3.1 Law of Universal Gravitation

MODUL PDP SPM
PASCA PKP
NEGERI PERAK
2020

PHYSICS Form 4

3.1:
Newton’s
Universal Law of
Gravitation

1

3.1 Newton’s Universal
Law of Gravitation

Learning standard:

Pupils are able to:

• explain Newton’s Universal Law of Gravitation: = 1 2
2

• solve problems involving Newton’s Universal Law of Gravitation for:

(i) two static objects on the Earth

(ii) objects on the Earth’s surface

(iii) Earth and satellites

(iv) Earth and Sun

• relate gravitational acceleration, g on the surface of the Earth with the universal

gravitational constant, G.

• justify the importance of knowing the values of gravitational acceleration of the

planets in the Solar System.

• describe the centripetal force in the motion of satellites and planets system.
2
, =

• determine the mass of the Earth and the Sun using Newton’s universal law of

gravitation and centripetal force.

2

notE

1. Man-made satellites:
 revolving in their respective orbits in outer space
 involved Newton’s Universal Law of Gravitation
 for communication purposes
 for weather forecasts
 for Earth observations

2. Gravitational force = universal force
 Gravitational force acts between any two bodies in the universe.
 Exists between two bodies
 Both bodies experience gravitational force of the same magnitude.
 There are: (as shown in Diagram 1)
o gravitational force between the Sun and the Earth
o gravitational force between the Sun and the Moon
o gravitational force between the Earth and the Moon

Diagram 1: Gravitational force as a universal force

3. Two relationships that involve gravitational force between two bodies are as shown in

Diagram 2.

(i) Gravitational force is directly proportional to the product of the masses of the two

bodies

∝
(ii) Gravitational force is inversely proportional to the square of the distance between the

centres of the two bodies

∝

3

Diagram 2: Gravitational force between two bodies

4. When the two relationships above are combined, Newton’s Universal Law of Gravitation is

obtained. ∝ 1 ∝
∝ 1 2 2

5. Withered leaf falls towards to Earth because:
(i) There is gravitational force between the Earth and the leaf (same magnitude).
(ii) The leaf and the Earth move towards one another.
(iii) The mass of the Earth is very much larger than the mass of the leaf, thus gravitational
force does not have an apparent effect on the Earth’s movement.
(iv) As such, we only observe the leaf falling to the ground.

6. Newton’s Universal Law of Gravitation states that:

 the gravitational force between two bodies is directly proportional to the product of

the masses of both bodies &

 inversely proportional to the square of the distance between the centres of the two

bodies.

 ∝ =


7. The gravitational force between two bodies is affected by:
(i) mass of the body
o the larger the mass of the body, the larger the gravitational force
o the smaller the mass of the body, the smaller the gravitational force
(ii) the distance between the two bodies (as shown in Diagram 3)

4

Diagram 3: Effects of mass and distance between two bodies on gravitational force

8. Two persons on the Earth’s surface will not feel the effect of the gravitational force because
the gravitational force between two bodies of small mass has a very small magnitude.

9. The relationship between gravitational acceleration, on the surface of the Earth and
universal gravitational constant, .
(i) Newton’s Second Law of Motion, =
Gravitational force, =
(ii)


2


M = jisim Bumi 2
m = jisim objek 2
M = mars=s ojafrtahkedEiaarnthtara pusat
m = mass oBfutmhei doebnjegcatn pusat 2
r = distanceobbjeetkween
the centre of the
Earth and the centre 2
of the object


2

5

10. Factors that influence the value of gravitational acceleration (The value of universal

gravitational constant and the mass of the Earth are constant)
(i) The distance between the centre of the Earth and the centre of the object,

 The more the distance , the less the gravitational acceleration.
(ii) Diagram 4 shows a sketch of a graph with various values of gravitational acceleration,

and the distance, from the centre of the Earth.

Diagram 4: Variation of g with r

11. Diagram 5 shows a satellite at height, ℎ from the surface of the Earth.
ℎ = height of the satellite from the surface of the Earth
= radius of the Earth
= distance of the satellite from the centre of the Earth (radius of the orbit)

Satellite at the height, ℎ from the surface of the

Earth
Distance from the centre of the Earth, = + ℎ

Gravitational acceleration,

= ( + ℎ)2

Satellite on the surface of the Earth, height, ℎ = 0

Distance from the centre of the Earth,
= radius of the Earth,

Gravitational acceleration on the surface of the

Earth,
2
=

Diagram 5: A satellite at height, h from the surface of the Earth

6

12. Importance of knowing the value of gravitational acceleration:
 The gravitational acceleration on each planet is different because the mass and the radius
of each planet are different
 In space exploration, the knowledge on the value of gravitational acceleration is
important to the astronauts for the continuity of life in outer space.

