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?

Newton’s Gravitational Law

Out into SpaceLesson 1

Learning Intentions...

Know that all masses attract each other with a gravitational force.

Describe a gravitational field Use F=Gm1m2

r2

The Apple story…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.

Inverse square law

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.

The Moon Calculate orbit period in

seconds Calculate orbit circumference

in metres Calculate orbit speed Calculate centripetal

acceleration Multiply this by 602. What do

you get?

Orbit radius384000 km

1 moon orbit27.3 days

g= 9.8 m/s2

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.

The Formula Gravitational attraction

obeys the inverse square Law.

It has a constant known as the gravitational constant,G.

G = 6.67x10-11 Nm2kg-2

m2m1

r

F F

F = G m1 m2

r2

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)

Worked examples:Using F = Gm1m2/r2

Data 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.

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?

Question 1 - answer

56 N (which is less than the weight as a one year old toddler)

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?

Question 2 - answer

Various Weight The same

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?

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?

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?

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?

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

Investigating the inverse square

Complete the table of separation and Gravitational force as comet approaches Earth

r (x106 m) F (N) 1/r2

100

75

50

20

10

Mass of Earth = 6 x 1024 kgMass of comet = 1 x 1018 kgG = 6.67x10-11 Nm2kg-2