3.1 NEWTON'S UNIVERSAL LAW OF GRAVITATION

CHAPTER 3
GRAVITATION

3.1 NEWTON’S UNIVERSAL LAW OF GRAVITATION
TEXT BOOK : PAGE 76 - 87

SUE ROSE

How do man-made
satellites help to
improve human life?

TDhoeryeoaureevvaerriowusontydpeers hoof mwan- Satellites are invented
mrdeoaspdeeescstaaivtseealoltirteeblsliittrseeivnaooblvuleitnegtroisnptahceei.r for communication
revolve in their orbits? purposes, weather
forecasts and Earth
observations. Why are
these satellites able to
revolve in their
respective orbit?

Curiosity about the universe has
encouraged scientists to launch
spaceships and satellites which
can overcome the Earth’s gravity.

At present, there are spaceships
which are moving far away from
Earth. Such spaceships enable
photographs of planets to be taken
to benefit scientific inventions and
technology.



LEARNING STANDARD 1

3.1.1 Explain Newton’s

Universal Law of

Gravitation

= m1m2


In 1667, Isaac Newton, observed an apple which fell vertically to the
ground and the movement of the Moon around the Earth. He concluded
that a force of attraction not only exist between the Earth and the apple but

also between the Earth and the Moon.

To discuss gravitational force between two bodies in the universe

1. A person who jumps up will return to the
ground. What force causes the person to
return to the ground?

Gravitational force

To discuss gravitational force between two bodies in the universe

2. Air molecules remain in the atmosphere
without escaping to outer space. What
force acts between the molecules in the
atmosphere and the Earth?

Gravitational force

To discuss gravitational force between two bodies in the universe

3. The Moon revolves around the Earth
without drifting away from its orbit. The
Earth exerts a pulling force on the Moon.
Does the Moon also exert a force on the
Earth?

Yes

4. A leaf falls from a tree.

(a) Are both the leaf and the Earth experience
the same gravitational force?

Yes

(b) What is the effect of these forces to the
movement of the fallen leaf and the Earth?

The leaf and the Earth moves
towards one another.

(c) Why does a fallen leaf move towards the
ground?

As the mass of the Earth is very
much larger than the mass of the
leaf, gravitational force does not
have an apparent effect on the
Earth’s movement. As such, we only
observe the leaf falling to the ground.

Gravitational Force

Gravitational force is known as
universal force because it acts
between any two objects in the
universe.

1. Gravitational force exists
between two bodies.

2. Both bodies experience
gravitational force of the
same magnitude.

Gravitational Force

Universal force that

acts between two Gravitational force
bodies in the universe between the sun

and earth The Earth

Gravitational force between
the earth and moon

The moon

The Sun Gravitational
force between

the Sun and
the Moon

In the year 1687, Isaac Newton presented two relationships that
involve gravitational force between two bodies:

Body 2

Body 1

m1 m2

Gravitational force is directly
proportional to the product
of the masses of the two
bodies, that is

Distance, r

F ∝ m1m2

Gravitational force is inversely proportional to the square of the
distance between the centers of the two bodies, that is

1 Body 1 Body 2
α 2
m1 m2

Distance, r

Formulation of
Newton’s Universal Law of Gravitation

∝ m1m2 m1m2

∝

∝ = m1m2


= m1m2


F = gravitational force between two bodies

m1 = mass of first body
m2 = mass of second body
r = distance between the center of the first body

and the center of the second body.
G = gravitational constant ( G = 6.67 x 10 -11 Nm2kg-2)

Example 1
Calculate the gravitational force between a durian and the Earth.
Mass of durian = 2.0 kg
Mass of the Earth = 5.97 x 10 24kg
Distance between the center of the durian and the center of the Earth = 6.37 x 106 m

m1 = 2.0 kg
m2 = 5.97 x 10 24 kg
r = 6.37 x 10 6 m

G = 6.67 x 10 -11 Nm2kg-2

= m1m2


F = (6.67 x 10-11) x 2.0 x 5.97 x 1024

(6.37 x 106)2

= 19.63 N

Example 2
A rocket at a launching pad experiences a
gravitational force of 4.98 × 105 N. What is
the mass of the rocket?
[Mass of the Earth = 5.97 × 1024 kg, distance
between the centre of the Earth and the
centre of the rocket = 6.37 × 106 m]

