PHYSICS STUDY GUIDE
CHAPTER 8: UNIVERSAL GRAVITATION
NEWTON’S FIRST LAW OF MOTION

Unless an unbalanced force is exerted on an object. The object will continue moving with
constant velocity.
NEWTON’S SECOND LAW OF MOTION

The acceleration of an object is directly proportional to the acceleration of the object.

The acceleration of an object is inversely proportional to the mass of the object.
NEWTON’S THIRD LAW OF MOTION

When two objects interact, object A exerts a force on object B. In turn, object B exerts a force
on object A.

These two forces are equal in magnitude, but opposite in direction.
LAW OF UNIVERSAL GRAVITATION

Law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is
about the universality of the gravitational force. Newton's place in the Gravitational force Hall of
Fame is not due to his discovery of the gravitational force, but rather due to his discovery that
gravitational forces are universal.

ALL objects attract each other with a force of gravitational attraction. Gravitational forces are
universal. This force of gravitational attraction is directly dependent upon the masses of both
objects and inversely proportional to the square of the distance that separates their centers.
The Gravitational force is represented with a unique mathematical model using a constant of
proportionality.
FG =
G· m1· m2
d2

FG
= Gravitational force
(Newtons)

G
= Universal Gravitational Constant
(N · m2 / kg2 )

m1
= mass of object 1
(kilograms)

m2
= mass of object 2
(kilograms)

d
= distance separating the objects’ centers (meters)

The precise value of G was determined experimentally by Henry Cavendish in the century after
Newton's death.

G = 6.673 x 10-11 N · m2 / kg2
Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects
of known mass and known separation distance. As a first example, consider the following problem.

Effect of mass on gravitaional force: Gravitational force is directly proportional to the mass of
both interacting objects:





More massive objects will attract each other with a greater gravitational force.
If the mass of either object increases, the force of gravitational attraction between them
also increases.
If the mass of one of the objects is doubled, then the gravitational force between them is
doubled.
If the mass of one of the objects is tripled, then the gravitational force between them is
tripled and so on.
Effect of distance on gravitaional force: Since gravitational force is inversely proportional to
the square of the separation distance between the two interacting objects.



More separation distance will result in weaker gravitational forces.
If the separation distance between two objects is doubled (increased by a factor of 2), then
the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second
power).
If the separation distance between any two objects is tripled (increased by a factor of 3),
then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the
second power).
EFFECT OF MASS ON GRAVITAIONAL FORCE
EFFECT OF DISTANCE ON GRAVITAIONAL FORCE
m
m
d
m
m
2d
m
FG
FG
m
FG
2m
FG
½d
2m
2d
m
3m
2d
A 5 kg bowling ball and a 6 kg bowling ball rest on a rack 0.4 m
apart.

Find the gravitational force between both objects.
FG =
G· m1· m2
d2
FG =
6.67x10 -11· 5· 6
0.4 2
FG = 1.25x10- 8
Newtons
FG
G·m·m
d2
=F
G·m·m
(2d)
F
2
G·m·m
(½ d)2
G · 2m · 2m
(2d)2
4
= 4F
=F
G · m · 3m
3F
(2d)2
4
GRAVITATIONAL CONSTANT vs. UNIVERSAL GRAVITATIONAL CONSTANT
Gravitational force applied to any object on Earth

FG =

G· mP
· mo
(rP )2
FG
= Gravitational force

G
= Universal Gravitational Constant

mP
= mass of the planet

rP
= radius of the planet

mo
= mass of the object
Substitute the values of G, mP, and rP and you will find the gravitaional constant of any planet (it is
all about being universal).
G· mP
gP =
(rP )2



gP
= Gravitational constant of the planet

G
= Universal Gravitational Constant

mP
= mass of the planet

rP
= radius of the planet
This is how we find the gravitational force on Earth:
FG = gP · mo
FEonO = g · m

FG
= Gravitational force

gP
= Gravitational constant of the planet

mo
= mass of the object
VELOCITY OF ORBITING OBJECTS
G· m1· m2
d2
Gravitational force applied to any object on Earth:
FG =

Centripetal force:
mP · v 2
FC =
rC

The source if this circular motion is a gravitational force.

Centripetal force must equal the gravitational force:

mP · v
rC
2
=
G · mP · mS
(rC )2
FC = F G

V
= velocity of the planet

mP
= mass of the planet

mS
= mass of the sun

rC
= Radius of the circle (radius of the orbit around the sun)

G
= Universal Gravitational Constant

Solve for the velocity of the orbiting object
v2 =

G · mS
rC

V
= velocity of the orbiting object

mP
= mass of the planet

mS
= mass of the sun

rC
= Radius of the circle (radius of the orbit around the sun)

G
= Universal Gravitational Constant
Solve for the velocity (take the square root)
Ving =
G · morbited
rcircle
NAME
Sun
Moon
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto

ving
= velocity of the orbiting object

G
= Universal Gravitational Constant

morbited = mass of the object being orbited

rCircle
= Radius of the circle (radius of the orbit)
PLANETARY DATA
RADIUS OF THE
MASS
PLANET
696 X 106
1.99 X 1030
6
1.738 X 10
7.34 X 1022
6
2.44 X 10
3.30 X 1023
6
6.05 X 10
4.87 X 1024
6
6.38 X 10
5.98 X 1024
6
3.40 X 10
6.42 X 1023
71.5 X 106
1.90 X 1027
6
60.3 X 10
5.69 X 1026
6
25.6 X 10
8.66 X 1025
6
24.8 X 10
1.03 X 1026
6
1.15 X 10
1.5 X 1022
RADIUS OF THE
ORBIT
5.79
1.08
1.50
2.28
7.78
1.43
2.87
4.50
5.91
X
X
X
X
X
X
X
X
X
1010
1011
1011
1011
1011
1012
1012
1012
1012