1. Name :- Jay Butani
Department :-
Division :-
Enrollment No. :-
Roll No. :-
Subject :-
Topic :- Law Of Gravitation

2. Law Of
Gravitation

3. Apple Falling
Incident
Universal
Gravitation
Example 1
Force Of
Attraction
Free-Fall
Acceleration
Contents
JAY BUTANI 3
Universal
Gravitation
Example 2
G Vs g
Newton’s
Universal
Gravitation
Mass of
Earth & Moon
Introduction
What Is Force ?
Calculation
Used By
Newton

4. INTRODUCTIOIN
Thank you for coming today!
• Sir Isaac Newton
• 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”

5. 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) (ii) Non-Contact Force. - electric, magnetic,
gravitational force.
What is FORCE ?

6. Apple Falling Incident
aftr
The apple was attracted to the
Earth
All objects in the Universe were
attracted to each other in the
same way the apple was
attracted to the Earth
JAY BUTANI 6

7. 7
Calculation Used By
Newton
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,
• A apple a moon = 9.8 m/s2 0.0027 m/s2
• Also, distance of the moon from the earth distance of
the apple from the earth moon d
• apple 3.85 ×105 km 6400 km = 3600. ....(i)
• A apple a moon = d moon d apple 2 = = = 60 ….(ii)

8. 8
Calculation Used By
Newton
•Newton guessed that, acceleration a ∝ 1 r
2 …..(1)
•He had, F ∝ ma ; (Newton’s second law)
…..(2)
•. ˙ . F ∝ m . ( From (1) ) r 2 …..(3)
•By Newton’s Third law of motion,
•F ∝ M …..(4)
•Combining 3 & 4, F ∝ Mm r

9. 9
Calculation Used By
Newton
•F = GMm / r 2
• 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

10. 2
21
r
mm
GF 
FORCE OF
ATTRACTION
Every particle in the Universe
attracts every other particle with a
force that is directly proportional to
the product of the masses and
inversely proportional to the square
of the distance between them.
JAY BUTANI 10

11. Universal Gravitation
G is the constant of universal gravitation
G = 6.673 x 10-11 N m² /kg²
This is an example of an inverse square law
Determined experimentally
Henry Cavendish in 1798

12. FREE-FALL ACCLERATION
• Have you heard this
claim:
• Astronauts are weightless in space, therefore there is no gravity in space?
• It is true that if an astronaut on the International Space
Station (ISS) tries to step on a scale, he/she will weigh
nothing.
• It may seem reasonable to think that if weight = mg, since
weight = 0, g = 0, but this is NOT true.
• If you stand on a scale in an elevator and then the cables are
cut, you will also weigh nothing (ma = N – mg, but in free-fall
a = g, so the normal force N = 0). This does not mean g = 0!
LAW OF GRAVITATION

13. Example of Satelite
A satelite at an altitude of twice the Earth radius
Earth Radius: rE = 6320 km Earth Mass: ME = 5.98
• 1024 kg FG = G(mME /r2 ) Mass of the Sate lite m
• At surface r = rE FG = weight or mg = G[mME /(rE ) 2 ]
• At r = 2rE FG = G[mME /(2rE ) 2 ] or (¼)mg = 4900 N

14. Example:- Earth, Sun &
Moon
Find the net force on the Moon due to the
.gravitational attraction of both the Earth & the Sun,
assuming they are at right angles to each other.
ME = 5.99 1024kg MM = 7.35 1022kg
MS = 1.99 1030 kg rME = 3.85 108 m
rMS = 1.5 1011 m F = FME + FMS

15. G Vs g
G g
Obviously, it’s very important to distinguish
between G and g
They are obviously very different physical
quantities G
The Universal Gravitational Constant › It is the
same everywhere in the Universe G = 6.673 10-11
N∙m2/kg2
Always same on every location g
The Acceleration due to Gravity g = 9.80 m/s2
(approx) on
Earth’s surface g varies with location

16. Gravitational force F_gFg​F, start subscript, g,
end subscript 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.
Fg​=r2Gm1/​m2
F_gFg​F, start subscript, g, end subscript is
the gravitational force between m_1m1​m,
start subscript, 1, end
subscript and m_2m2
Newton's universal law of gravitation
The force is directly proportional to
the product of their masses and
inversely proportional to the square
of the distance between their centers
of mass. This is called an inverse-
square law.

17. JAY BUTANI 17

18. That’s all. Thank you!