F = 4.98 x 105

m1 = 5.97 x 1024 kg
m2 = ?
r = 6.37 x 106 m

G = 6.67 x 10-11 N m2 kg-2

= m1m2 4.98 x 105 = (6.67 x 10-11) x 5.97 x 1024 x m2
(6.37 x 106)2

m2 = (4.98 x 105)(6.37 x 106)2
6.67 x 10-11 x 5.97 x 1024

= 5.07 x 104 kg

LEARNING STANDARD 2

Solve problems involving Newton’s Law of Gravitation for
(i) Two statics objects on the Earth.
(ii) Objects on the Earth’s surface
(iii) Earth and satelites
(iv) Earth and Sun

Solving Problems Involving Newton’s
Universal Law of Gravitation
Gravitational force acts between any
two bodies, including those on Earth,
planets, the Moon or the Sun. What
are the effects of mass and distance
between two bodies on gravitational
force?

Imagine you and your friend are bodies on Earth.
.

Your mass m1 = 55 kg, and your friend,m2 = 65 kg.

Calculate the gravitational force, F if the
distance between both of you, r is 2.0 m

= m1m2


= (6.67 x 10 −11)(55)(65)

m2 = 65kg m1 = 55kg

= . × − N

r = 2.0 m

Lets increase the value of the distance from 2 m to 4 m.

= m1m2

r = 4.0 m

r = 2.0 m = (6.67 x 10 −11)(55)(65)



= . × − N

= , = . × − N
= , = . × − N

When the distance between two
bodies between them is increase,
The gravitational force is decrease.

Hence, more separation distance will
result in weaker gravitational forces

Change partners

r = 2.0 m = m1m2


= (6.67 x 10 −11)(55)(75)



= . × − N

m1 = 55 kg m2 = 75 kg

How do the masses of two bodies influence the gravitational
force between them?

r = 2.0 m = , = . × − N

= , = . × − N

When the masses is increase, the
gravitational force between them will also
be increase.

m1 = 55 kg m2 = 75 kg

What is the effect of distance between two bodies on gravitational force
between them?

r = 4.0 m

r = 2.0 m = , = . × − N
= , = . × − N

When the distance between two
bodies between them is increase,
The gravitational force is decrease.

Hence, more separation distance will
result in weaker gravitational forces.

Why is the magnitude of gravitational force between you and
your friend is small?

The masses between two bodies of small mass
has a very small magnitude.

The larger the mass of the body, the F2 > F1
larger the gravitational force.

The larger distance between the bodies,
the smaller the gravitational force. F2 < F1

To solve problems involving Newton’s Universal Law of Gravitation for:
(i) objects on the Earth’s surface
(ii) the Earth and satellite
(iii) the Earth and the Sun

1) What is gravitational force on the man-made satellite before it
launched?

Activity 3.3 page 82

= m1m2 The Earth
Mass = 5.97 x 1024kg
Radius = 6.37 x 106 m

= (6.67 x10−11 )(5.97 x 1024)(1.20 x103)
6.37 x 106

= .

Man- made satellite Activity 3.3 page 82
Mass = 1.20 x 103 kg
Distance between the
Earth and the satellite

= 4.22 x 107m

2) Compare the mass of the Earth, mass of the The Moon / Bulan
man-made satellite and the mass of the Sun m = 7.35 x 1022 kg

The Earth / Bumi Man- made satellite
m = 5.97 x 1024kg Satelite buatan
R = 6.37 x 106 m m = 1.20 x 103 kg

The Sun / Matahari Distance between the
m = 7.35 x 1022 kg Earth and the satellite
Distance between the Earth and
the Sun = 1.50 x 10 11 m = 4.22 x 107 m

Activity 3.3 page 82

m sun > mearth > mmoon > msatellite

distance > distance jarak > jarak

Earth-sun Earth-satellite Bumi-Matahari Bumi-Satelite

3) Compare between the Earth – satellite
distance and the Sun- Earth distance.

3 ) Predict the difference in the

magnitude of the gravitational force

between :

(a) man-made satellite and the Earth

(b) the Sun and the Earth

= m1m2


mSun > mearth > mmoon > msatellite

distance > distance The gravitational force

Earth-Sun Earth- satellite between the Sun and the
Earth is bigger.

