3.1 NEWTON'S UNIVERSAL LAW OF GRAVITATION

5. Mass of the Earth is 5.97 x 1024 kg and
radius of the Earth is 6.37 x 106 m.
Calculate gravitational acceleration on
the surface of the Earth.

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

g = 9.8 ms-2

6. A radar imaging satellite orbits around the
Earth at a height of 480 km. What is the value
of gravitational acceleration at the position of
the satellite?

• 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 h = 480 km = 480 000 m

g = . GM .

(R + h)2

= 6.67 x 10-11 x 5.97 x 1024

(6.37 x 106 + 4.8 x 105)2

g = 8.49 ms-2

7. Discuss the condition where the value
of gravitational acceleration is almost
zero.

Microgravity is the condition
in which people or objects
appear to be weightless.
The effects of microgravity
can be seen when
astronauts and objects float
in their spacecraft or
spacewalk (outside). Heavy
objects move around easily.

LEARNING STANDARD 4

3.1.4 Justify the importance of knowing the
values of gravitational acceleration of
the planets in the Solar System

.

To compare different gravitational accelerations for the Moon, the Sun and
the planets in the Solar System

Gravitational force is a universal
force. The formula g = GM/R2
can be used to calculate
gravitational acceleration on the
surface of the other bodies such
as planets, the Moon and the
Sun.

Body Mass, M / kg Radius, R / m g / ms-2
Sun/Matahari 1.99 x 1030 6.96 x 108 274.0
Mercury/Utarid 0.330 x 1024 2.44 x 106
Venus/Zuhrah 4.87 x 1024 6.05 x 106 3.7
5.97 x 1024 6.37 x 106 8.9
Earth/Bumi 0.642 x 1024 3.40 x 106 9.8
Mars/Marikh 1898 x 1024 7.15 x 107 3.7
Jupiter/Musytari 568 x 1024 6.03 x 107 24.8
Saturn/Zuhal 10.4
86.8 x 1024 2.56 x 107
Uranus/Uranus 102 x 1024 2.48 x 107 8.8
Neptune/Neptun 0.015 x 1024 1.19 x 106 11.1
0.073 x 1024 1.74 x 106 0.7
Pluto/Pluto 1.6
Moon/Bulan

Discussion: Jupiter
Which planet has the largest gravitational acceleration?

Which planet has closest to the gravitational acceleration on

the Earth? Saturn

What factors determine the value of the gravitational Mass & Radius
of the planet
acceleration of a planet?

GRAVITATIONAL ACCELERATION

SUN MOON MARS

274 ms -2 02 03

1.625 ms -2 3.711 ms -2

VENUS JUPITER

04 05

9.5 ms -2 24.5 ms -2

It keeps satellite in orbits

gravity influences the paths taken by
everything traveling through space

Slow down space craft
during landing

Rain to fall Heat to dissipate

Body fluid flow

Air and water to separate

THE EFFECTS OF GRAVITY ON THE GROWTH OF HUMANS

Factor Effect of low gravity Effect of high gravity

Difference in Density of body Density of body increases
density decreases

Bone fragility Bone becomes more No obvious change
fragile due lack of
calcium

Size of lungs Becomes bigger and Become smaller and
expands compress

Blood Blood collects at the Blood collects at the
circulatory top of the body. bottom of the body due to
system
its difficulty to flow
upwards.

Blood Decrease in blood Increase in blood pressure
pressure
pressure and the rate and the rate of the

of the heartbeat. heartbeat.

LEARNING STANDARD 5

3.1.5 Describe the centripetal force in
the motion of satellites and
planets system

m
=

Centripetal Force in the Motion of
Satellites and Planets

Diagram shows four positions of a
satellite which orbits around the
Earth at a uniform speed. Observe
the direction of the velocity of the
satellite at each position.

• A body moves in a circular motion
always experience change in the
direction of motion even though its
speed is constant.

• Therefore, the velocity of the body
changes.

Centripetal Force in the Motion of
Satellites and Planets

• A force is required to change the
direction of motion of a body.

• The force that acts on a body which
moves in a circular motion is

centripetal force.

ACTIVITY 9 CENTRIPETAL FORCE KIT

When the rubber stopper makes a circular motion, the
stretched string exerts a force on the rubber stopper.

