Universal Law
of Gravitation
EQ: What is Newton’s law of universal
gravitation and how does the mass and
distance between objects affect the
gravitational force?
http://ed.ted.com/lessons/jon-bergmannhow-to-think-about-gravity
Because of Newton’s 3rd law every body in the
universe exerts a force of attraction on every
other body.
• This is Newton’s Universal Law of Gravitation
The force between two
objects, due to their masses,
is called the gravitational force
(Fg)- the gravitational force is
affected by mass and
distance.
GmM
Fg 
2
r
Universal Gravitational Constant6.67
2
m
x10-11 N  kg 2
GmM
Fg 
2
r
Masses of the 2
objects (kg)
Distance between
Gravitational
force (N)
the objects from their center (m)
Example 1:What is the gravitational
force between the Earth and the Moon?
mEarth = M = 6.0 x 1024 kg
mMoon = m = 7.4 x 1022 kg
r = 3.8 x 108 m
2
m
-11
G = 6.67 x 10 N 
kg 2
Fg = 2.1 x 1020
Example 2: What is the gravitational force between the
Earth and Venus?
mEarth = M = 6.0 x 1024 kg
mVenus = m = 5.0 x 1024 kg
r = 3.8 x 1010 m
m2
G = 6.67 x 10-11 N  kg 2
Answer:
F = 1.386x1018 N
The sun has a mass of 2.0 x 1030 kg and a
radius of 7.0 x 105 km. What mass must
be located at the sun’s surface for a
gravitational force of 470 N to exist
between the mass and the sun?
The gravitational attraction between the Earth
and Mars is 8.7 x 1016 N. The distance
between the two planets is 5.5 x 1010m.
Earth has a mass of 6.0 x 1024 kg. What’s the
mass of Mars?
GmM
Fg 
2
r
Answer behind Exit Ticket:
Distance also plays a role in the force of gravity.
-Explain how the force changes with respect to
distance.
-Explain how the acceleration between 2 objects
changes with respect to distance. (Hint: think
about Newton’s 2nd Law of motion and the
relationship between force, mass, and
𝐹
acceleration 𝑎 = )
𝑚
Determine the force of gravitational attraction
between the earth (m = 5.98 x 1024 kg) and a
70-kg physics student if the student is standing
at sea level, a distance of 6.38 x 106 m from
earth's center.
Determine the force of gravitational attraction
between the earth (m = 5.98 x 1024 kg) and a
70-kg physics student if the student is in an
airplane at 40000 feet above earth's surface. This
would place the student a distance of 6.39 x 106
m from earth's center.
There is also a way to determine the
gravitational field around one object:
GmM
Fg 
2
r
GmM

mg
 
r2
GmM
w
2
r
GmM
mg 
r2
GM
g 2
r
This is now
the gravitational
Field Strength(GFS)
Example 3: What is the Gravitational Field Strength in
Earth?
• Radius of the Earth – 6.37 x 106 m
Is Gravity Diluted?
The distance d is in the denominator of this
relationship, it can be said that the force of gravity is
inversely related to the distance. This mathematical
relationship is sometimes referred to as an inverse
square law since one quantity depends inversely upon
the square of the other quantity
Check your understanding
Suppose that two objects attract each
other with a gravitational force of 16
units. If the distance between the two
objects is doubled, what is the new
force of attraction between the two
objects?
Answer: F = 4 units
If the distance is increased by a factor of 2, then force will be decreased
by a factor of 4 (22). The new force is then 1/4 of the original 16 units.
F = (16 N) / 4 = 4 units
Check your understanding
Suppose that two objects attract each
other with a gravitational force of 16
units. If the mass of both objects was
doubled, and if the distance between
the objects remained the same, then
what would be the new force of
attraction between the two objects?
Answer: F = 64 units
If each mass is increased by a factor of 2, then force will be increased by
a factor of 4 (2*2). The new force is then 4 times the original 16 units.
F = (16 units ) • 4 = 64 units
Both the ULG and the GFS follow the
Inverse square law:
• ULG-If the distance between two objects is doubled
the gravitational attraction is (1/4) of the original.
OR
• GFS-If we travel beyond the Earth by a distance
that is double it’s radius than we will only feel a
quarter of Earth’s gravitational pull (9.81 m/s2/4 =
2.45 m/s2).
re = 6.4 x 106 m
1x
1 re =
2x
3x
¼ re=
1/9 re =
9.81 m/s2 2.24 m/s2
4x
1/16 re =
1.09 m/s2 .61 m/s2