Introduction to Gravitation Newton's Law and an important deduction which shows relation between 'acceleration due to gravity g' and 'mass of body m'.

1. Presented By:-
Name – Akshat Saxena

2.  What is Force?
 Who discovered Gravitational law?
 Discovery of Gravitational Force.
 Calculation used by Newton.
 Calculating the constant.
 Gravity- A special Case.
 Effect of Gravity and its Uses.

3. Sir Issac newton gave many laws of nature.
In his First law of motion, he described the inherent
property of matters,qualitatively.
In his second law,he wrote “A force action on a body
gives it an accelaration which is in the direction of force
and has a magnitude given by ma.”
So,it describes force quantitatively also.
In his third law,he describes how force are exerted.
Therefore,we can say he discovered “Force”.

4. The force is an external effort(cause) in the form of a push
or pull which either changes or tends to change the state of
rest or the uniform motion of a body along a straight line.
They are classified into two categories:-
(i) Contact Force.
- Frictional force, normal reaction,tensile force etc.
(ii) Non-Contact Force.
- electric,magnetic,gravitational force.

5.  Sir Isaac Newton (1642-1727)
 Perhaps the greatest genius of
all time
 Invented the reflecting
telescope
 Invented calculus
 Connected gravity and
planetary forces
Philosophiae naturalis
principia mathematica

6.  In 1665, Issac Newton performed brilliant
theoretical and experimental tasks in mechanics
and optics.
 In this year, he focused his attention on the
motion of the moon about the earth.
 While doing so, he had a question that what is
the force that makes moon to revolve.

7. He had data that moon revolves round the earth in
27.3 days.
Its distance from earth is R = 3.85 ×105
km.
The acceleration of moon is ,therefore,
α = ω2
R
α = 2π 2 × R ( velocity = disp. )
T time
= 4π2
×(3.85 ×105
km)
(27.3 days)2
Displacement and time were converted into SI units.
He had a belief that earth is making the moon to
revolve.But How?
= 0.0027 m/s2

8. Newton was sitting under an apple tree when an apple
fell down from the tree on the earth.
This sparked the idea that the
earth attracts all bodies towards
its centre.
He declared that the laws of
nature are same for earthly
and celestial bodies.

9. The acceleration of a body falling near the earth’s surface is
about 9.8 m/s2
and moon’s acceleration is 0.0027m/s2
.Thus,
aapple
amoon
=
9.8 m/s2
0.0027 m/s2
Also,
distance of the moon from the earth
distance of the apple from the earth
dmoon
dapple
3.85 ×105
km
6400 km
= 3600. ....(i)
aapple
amoon
= dmoon
dapple
2
= =
= 60 ….(ii)
By comparing (i)&(ii)

10. Newton guessed that,
acceleration a ∝ 1
r2
…..(1)
He had,
F ∝ ma ; (Newton’s second law) …..(2)
. ˙ . F ∝ m . ( From (1) )
r2
…..(3)
By Newton’s Third law of motion,
F ∝ M …..(4)
Combining 3 & 4,
F ∝ Mm
r2

11. F = GMm
r2
where,
– F = Force of attraction between the two particles.
– M = mass of first particle.
– m = mass of second particle.
– r = distance between the centers of the first and second particle.
– G = Universal gravitational constant. = 6.67 × 10-11
N·m2
/kg
Dimensional formula of F is [MLT-2
]
S.I. Unit = N (Newton)
C.G.S. Unit = dyne

12. m1 m2
ř12 ř21
r
F12 = - Gm2m1
r2
F21 = - Gm1m2
r2
ř21
ř12
Note : -(minus) sign denotes that opposite direction of force and Distance.

13.  Always acts as “Force of Attraction”.
 Form an action-reaction pair.
 Central Forces.
 Independent of the presence of other bodies and
properties of the intervening medium.
 Weakest Force.

14. The force of attraction between any two material
particles is directly proportional to the product of the
masses of the particles and inversely proportional to
the square of the distance between them. It acts along
the line joining the two particles.
i.e,
F ∝ Mm
r2

15.  First measurement was done by Cavendish in
1798,about 71 years after the law was formulated.
 The Gravitational constant G is a small quantity and its
measurement needs very sensitive arrangement.
 Value of G was given through Cavendish Experiment.
Calculating the Gravitational Constant

16. In 1798 Sir Henry Cavendish suspended a rod with two
small masses (red) from a thin wire. Two larger mass
(silver) attract the small masses and cause the wire to
twist slightly, since each force of attraction produces a
torque in the same direction. By varying the masses
and measuring the separations and the
amount of twist, Cavendish was the first
to calculate G.
G = 6.67 × 10-11
N·m2
/kg2
Cavendish’s Experiment

17.  Earth was treated as a single particle placed at its centre.
 Newton spent several years to prove that a spherically
symmetric body can be replaced by a point particle as its
centre.
 In this process he discovered the methods of Calculus.
 He did it by use of Calculus.
 It was then, applicable for the bodies if their entire mass
were concentrated at their centre of mass.
 Hence, it is applicable to all, whatever the size may be.
Assumptions

18.  It is a Universal Law. It explains motion of heavenly
bodies.
 The predictions of eclipses comes true.
 Tides in oceans because of attraction between moon
and ocean water.
 The predictions about orbits and time periods of
artificial satellites found to be correct.

19. Gravity is the force by which earth attracts a body
towards its centre.
F e= GMem
Re
2
where,
– Fe = forces of attraction between Earth and particle of mass m.
– Me = mass of Earth.
– m = mass of particle.
– Re = distance between the centers of the Earth and particle.
– G = Universal gravitational constant. = 6.67 × 10-11
N·m2
/kg

20.  Follows Newton's Law of Universal Gravitation
 By Newton’s second law , F = mg
 Compare with F = mg so g = GM/r2
 g depends inversely on the square of the distance
 g depends on the mass of the planet
 Nominally, g = 9.81 m/s2
or 32.2 ft/s2
• At the equator g = 9.78 m/s2
• -At the North pole g = 9.83 m/s2
• g on the Moon is 1/6 of g on Earth.

21.  Provides necessary centripetal force to moon to
revolve.
 Provides force to Satellites to revolve round the
earth.
 To make the bodies fall from height.
 Formation of Tides in the ocean.

22. Fg,lead =
GMEarthMlead
REarth
2
Fg,wood =
GMEarthMwood
REarth
2
22
, 1
•
Earth
earth
leadEarth
leadearth
lead
leadg
lead
R
GM
MR
MGM
M
F
a ===
22
, 1
•
Earth
earth
woodEarth
woodearth
wood
woodg
wood
R
GM
MR
MGM
M
F
a ===
Lead Wood
aawoodwood
aaleadlead
Q. If two bodies one of lead and other of wood of same volume
are fallen from same height from the state of rest. Then which will strike
to the ground first?(Neglect air-resistance)
Sol.
…..(a)
…..(b)

23. Let, h be their height above the ground.
By second equation of motion,
S = ut + 1/2at2
For lead,
h = 1/2aleadt1
2
; …..(c)
For wood,
h = 1/2awoodt2
2
; ..…(d)
Equating (c)&(d),
1/2aleadt1
2
= 1/2awoodt2
2
t1
2
= t2
2
Or,
t1 = t2
Thus, they will reach earth at same instant.
(From (a) &(b))

24.  www.wikipedia.org/Gravitation
 www.physicsclassroom.com
 www.google.books.com
Books
Prof. H.C.Verma : Concept of Physics Vol. I
Kumar,Mittal : ISC PHYSICS Class XI
Modern ABC : Physics Vol.I

25. THANK YOU