3.1.3 Relate gravitational acceleration, g on the surface of the Earth with the universal gravitational constant, G 3.1.4 Justify the importance of knowing the values of gravitational acceleration of the planets in the Solar System. 3.1.5 Describe the centripetal force in the motion of satellites and planets system. Centripetal Force, F = 푚푣2푟 3.1.6 Determine the mass of the Earth and the Sun using Newton’s universal law of gravitation and centripetal force.

1. Gravitation
KSSM TINGKATAN 4 | DLP
Gravitational
acceleration

2. designed by tinyPPT.com
answer these questions.
We are going to
What are Newton’s
Universal Law of Gravitation
and Kepler's’ Laws?
01
Why we need to know the
values of the gravitational
acceleration of planets in the
Solar System?
02
03 How do man-made
satellites help to
improve human life?
05

3. designed by tinyPPT.com
Success
Criteria
(Learning
standard)
01
Students will be able to
state and write Newton’s
Universal Law of Gravitation
Students will be able to
state, explain and write
Kepler’s Law
Students will be able to
explain about satellites
orbiting.
Students will be able to
solve problems about
escape velocity
explain these.
We will be able to
02
03
04

4. There are various types
of man-made satellites
revolving in their
respective orbits in outer
space.
Satellites are invented
for:
• communication
purposes,
• weather forecasts and
• Earth observations.
Why are these satellites able to
revolve in their respective orbits?

5. Ibn al-Haytham wrote
about gravity before
Newton!
Ibn al-Haytham’s name is frequent. Talented man he
was. Father of ‘History of Science’, George Sarton
indirectly writes that Newton was influenced by ibn
al-Ibn al-Haytham and, Isaac Newton did keep a copy
of ibn al-Haytham’s magnum opus, Kitab al-
Manazir (Book of Optics) in his personal library.
This Photo by Unknown Author is licensed under CC BY-SA
This Photo by Unknown Author is licensed under CC BY-SA

6. This Photo by Unknown Author is licensed under CC BY-SA
Then, it is said, in 1667, the scientist, Isaac Newton,
observed an apple which fell vertically to the ground
and the movement of the Moon around the Earth.
From what he read, he subsequently concluded that a
force of attraction not only exists between the Earth
and the apple but also between the Earth and the
Moon.

7. Curiosity 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
the Earth.

8. This Photo by Unknown Author is licensed under CC BY-NC-ND
Such spaceships enable
photographs of planets to be
taken to benefit scientific
inventions and technology.

9. 3.1 Newton’s Universal Law of
Gravitation
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10. Gravitational force
known as universal force
∵ it acts between
in the universe.
This Photo by Unknown Author is licensed under CC BY-NC-ND
any two bodies

11. Info
01
Gravitational force exists
between two bodies.
Both bodies experience
gravitational force of the
same magnitude.
02
Why does a fallen leaf move
towards the ground?
Both the leaf and the Earth experience the same
gravitational force.
This causes the leaf and the Earth to move towards
one another.
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.

13. 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.
F = G
m1
m2
𝑟2
G = gravitational constant (G = 6.67 × 10–11 N m2 kg–2)
*G can be determined through experiment.
Two bodies of masses m1 and m2 that are
separated at r, experience a gravitational
force of F respectively.

15. 3.1 Newton’s Universal Law of
Gravitation
Relating Gravitational Acceleration, g on the Surface of the Earth
with Universal Gravitational Constant, G
This Photo by Unknown Author is licensed under CC BY-SA

16. According to
Newton’s Second Law of Motion,
gravitational force can
be expressed as
From Newton’s
Universal Law
of Gravitation,
gravitational
force
is expressed as
F = mg
𝐹 = 𝐺
𝑚1𝑚2
𝑟2
So, What is the relationship between g and G?
From Newton’s Second
Law of Motion,
F = ma.
When involving
gravitational
acceleration, g,
F = mg

17. Activity 3.4
Aim: To derive the formula for gravitational
acceleration, g using the formulae F = mg
and F = GMm/r2
Instructions:
1. Work in pairs.
2. Discuss and complete Figure
3.9 to derive the relationship
between g and G.
Discussion:
1. What is the relationship between
gravitational acceleration, g and
gravitational constant, G?
2. What are the factors that influence
the value of gravitational
acceleration?

19. Activity 3.5
Aim: To discuss the variation in the values
of g with r
Discussion:
1. What is the value of gravitational
acceleration on the Earth’s surface?
2. Plot a graph of g against r.
3. How does the value of gravitational
acceleration change when the distance
from the centre of the Earth increases?
4. Discuss the condition where the value
of gravitational acceleration is almost
zero.
𝐺𝑀
4𝑅2
𝐺𝑀
9𝑅2
𝐺𝑀
16𝑅2
𝐺𝑀
25𝑅2
𝐺𝑀
𝑅2
Instructions:
1. Calculate the value of gravitational
acceleration for the five distances
given in Figure 3.10
2. Complete the table.

20. R 2R
g=
𝐺𝑀
𝑅2
𝐺𝑀
4𝑅2
𝐺𝑀
9𝑅2
𝐺𝑀
25𝑅2
3R 4R 5R
𝐺𝑀
16𝑅2
g
r
Value g is inversely
proportional to the square
of the distance from centre
of the Earth for r ≥ R.
Value g is directly
proportional to the
distance from the centre of
the Earth for r ≺ R.
𝐺𝑀
4𝑅2
𝐺𝑀
9𝑅2
𝐺𝑀
16𝑅2
𝐺𝑀
25𝑅2
𝐺𝑀
𝑅2
Variation of g with r

21. Distance of satellite
from the centre of the
Earth is r = (R + h).
So, gravitational
acceleration,
g =
𝐺𝑀
(𝑅+ℎ)2
On the surface of the
Earth, height, h = 0.
Then, r = R.
So, gravitational
acceleration,
g =
𝐺𝑀
𝑅2
M is the mass of the Earth
R is the radius of the Earth

22. Example 1

23. Example 2

24. Importance of Knowing the Value of
Gravitational Acceleration
to calculate g on
the surface of
other bodies like
Planets, the Moon,
the Sun.
Fg is a universal force. When the g on the surface of a planet is known,
magnitude of Fg on an object on the
surface of the planet can be calculated.
g affects the growth of humans

25. Gravitational accelerations for the Moon, the
Sun and the planets in the Solar System

26. Activity 3.8
Aim: To gather information on the
effects of gravity on the growth of
humans.
Instructions:
1. Gather information on the effects of
gravity on the growth of humans by
visiting websites or from other suitable
reading materials.
3. Complete the Table.
4. Present a multimedia presentation
entitled Effects of Gravity on the
Growth of Humans.