Q1 What is the direction of the force?

in a direction towards the centre of the circle.

What is the relationship between speed of the rubber
stopper and the centripetal force?

Q2 When the speed of the rubber stopper

increase the centripetal force is increase.

How does the centripetal force change when
the rubber stopper makes a circular motion
with a smaller radius

Q3 we can feel the increase of the tension

in the string. So the centripetal force is
increase.

A force acts on the body in a
direction towards the center
of the circle for a body in
circular motion.

m
=

F = centripetal force
m = mass
v = linear speed
r = radius of circle

Centripetal Force in the Motion of
Satellites and Planets

• Linear speed, v shows how fast a
body moves in a circular motion.

➢ Give 3 factors that effect the
centripetal force

1. mass of object
2. linear speed
3. radius of circle



Example 1

• A hammer throw athlete swingin an iron
ball in a horizontal circle before releasing
it. What is the centripetal force that acts
on the iron ball when the iron ball is
moving a speed of 20 ms-1.

m = 7.2 kg F = mv2 = (7.2)(20)2 = 1 600 N
r = 1.8 m r 1.8
v = 20



CAN A SATELLITE ORBIT THE EARTH WITHOUT BEING DRIVEN BY A ROCKET ENGINE?

Prediction of Isaac Newton that a
satellite can orbits around the Earth
without being driven by a rocket engine.

Object launched with low linear speed
will follow trajectory 1 and reaches the
Earth at Q.

Object launched with sufficiently high
linear speed will follow trajectory 2
circulating the Earth. The object will
not return to the Earth.



The prediction of Newton is now a reality with so
many man-made satellites orbiting around the
Earth without being driven by any thrust.

Satellites always experience gravitational force
acting towards the centre of the Earth. The
gravitational force on satellites acts as centripetal
force

By comparing the formula for force and formula for
centripetal force, obtain centripetal acceleration, a.

F = ma = mv2
r

a = v2
r

v = linear speed of satellite
r = radius of the orbit of satellite

Example 2: Text pg 93
A weather satellite orbiting the Earth at a
height, h = 480 km. What is the centripetal
acceleration of the satellite?
Linear speed of the satellite = 7.62 x 103 m s-1.
The radius of the Earth, R = 6.37 x 106 m.

Height of satellite, h = 480 000 m

a = v2 = _ (7.62 x 103)2 _ = 8.48 ms-2

r (6.37 x 106 + 480 000)

LEARNING STANDARD 6

3.1.6 Determine the mass of the Earth
and the Sun using Newton’s
universal law of gravitation and
centripetal force.

M = mass of the Earth

m = mass of the Moon
Determine the mass of the Earth and r = radius of the Moon’s orbit
the Sun
T = period of revolution of the Moon around the Earth

v = linear speed of the Moon

Distance travelled by the Moon = 2πr

when making one complete orbit

around the Earth.

Linear speed of the Moon, v = Distance

Time

v = 2πr

T

F = GMm F = mv2
r2 r

F = GMm F = mv2
r2 r

GM rv2

GM rv2

GM (2πr)2 r = 4π2r3
T2 T2

M = 4π2r2r
GT2

What is the formula to determine the mass of the Earth? M = 4π2r3
GT2

State the data needed to calculate the mass of the Earth.

• Radius of the orbit of any satellite of the Moon
• Period of revolution

State the data needed to calculate the mass of the Sun

• Radius of the orbit of any planet
• Period of revolution of planet concerned

Period of revolution of the Moon around the Earth, T = 2.36 x 106 s
and the radius of the Moon’s orbit, r = 3.83 x 108 m. Calculate the
mass of the Earth, M.

M = 4π2r3 = _ 4π2(3.83 x 108)3 __
GT2 6.67 x 10-11 x (2.36 x 106)2

= 5.97 x 1024 kg

The Earth revolves the Sun in a period of one year and the radius
of the orbit is r = 1.50 x 1011 m. Calculate the mass of the Sun.

M = 4π2r3 = _ 4π2(1.50 x 1011)3 __
GT2 6.67 x 10-11 x (31,536 000)2

= 2.0 x 1030 kg