the sky.
⋆ Not only did early humans navigate by means of the
sky, but the motions of objects in the sky predicted
the changing of the seasons, etc.
⋆ There were many early attempts both to describe
and explain the motions of stars and planets in the
sky.
⋆ All were unsatisfactory, for one reason or another.
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3. Tycho and Kepler
⋆ In the late 1500’s, a Danish nobleman named Tycho
Brahe set out to make the most accurate
measurements of planetary motions to date, in
order to validate his own ideas of planetary motion.
⋆ Tycho’s data was successfully interpreted by the
German mathematician and scientist Johannes
Kepler in the early 1600’s.
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4. Kepler’s Laws of Planetary motion
⋆ After analyzing experimental dates kepler gives three laws related with
planetary motion.
⋆ 1ST LAW{Law of orbits} :- According to 1st law of kepler all planets revolve
around the sun in elliptical path with sun situated at one of its focus.
⋆ 2ND LAW{Law of areas} :- According to this law, the vector joining the sun with
planet sweeps equal area in time interval.
∆A/∆T= Constant
This law shows that revolving speed of planet varies throughout its orbit and it is
maximum at perihelion position and minimum at aphelion.
⋆ 3rd LAW{Law of time period} :- The square of time period of revolving planet is
proportional to the cube of length of semi major axis.
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5. UNIVERSAL LAW OF GRAVITATION
⋆ This law was given by newton and also called
Newton’s law of gravitation.
⋆ According to this law, All massive objects in the
universe attracts to each other by a force called
gravitational force whose magnitude is proportional
to product of masses of bodie and inversely
proportional to square of distance between them.
F=G x m₁m₂/r2
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6. ⋆ Force of gravity:- The gravitational force between
two objects one of which is either earth or any other
planet is called force of gravity.
⋆ Acceleration due to gravity:- Acceleration of any
moving object produces due to force of gravity is
called acceleration due to gravity. It is represented
by g.
g=F/M
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7. GRAVITATIONAL FORCE
⋆ If g is the strength of the gravitational field at some
point, then the gravitational force on an object of
mass m at that point is
Fgrav = mg.
⋆ If g is the gravitational field strength at some point
(in N/kg), then the free fall acceleration at that
point is also g (in m/s2).
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8. GRAVITATIONAL FORCE BETWEEN HOLLOW
SPHERICAL SHELL AND POINT MASS
⋆ When point mass is outside the spherical shell:- The gravitational
force between spherical shell and point mass placed outside is equal
to the value of gravitational force. As if the entire mass of spherical
shell is concentrated at the centre of the spherical shell.
F= GMm/r2
⋆ When point mass is inside the spherical shell:- In this case, the net
gravitational force upon the mass particles placed inside the
spherical shell would be zero.
Fm= zero 8

9. ACCELERATION DUE TO GRAVITY
OF EARTH
⋆ ‘g’ on the surface of the earth Suppose total mass of the earth is Me
and its radius is Re.
⋆ To find out total force of gravity on a mass particle of mass ‘m’ placed
on the surface of the earth, earth can be divided into infinite number
of spherical shell of masses M₁, M₂, M₃,…
F= F₁+F₂+F₃ …
= G M1m/RE2 + G M2m/RE2 + G M3m/RE2 + …
=Gm/RE2 [M1 + M2 + M3 + …]
F= G MEm/RE2
g= F/m = G MEm/RE2m = G ME/RE2
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10. ⋆ Acceleration due to gravity does not depend upon the mass of the body
‘m’. It depends on the distance of the place on the earth surface from
centre of the earth.
⋆ Variation of ‘g’ on earth surface g= G ME/RE2
⋆ A ‘g’ varies on earth’s surface due to two region:-
(i) Earth is slightly flat at force. So, its polar radius is smaller than its
equator radius.
(ii) due to spin motion of earth, every object on its surface perform
circular
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11. (2) ‘g’ below the earth surface Suppose we have to find out acceleration due
to gravity at a point inside the earth at depth ‘d’.
⋆ The force of gravity due to spherical shell of thickness ‘d’ will be zero.
⋆ Force of gravity at point P will be only due to inner sphere of RE -d.
g(d)= g(1- d/ RE )
⋆ This equation shows that acceleration due to gravity decreases linearly
w.r.t depth and becomes 0 at the center of earth.
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12. (3) ‘g’ above the earth surface Consider a point above the earth’s surface at
a height h.
⋆ force of gravity on any mass particle [m] place at that point.
g(h)= g(1 +h/ Re )¯²
⋆ When h <<< RE , Then applying binomial theorem,
g(h)= g(1- 2h/ RE )
⋆ Acceleration due to gravity(g) also decreases on moving above the
surface of the earth.
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13. ⋆ Gravitational field- The region around any massive objects is called gravitational
field. It’s intensity at any point is defined as force experienced by unit mass.
⋆ Gravitational potential energy- It is defined as the energy possessed by any
massive objects due to its position in gravitational force field.
Gravitational potential energy of any object at any point in
gravitational field is equal to amount of work done in bringing the objects from
infinity to that point.
⋆ Amount of work done is displacing the object from point p by very small
distance dr. U= -GME m/r
U= gravitational potential energy.
⋆ negative sign of gravitational potential energy shows that massive object is
bound to be in the field of earth’s gravitational field.
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14. GRAVITATIONAL POTENTIAL
ENERGY OF THE SYSTEM OF
PARTICLES
Gravitational Potential Energy of system of
particles is equal to the algebraic sum of
potential energy of each pair of the system.
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15. GRAVITATIONAL POTENTIAL
⋆ Gravitational potential at any point in gravitational
field is defined as amount of work done in moving to
bring mass from infinity to that point.
V= w/m= J/kg
V= -GME /r
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16. ESCAPE VELOCITY
⋆ Minimum required speed to any object at a point in a
gravitational field. So that object can escape from
gravitational pull.
⋆ Suppose an object of mass ‘m’ at a point distance
‘r’ from the Centre of earth is provided speed ‘v’.
⋆ So, total energy of the object
T.E= K.E + P.E = ½ mv² - G MEM/r
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17. SATELLITE
⋆ Satellites are those objects which revolves around
the sun.
⋆ On the basis of their origin, they are of two types:-
(i)Natural satellite:- moon → satellite of earth
(ii)Artificial or man- made satellite
⋆ 1st artificial satellite of earth is SPUNTIK -
1launched by Russia in 1957.
⋆ 1st Indian artificial satellite of earth →Aryabhatta
in 1957. 17

18. GEOSTATIONARY
SATELLITE
⋆ Those satellite which revolves in equatorial plane of
the earth with same angular velocity (time period)
and in same direction as done by earth about its
axis is called geostationary satellite.
⋆ That means, satellite whose time period of
revolution is 24 hrs. these satellite seems to be
stationary to the observer on earth’s surface.
⋆ Application:- These satellite are widely used is
communication.
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19. POLAR SATELLITE
⋆ These satellite revolves around the earth in polar
plane. They are low altitude satellite used in
weather prediction, remote serving etc.
⋆ Polar satellite scan the whole earth in 24hrs.
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