Topic 7
Gra-vi-ta-tion-al Field
by mr jimmy goh
Overview of this topic
1.
2.
3.
4.
Newton’s Law of Gravitation
Gravitation field & Gravitational field
strength
Gravitational potential energy & potential
Satellites in orbit
Learning outcomes
1. Newton’s law of Gravitation
2. Field strength (vector)
Learning outcomes
3. Potential (scalar)
4. Satellite in orbit
7.1 Introduction
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What do you know about Earth?

Oblate spheroid: a sphere flattened along the axis from
pole to pole such that there is a bulge around the equator.
North pole
Diameter at the
equator is 43 km
longer than the pole
to pole diameter
Rotates about its
pole to pole axis
W
E
Equator
Average radius of
Earth is 6400 km
Axis of
rotation
SUN
Rotates from
West to East
South pole
7.1 Introduction
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

Earth is a rocky planet with a huge mass of 6.0 x 1024 kg.
Because of its mass, it has a strong gravitational field
around it that attracts everything that has mass towards
itself.
What happens when you drop an apple in air?
It will fall down.
It will accelerate
towards the centre
of the Earth.
7.1 Introduction

Earth is not the only planet that can attract other masses.
Ocean tides are caused by the
gravitational attraction of the Moon
on the earth’s oceans
Gravitational force is responsible for
keeping the Earth in its orbit around
the Sun.
7.2 Newton’s law of Gravitation
7.2 Newton’s law of Gravitation
Not radius!
7.2 Newton’s law of Gravitation
7.2 Newton’s law of Gravitation
7.2 Newton’s law of Gravitation
3.8  108 m
FCE
FCM
x
Net gravitational field
strength & potential by
Earth & Moon Model
7.2 Newton’s law of Gravitation
FCE
Square
root both
sides
FCM
7.3 Gravitational Field
Do you have
gravitational field?
7.3 Gravitational Field
 The gravitational field near
Earth’s surface is uniform
 The closer the field lines, the
stronger the field strength.
These are called the field lines.
 The field lines should be
drawn parallel to each other
and of equal spacing.
7.3 Gravitational Field
 The gravitational field around Earth is
non-uniform.
 The field lines should be drawn radially
pointing towards the centre of Earth.
 The field lines get further apart (field
strength decreases) as it gets further
from Earth.
7.3 Gravitational Field
Also known as the
acceleration due to gravity
7.4 Gravitational Field Strength
For example, if a 5 kg point mass is placed at distance r1 away from Earth and it
experiences a gravitational force of 20 N, calculate the gravitational field strength
at r1.
At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2
At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2
5 kg 5 N
What happen if
a 100 kg is
placed at r2?
5 kg
20 N
20 N
r1
r2
r1
5 kg
Also known as the
acceleration due to gravity
7.4 Gravitational Field Strength
For example, if a 5 kg point mass is placed at distance r1 away from Earth and it
experiences a gravitational force of 20 N, calculate the gravitational field strength
at r1.
Field strength gives a
At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2
At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2
100 kg
What happen if
a 100 kg is
placed at r2?
100 N 5 kg
clearer indication..
20 N
20 N
r1
r2
r1
5 kg
Also known as the
acceleration due to gravity
7.4 Gravitational Field Strength
For example, if a 5 kg point mass is placed at distance r1 away from Earth and it
experiences a gravitational force of 20 N, calculate the gravitational field strength
at r1.
At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2
At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2
1 N kg-1
4 N kg-1
r1
r2
4 N kg-1
r1
7.4 Gravitational Field Strength
F
F2
F3
F1
7.4 Gravitational Field Strength
Source mass
7.4 Gravitational Field Strength
Gravitational field
strength &
potential Model
7.4 Gravitational Field Strength
g4
g3
g1
g2
7.4 Gravitational Field Strength
7.4 Gravitational Field Strength
gE
gM
7.4 Gravitational Field Strength
gE
gM
7.5 Gravitational Potential Energy
In topic 5 (Work Energy Power), G.P.E. = mgh
Therefore, mgh does not give
us the actual G.P.E. of object.
5 kg
Furthermore, the g value
10 m
(9.81) is only for short
heights from Earth surface.
15 m
Reference = 0 m
Reference = 0 m
G.P.E.
= mgh
G.P.E.
= mgh
= (5) (9.81) (10)
= (5) (9.81) (15)
= 491 J
= 736 J
Which is the actual G.P.E. of the 5 kg object?
Instead, mgh indicates the
change in G.P.E. of object.
7.5 Gravitational Potential Energy
M
m
r
As r increases
U = - 100 J
U increases
U = - 50 J
Infinity
U=0J
(max)
7.5 Gravitational Potential Energy
7.5 Gravitational Potential Energy
7.6 Gravitational Potential
7.6 Gravitational Potential
7.6 Gravitational Potential

Gravitational field
strength &
potential model
7.6 Gravitational Potential
866 m
gA
500 m
gB
gC
7.6 Gravitational Potential
866 m
500 m
7.7 Relationship between F & U
7.7 Relationship between g & ɸ
Gravitational field
strength &
potential model
7.7 Relationship between g & ɸ
7.7 Relationship between g & ɸ
ɸ /MJ kg-1
400 000
r /m
- 58.94
- 59.03
- 59.12
-62.72
7.8 Satellite in orbit
Are we orbiting
around the
Earth?
Make a guess..
How many are
there to-date?
7.8 Satellite in orbit
Fg
7.8 Satellite in orbit
7.9 Kepler’s Third Law
What happen to the
period of rotation if the
mass of satellite is
increased?
Kepler’s 3rd Law
Model
What can this tell us about
the rotation of different
planets around the Sun?
North pole
7.10 Geostationary Satellites
W
E
Equator
South pole
Geostationary
Orbit Model
7.10 Geostationary Satellites
satellite
Axis of rotation
7.10 Geostationary Satellites
7.10 Geostationary Satellites
Different Satellites
Low Altitude Orbit Satellites
Low orbit video
7.10 Geostationary Satellites
7.10 Geostationary Satellites
7.10 Geostationary Satellites
7.10 Geostationary Satellites
7.10 Geostationary Satellites
Since V = r ω = r ( 2π / T),
7.10 Geostationary Satellites
7.11 Energy of a Satellite in orbit
7.11 Energy of a Satellite in orbit
Only for satellite in orbit!
2
2
7.11 Energy of a Satellite in orbit
EP = 2 ET
EK = − ET
7.11 Energy of a Satellite in orbit
Add in: Mass of Earth = 6.0 x 1024 kg
7.11 Energy of a Satellite in orbit
Mass of Earth = 6.0 x 1024 kg
Gravitation
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The solution for the three Inquiry ICT
worksheets will be posted on LMS on
next Mon.
Please complete an online survey.
URL is on the last page of tutorial.
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End