Download Newton`s Universal Law of Gravitation

Newton’s Universal Law of
Gravitation
Chapter 8
Gravity
What is it?
The force of
in the universe.
It depends upon:
• The
• the
•
(
between any
between the two bodies.
of the two bodies.
of the
)
Universal Gravitation
In 1666, Isaac Newton developed a basic
mathematical relationship:
F
This relationship was used to describe the attractive
force between the
and the
where ___ is a line drawn through the
of
the two bodies.
Universal Gravitation
Newton further developed this equation to
include the mass of the objects after seeing an
fall to the ground to:
F=
•
Where:
–
–
–
G = Universal gravitational constant (6.67 x 10-11 Nm2/kg2)
m1 and m2 are two masses on interest.
r = distance between two bodies (
to
)
Gravitational Fields
Objects with MASS produce
Field lines point
from ALL DIRECTIONS
m and r vs. Force (The
Relationship)
m1m2
Fg  G 2
r
What affect does changing the mass have on gravitational
force?
If you
the mass on one body, you will
the gravitational force.
What affect does changing the distance have on gravitational
force?
If the distance between two objects is
, the
gravitational force will
by _____.
If the distance between two objects is
, the
gravitational force will
by _____.
• The inverse square relationship – F  _____
The Effects of Mass and Distance on Fg
m1m2
Fg  G 2
r
The Inverse Square Relationship
Acceleration of Gravity (m/s2)
12
rE = 6380 km
Shuttle orbit
(400 km)
g=
10
8
6
Geosynchronous Orbit
(36,000 km)
g=
4
2
0
0
5,000
10,000
15,000
20,000
25,000
30,000
Distance above Sea Level (km)
35,000
40,000
Determining the
the
1.
Newton’s 2nd Law of Motion:
Fg = ____
2.
Newton’s Universal Law of Gravitation:
Fg =
of
Determining the mass of the
Earth
Substituting in know values for G, g and r
G = 6.67 x 10-11 Nm2/kg2
g = 9.81 m/s2
r = 6.38 x 106 m
mE =
Why do all objects fall at the
arock
rate?
Fg
M Earth M rock

; Fg  G
2
M rock
REarth
arock
M Earth M rock
M Earth
G 2
G 2
REarth M rock
REarth
The gravitational acceleration of an object like a rock does
not depend on its
because _____ in the equation
foracceleration
_____ in the equation for
gravitational force
This “coincidence” was not understood until Einstein’s
general theory of relativity.
Example 1:
How will the gravitational force on a satellite
change when launched from the surface of
the Earth to an orbit
1 Earth radius above the surface of the Earth?
2 Earth radii above the surface of the Earth?
3 Earth radii above the surface of the Earth?
r
r
Why?
Don’t forget the
Example 2:
The Earth and moon are attracted to one another by
a
force. Which one attracts
with a greater force? Why?
.
Kepler’s Laws of Planetary
Motion
Law #1:
The paths of planets are
one of the
.
with the sun at
Kepler’s Laws of Planetary
Motion
Law #2:
The
enclosed by the path a planet sweeps out
are
for
time intervals.
Therefore, when a planet is closer to the sun in its orbit
(perihelion), it will move
than when further away (aphelion).
Kepler’s Laws of Planetary
Motion
Law #3:
The square of the ratio of the periods of any two planets
revolving around the sun is equal to the cube of the ratio of
their average distances from the sun.
2
3
=
• When dealing with our own solar system, we relate everything to
the Earth’s period of revolution in years (TE = ____) and distance
from the Sun (r = ____) such that ____ = ____.
The
will be the
a planet is from the sun, the
of its orbit around the sun.
Graphical version of Kepler’s Third Law
An asteroid orbits the Sun at an average distance
a = 4 AU. How long does it take to orbit the Sun?
A.
B.
C.
D.
4 years
8 years
16 years
64 years
We need to find p so that ____ = ____
Key Ideas
Gravity is a force of
between any
masses.
Gravitational force is proportional to the
of the bodies
and
proportional to the
of the
.
Acceleration due to gravity
with
from
the surface of the Earth.
All planets travel in
.
Planets sweep out
areas in their orbit over
periods of time.
The square of the ratio of the
orbiting the sun is
proportional to the cube of their
from the sun.