1) Newton proposed that gravity is a force that acts at a distance between all masses in the universe, not just between the Earth and objects near it. 2) Newton developed mathematical formulas to describe gravity, including that the gravitational force between two objects decreases with the inverse square of the distance between them. 3) Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

1. Gravity
Newton rationalized that if the earth puts a force
on an apple, then who’s to say that it doesn’t
exert a force on the moon?
Contact vs. Non-contact Forces
↓  Newer concept: force
Must be touching acting at a distance
(gravity, magnets,
electricity…)

2. Gravity must be
proportional to both
masses because of
Newton’s 3rd
Law
(Equal and opposite
forces)
F α M m
Newton’s Math Proof
Force of gravity must
decrease by the
inverse square of the
distance.
F α 1/r2
This is known as the
inverse square law!
It is repeated in
electricity and
magnetism!
Combine
These!
2
Mm
F
r
α 2
GMm
F
r
=

3. Keeping Relationships Simple
• Proportions: Compare two quantities while their
outcome remains constant. Symbol: α
• Inverse relationship means you are comparing
two quantities and as one quantity gets larger
the other gets smaller.
• F = ma
• When the F is kept constant the m is inversely
proportional to the a.

4. Still Keeping it Simple
Inverse Square relationship means that as
one quantity gets larger the other gets
smaller by the square of the smaller
quantity.
F α 1/r2
When r goes up, F goes down.

5. Keep is Simple Direct
• Direct Relationship means that as one
quantity gets larger the other gets larger
as well.
• F α a
• As F increases so does the a.
• F = ma, mass will be kept constant.

6. Law of Universal Gravitation
Every particle in the universe attracts every other
particle with a force that is proportional to the
product of their masses and inversely
proportional to the square of the distances
between them. This force acts along a line
joining the 2 particles.
2
GMm
F
r
=
G = gravitational constant (small or large?)
G = 6.67 x 10-11
Nm2
/kg2
It took 100 years later for this law to be proven.
Henry Cavendish performed the experiment.

7. Sample Problem
A 50 kg girl & a 70 kg boy are 50 cm apart on a
park bench. Find the force of attraction…
Field  Area around an
object that affects
other objects.
Gravitational Field
 Area around a
mass that affects
other masses
What represents the
gravitational field around the
earth?
At Crown Point, the radius
of the Earth is 6.37101 x
106
m. If the Earth has a
mass of 5.98 x 1024
kg.
Then calculate the Earth’s
gravitational field in Crown
Point.
11 24
2 6 2
2
6.67 10 (5.98 10 )
(6.37101 10 )
9.83 /
GM x x
g
r x
g m s
−
= =
=