4 ) Calculate :
(a) The gravitational force between Earth - Satellite
(b) The gravitational force between Earth - Sun

= m1m2

The Moon
Mass = 7.35 x 1022 kg

The Earth Man- made satellite
Mass = 5.97 x 1024kg Mass = 1.20 x 103 kg
Radius = 6.37 x 106 m Distance between the
Earth and the satellite
The Sun
Mass = 7.35 x 1022 kg = 4.22 x 107m
Distance between the Earth and
the Sun = 1.50 x 10 11 m Activity 3.3 page 82

Man- made satellite / satellite Buatan The Earth / Bumi
Mass = 1.20 x 103 kg Mass/Jisim = 5.97 x 1024kg
Radius/Jejari, R = 6.37 x 106 m
Distance between the Earth and the
satellite, h = 4.22 x 107m

(a)The gravitational force between Earth – Satellite

= m1m2
( + )

. × − . × . ×
= . × + . ×

= 202.56 N

The Earth / Bumi The Sun
Mass= 5.97 x 1024kg Mass = 7.35 x 1022 kg
Radius, R = 6.37 x 106 m Distance between the Earth and
the Sun = 1.50 x 10 11 m

(a)The gravitational force between Earth – Sun

= m1m2


=F = 6.67 x 10-11 x 1.9 x 1030 x 5.97 x 1024
(1.50 x 1011)2

F = 3.36 x 10 22 N

5. The gravitational force between the Earth and the Moon is 2.00 x 1020 N. What
is the distance between the centre of the Earth and the centre of the Moon?

= m1m2 Moon
r

Earth

2.0 x 1020 = 6.67 x 10-11 x 5.97 x 1024 x 7.35 x 1022
r2

r2 = 6.67 x 10-11 x 5.97 x 1024 x 7.35 x 1022
2.0 x 1020

r = 382,541,674 m = 3.82 x 108 m

LEARNING STANDARD 3

Relate gravitational acceleration, g on
the surface of the Earth with the
Universal gravitational constant, G

Relating Gravitational Acceleration, g on the surface of
the Earth with Universal Gravitational Constant, G.

According to Newton’s Second Law of Motion,
gravitational force can be expressed as F = mg
From Newton’s Universal Law of Gravitation,
gravitational force:F = Gm1m2

r2
What is the relationship between g and G?

Newton 2nd Law of Motion Gravitational force

= Mm
=
=

=

EQUAL

EQUAL α

Mm
=

M
=

1. What is the relationship between gravitational acceleration, g and
gravitational constant, G?

M α
=

g is directly proportional to G

2. What are the factors that influence the value of gravitational
acceleration?

Mass of an object
Distance of the object

To discuss the variation in the values of g with r

• Mass of the Earth
m = 5.97 x 1024 kg

• Radius of the Earth
• R = 6.37 x 106 m
• Gravitational constant,

G = 6.67 x 10-11 Nm2kg-2

1. Calculate the value of
gravitational acceleration for the
five distances.

Distance from centre of Gravitational acceleration,
the Earth, r
R GM = 6.67 x 10-11 x 5.97 x 1024 = 9.8
2R R2 (6.37 x 106)2
3R
GM = 6.67 x 10-11 x 5.97 x 1024 = 2.45
4R R2 (2 x 6.37 x 106)2
5R
GM = 6.67 x 10-11 x 5.97 x 1024 = 1.09
R2 (3 x 6.37 x 106)2

GM = 6.67 x 10-11 x 5.97 x 1024 = 0.6125
R2 (4 x 6.37 x 106)2

GM = 6.67 x 10-11 x 5.97 x 1024 = 0.392
R2 (5 x 6.37 x 106)2

1. What is the value of gravitational
acceleration on the Earth’s surface?

9.8 ms-2

2. Plot a graph of g against r.

Graph shows the variation of
gravitational acceleration
with the distance from the
centre of the Earth

1. How does the value of gravitational 2. How does the value of gravitational

acceleration change when the distance acceleration change when the distance

from the centre of the Earth r < R? from the centre of the Earth increases

(r ≥ R)?

Directly proportional Inversely proportional