Gravitational Field Lectures by Mr Jimmy Goh (for LMS)

Topic 7

Gra-vi-ta-tion-al Field

by mr jimmy goh

What do you know about the

Gravitational field?

Gravity?

Weight?

9.81?

Pull things downward?

Make things feel heavy?

Overview of this topic

1. Newton’s Law of Gravitation

2. Gravitation field & Gravitational field

strength

3. Gravitational potential energy & potential

4. Satellites in orbit

Learning outcomes

2. Field strength (vector)

1. Newton’s law of Gravitation

Learning outcomes 3. Potential (scalar)

4. Satellite in orbit

7.1 Introduction

Guess my weight.

What is the unit of weight?

What is weight?

A force due to gravitational field of Earth

What affects its magnitude?

The mass of the object

The value of g (also known as acceleration due to gravity)

7.1 Introduction

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.

Average radius of

Earth is 6400 km

North pole

South pole

Equator

Diameter at the

equator is 43 km

longer than the pole

to pole diameter

Axis of

rotation

SUN E W

Rotates about its

pole to pole axis

Rotates from

West to East

7.1 Introduction

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!




3.8 108 m

x

Net gravitational field

strength & potential by

Earth & Moon Model

FCE FCM

1 to 1 computing project/2 Net gravitational field strength & potential by Earth & Moon Model.jar


FCE FCM

Square

root both

sides

7.3 Gravitational Field

Do you have

gravitational field?


The gravitational field near

Earth’s surface is uniform

The closer the field lines, the

stronger the field strength.

The field lines should be

drawn parallel to each other

and of equal spacing.

These are called the field lines.


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.


7.4 Gravitational Field Strength

20 N

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.

5 kg

r1

At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2

Also known as the

acceleration due to gravity

r1

5 kg 20 N 5 N

r2

5 kg

At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2

What happen if

a 100 kg is

placed at r2?


20 N



at r1.

5 kg

r1

At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2

Also known as the


r1

5 kg 20 N 100 N

r2

100 kg

At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2

What happen if

a 100 kg is

placed at r2?

Field strength gives a

clearer indication..


4 N kg-1



at r1.

r1

At r1, g = 20 N / 5 kg = 4 N kg-1 or 4 m s-2

Also known as the


r1

r2

At r2, g = 5 N / 5 kg = 1 N kg-1 or 1 m s-2

4 N kg-1 1 N kg-1


F

F1

F2

F3


Source mass


Gravitational field

strength &

potential Model

1 to 1 computing project/1 Gravitational field strength & potential Model.jar


g1 g2 g3

g4



gE gM


gE gM


7.5 Gravitational Potential Energy

In topic 5 (Work Energy Power), G.P.E. = mgh

5 kg

10 m

G.P.E. = mgh

= (5) (9.81) (10)

= 491 J

15 m

Reference = 0 m

Reference = 0 m

G.P.E. = mgh

= (5) (9.81) (15)

= 736 J

Which is the actual G.P.E. of the 5 kg object?

Therefore, mgh does not give

us the actual G.P.E. of object.

Instead, mgh indicates the

change in G.P.E. of object.

Furthermore, the g value

(9.81) is only for short

heights from Earth surface.


Infinity

U = 0 J

(max) r

M

m As r increases

U = - 100 J U = - 50 J

U increases


r

s Fext

That point Gravitational field

strength &

potential Model

1 to 1 computing project/1 Gravitational field strength & potential Model.jar


r

s Fext

That point

Because F and s

are in opposite

direction!


7.6 Gravitational Potential



gA gB

gC


gA gB

gC

Compare & Contrast

-ve sign:

pointing in –ve

direction -ve sign: less

than zero

7.7 Relationship between F & U

7.7 Relationship between g & ɸ



r /m

ɸ /MJ kg-1

-62.72

- 59.12

- 59.03

- 58.94

400 000

7.8 Satellite in orbit Launching a

satellite video

Blast into Space, Spectacular Fall to Earth - YouTube.flv

7.8 Satellite in orbit

7.8 Satellite in orbit

7.9 Kepler’s Third Law

Kepler’s 3rd Law

Model

What can this tell us about

the rotation of different

planets around the Sun?

What happen to the

period of rotation if the

mass of satellite is

increased?

1 to 1 computing project/4 Kepler's 3rd law Model.jar

7.10 Geostationary Satellites

Geostationary

Orbit Model

North pole

South pole

Equator

E W

1 to 1 computing project/3 Geostationary Orbit Model.jar


Axis of rotation





Since V = r ω = r ( 2π / T),

7.11 Energy of a Satellite in orbit


2

2

Only for satellite in orbit!


EK = − ET

EP = 2 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

Documents

Gravitational Field Lectures by Mr Jimmy Goh (for LMS)