1. Some Questions
•
•
•
What causes the weight that everyone
feels?
What affects the size of the Earth’s pull
on you? Why would you weigh a different
amount on the Moon?
If the Earth is pulling down on you, then
what else must be occurring, by Newton’s
3rd Law?

2. Newton’s Gravitational
Law
Out into Space
Lesson 1

3. Learning Intentions...
Know
that all masses attract each
other with a gravitational force.
Describe a gravitational field
Use F=Gm1m2
r2

4. The Apple story…
Inverse square law
Newton was thinking about
his ideas of gravity in an
orchard.
He was wondering whether
the inverse square law could
explain the weakness of
gravity.

5. Mathematics and science
Newton
used a=v2/r to calculate the
acceleration of the moon.
By geometry he knew the orbit of the
moon was 60 times the radius of the Earth.
If the acceleration of an apple is 602 times
bigger than the moon it would mean gravity
was an inverse square relationship.

6. The Moon
1 moon orbit
27.3 days
Orbit radius
384000 km
Calculate
g= 9.8 m/s2
orbit period in
seconds
Calculate orbit circumference
in metres
Calculate orbit speed
Calculate centripetal
acceleration
Multiply this by 602. What do
you get?

7. Newton’s universal law of
gravitational attraction
In
1687 Newton
published the
“Principia”.
The centre piece
was the
gravitational law.
•All particles in the Universe
attract all other particles
•The force is proportion to the
mass of each object.

8. The Formula
m2
m1
F
F
r
 Gravitational
attraction obeys
the inverse square Law.
 It has a constant known as
the gravitational constant,G.
 G = 6.67x10-11 Nm2kg-2
F = G m1 m2
r2

9. Remarkable Law
Formation
of planets and stars
Wobbles in planets orbits (discovery
of Neptune)
Calculate mass of astronomical
bodies
Complicated motion of more than 2
bodies (Saturn’s rings)

10. Data
Worked examples:
Using F = Gm1m2/r2
required:
G = 6.67
10-11 N m2 kg-2,
mass of the Earth = 6.0
1024 kg,
radius of the Earth = 6.4 106 m,
mass of the Sun = 2.0 1030 kg,
average distance from the Earth to
the Sun = 1.5 1011 m.

11. Question 1
Communications
satellites orbit the
Earth at a height of 36 000 km. How
far is this from the centre of the
Earth? If such a satellite has a mass
of 250 kg, what is the force of
attraction on it from the Earth?

12. Question 1 - answer
56
N (which is less than the weight
as a one year old toddler)

13. Question 2
What
is the force of attraction from
the Earth on you? What do we call
this force? What is the force of
attraction on the Earth from you?

14. Question 2 - answer
Various
Weight
The
same

15. Question 3
What
is the force of attraction from
the Sun on you? How many times
smaller is this than the force of
attraction from the Earth on you?

16. Question 4
The
average force of attraction on
the Moon from the Sun is 4.4 1020
N. Taking the distance from the Sun
to the Moon to be about the same as
that from the Sun to the Earth, what
value of mass does this give for the
Moon?

17. Question 5
Using
the mass of the Moon you
calculated in question 4, what is the
pull of the Earth on the Moon, if the
Moon is 380 000 km away? How does
this compare with the pull of the Sun
on the Moon?

18. Question 6
What
is the force of attraction
between two people, one of mass 80
kg and the other 100 kg if they are
0.5m apart?

19. Question 7
What
is the force of attraction
between the Earth and the Sun?
Mass of the Sun = 2 x 1030 kg,
distance from the Earth to the Sun =
1.5 x 1011 m

20. Investigating the inverse
square
Complete
the table of
r (x106 m) F (N) 1/r2
separation and
100
Gravitational force as
comet approaches Earth 75
50
Mass of Earth = 6 x 1024 kg
Mass of comet = 1 x 1018 kg
20
-11 Nm2kg-2
G = 6.67x10
10