11/6/2014
Newton’s Law of Universal
Gravitation
and
Circular Motion
Newton’s Law of Universal Gravitation
• Newton noted the planets from Kepler’s work
followed a nearly circular orbit.
• He theorized that there must be a force to
keep the planets from going off in a straight
line.
• Gravitational force is a field force that always
exists between two masses, regardless of the
separation medium or distance.
• Remember all forces add like vectors.
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11/6/2014
Newton's Law of Universal Gravitation Equation
FG 
G  m1  m2
r12 2
Where FG is the Gravitatio nal Force
G is the Gravitatio nal Constant
G  6.67 x 10 -11
Nm2
kg 2
m1  one of the two masses
m2  the other of the two masses
r 12  the radial distance between the
center of the two masses
Earth moon sun mass distance chart
Earth
Moon
Sun
Mass
5.97 x1024 kg
Radius (mean)
6.38 x 106 m
Mass
7.35 x1022 kg
Radius (mean)
1.74 x 106 m
Mass
1.99 x1030 kg
Radius (mean)
6.96 x 108 m
Earth-Sun
distance (mean) 1.496 x 1011 m
Earth-Moon
distance (mean) 3.84 x 108 m
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11/6/2014
Newton's Law of Universal Gravitation
Equation
You should be able to solve Newton’s Universal
Law of Gravitation for the following variables:
r=
m1 =
m2 =
Newton's Law of Universal Gravitation
Equation
You should be able to discuss what happens to
the gravitational force when changing the
following variables in Newton’s Universal Law of
Gravitation:
• Increasing one or both masses
• Decreasing one or both masses
• Increasing the radial distance
• Decreasing the radial distance
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11/6/2014
Newton's Law of Universal Gravitation
Equation for Multiple Masses
All forces add like vectors.
How do vectors add?
Consider three spherical masses in a row as
m
m
m
shown to the right.
r
r
All forces are linear so
r
to find the gravitational force on m1 you add the
forces.
FBD on m
F
F
Lets look at the FBD on m1
1
2
3
12
23
13
1
12
13
Newton's Law of Universal Gravitation
Equation for Multiple Masses
Using the diagram below, now draw the FBD on m2.
FBD on m
Using the FBD, calculate the
F
F
gravitational force if
2
21
m1 = 2kg, m2 = 4kg, m3 = 6kg
and
r12 = 4m , r23 = 2m , r13 = 6m
23
m1
m2
r12
m3
r23
r13
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11/6/2014
Newton's Law of Universal Gravitation
Equation for Multiple Masses
All forces add like vectors. So draw the FBD on
m1 considering three spherical masses as shown
below.
FBD on m1
m1
r12
m2
r13
m3
Find the gravitational force on m1.
Newton's Law of Universal Gravitation
Equation for Multiple Masses
m1 = 2kg, m2 = 4kg, m3 = 6kg
r12 = 4m, r13 = 6m
Find the gravitational force on m1.
m1
r12
FBD on m1
m2
r13
m3
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