13. The effects of gravity on the growth of humans:
(a) Effect of high gravity
(i) Difference in density – density increases
(ii) Bone fragility – seldom happens
(iii) Size of lungs - compressed
(iv) Blood circulatory system – better (heart pumps harder)
(v) Blood pressure - high
(vi) Muscular system – stronger
(b) Effect of low gravity
(i) Immune system is weaker
(ii) Skin becomes thinner
(iii) Vision deteriorates
(iv) Height increases almost 2 inches
(v) Anxiety
(vi) Face swelling and legs become smaller
(vii) Space sickness = sea sickness / car sickness
(viii) Bones become less dense
(ix) The heart pumps less
(x) Loss of body coordination system

14. Uniform circular motion: a body moves in a circle at uniform speed

Diagram 6: Satellite in circular motion
15. An object in circular motion always experiences changes in the direction of its motion (fixed

speed).

7

16. Centripetal force:
 A force that acts on the body which is in a circular motion and its direction is towards

the centre of the circle.

Centripetal
force,


17. The factors that affect centripetal force:
(i) Mass of the body, m
o The more the mass, the more the centripetal force.
(ii) Linear speed, v
o The more the linear speed, the more the centripetal force.
(iii) Radius of the circle, r
o The more the radius of the circle, the less the centripetal force.

18. Centripetal acceleration, : = 2
=
2
= linear speed of satellite =
= radius of the orbit of satellite
= 2


19. The formula for the mass of the Earth and the Sun can be derived by using the formula of
Newton’s Universal Law of Gravitation and the formula for centripetal force:

2

2


8

2
2

2
2

2
2

�2 �2
2

4 2 3
2

9

MIND MAP

10

FAQ

No Question and Answer
1Q
What is gravitational force in physics?
A
The gravitational force is a force that attracts any two objects with mass. ... In fact,
2Q every object, including you, is pulling on every other object in the entire universe!
A This is called Newton's Universal Law of Gravitation

3Q What are 5 facts about gravity?
A
● Objects with mass are attracted to each other, this is known as gravity.
4Q
A ● Gravity keeps Earth and the other planets in our solar system in orbit
around the Sun. ...
5Q
A ● Tides are caused by the rotation of the Earth and the gravitational effects of
the Moon and Sun
6Q
A What are Kepler's 3 laws?

There are actually three, Kepler's laws that is, of planetary motion

1) every planet's orbit is an ellipse with the Sun at a focus;

2) a line joining the Sun and a planet sweeps out equal areas in equal times; and

3) the square of a planet's orbital period is proportional to the cube of the semi-
major axis

Is gravity a force or acceleration?

On Earth all bodies have a weight, or downward force of gravity, proportional to
their mass, which Earth's mass exerts on them. Gravity is measured by the
acceleration that it gives to freely falling objects. At Earth's surface the
acceleration of gravity is about 9.8 ms-2

Is there gravity underwater?

Gravity isn't affected at all by being underwater. Gravity is a pull between any two
objects. But it's very weak so it isn't detectable unless one of the objects is huge
like the earth. The force of gravity is called the weight .

What is the effect of gravity on the human body?

As the human body consists mostly of fluids, gravity tends to force them into the
lower half of the body, and our bodies have many systems to balance this
situation. When released from the pull of gravity, these systems continue to work,
causing a general redistribution of fluids into the upper half of the body

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EXERCISE 3.1

SECTION A
1 Two factors affecting the magnitude of the force of gravity between 2 objects are...

[Mengetahui]
A Mass and distance
B Mass and matter
C Distance and weight
D Weight and mass

2 What is the gravitational force between two identical 50,000 kg asteroids whose
centers of mass are separated by 1000 m?
[mengaplikasi kuantitatif]
A 2500 N
B 3.3 x 10-12 N

C 1.67 x 10-4 N

D 1.67 x 10-7 N

3 Two spherical objects have masses of 9000 kg and 2500 kg. Their centers are
separated by a distance of 1.5 m. Find the gravitational attraction between them
[mengaplikasi kuantitatif]
A 6.67 X 10-4 N

B 1.00 X 10-3 N

C 1.00 X 10-5 N

D 6.67 X 10-6 N

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4 Mass of the Mars is 0.642 x 1024 kg and diameter of the Mars is 6792 km. Calculate
gravitational acceleration on the surface of the Mars.
[G = 6.67 × 10–11 N m2 kg–2]
[mengaplikasi kuantitatif]
A 12609

B 0.92

C 3.71

D 7.31

5 You swing a bucket of water attached to a string in a circle above your head. What
keeps the water in the bucket?

[Memahami]

A Friction
B Gravity
C Centripetal force
D inertia

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SECTION B
1. State Newton’s Universal Law of Gravitation.

[Mengetahui]

…………………………………………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………………

2. State two factors which influence the magnitude of the gravitational force between
two bodies.

[Mengetahui]

…………………………………………………………………………………………………….…………………………….

3. Communications satellites orbit the Earth at a height of 46 000 km.
Given: Radius of the Earth = 6.4 x 106 m

a) How far is this from the centre of the Earth? [Memahami]

………………………………………………………………………………………………………………………

b) If such a satellite has a mass of 350 kg, what is the force of attraction on it
from the Earth?
Given: G = 6.67 x 10-11 N m2 kg-2, mass of the earth = 6 x 1024 kg

[mengaplikasi kuantitatif]

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4. Calculate the force of gravity that exists between a 60 kg person and 80 kg person
who are 150 cm apart from each other.
[mengaplikasi kuantitatif]

5. What is the force of gravity that is exerted on the earth by the sun? The mass of the
sun and the earth are 1.99 x 1030 kg and 5.97 x 1024 kg respectively. The distance
between the earth and sun is 1.496 x 1011 m.
[mengaplikasi kuantitatif]

6. Planet P and planet Q have mass of 3 x 1024 kg and 4.5 x 1025kg. The gravitational
force between the two planets is 3.6 x 1020 N. How far apart is planet P from planet
Q?
[mengaplikasi kuantitatif]

7. A bottle with mass 0.3 kg tied at the end of string and spin horizontally with speed 5
m s–1. The centripetal force produced is 10 N.
a) What is the radius of the spinning orbit?

b) If the speed increases to 15 m s–1, what is the centripetal force acts?
[mengaplikasi kuantitatif]

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VIDEO + REINFORCEMENT TEST

TITLE link QR CODE
https://youtu.be/SZj6DuB0vvo
Uniform Circular Motion and
Centripetal Force

Kepler's Three Laws Explained https://youtu.be/kyR6EO_RM
KE

Newton's law of gravitation (1) https://youtu.be/70zRsEWpKD
0

PROBLEM SOLVING IN NEWTON'S https://youtu.be/6k-I4-diPeo
UNIVERSAL LAW OF GRAVITATION
(2)

PROBLEM SOLVING IN NEWTON'S https://youtu.be/CwPlV8ETiP
UNIVERSAL LAW OF GRAVITATION M
(3)

Reinforcement Test https://drive.google.com/file/
Answer (Reinforcement Test) d/1j7H0zJVwY2vP6hJr6CpPpKy
uD7979zbY/view?usp=sharing

https://drive.google.com/file/
d/1sSZoRbWc8PSaf98tIZbUzED
3ua6vqnd_/view?usp=sharing

16

ANSWER
Exercise 3.1

SECTION A Answer
A
No D
1 A
2 C
3 D
4
5

SECTION B

Structured question.

1 Newton’s Universal Law of Gravitation states that the gravitational force between
two bodies is directly proportional to the product of the masses of both bodies and
inversely proportional to the square of the distance between the centres of the two
bodies

2 Mass of the objects and distance between the centre of the first body and the centre
of the second body

3 a) Distance = 46 000 x 103 m. + 6.4 x 106 m
= 5.24 x 107 m

b)

= 6.67 ×10−11 × 350 × 6 ×1024
5.24 ×107 2
( )F

F = 51.013 N

4 F = 6.67 ×10−11 × 60 × 80

(1.5)2

F = 1.423×10−7 N

( )5
F = 6.67 ×10−11 ×1.99 ×1030 × 5.97 ×1024
1.496 ×1011
2

F = 3.54×1022 N

17

( )6 r 2 = 6.67 ×10−11 × 3×1024 × 4.5×1025
3.6 ×1020
r = 5.0×109 m

7 10 = 0.3× 52
r
a)

r = 0.75 m

b) F = 0.3×152
0.75

F = 90 N

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