Transcript 7.1 The Gravitational Force

Section
7.1
Planetary Motion and Gravitation
Kepler’s Laws
Kepler discovered
the laws that
describe the motions
of every planet and
satellite.
Kepler’s first law
states that the paths
of the planets are
ellipses, with the Sun
at one focus.
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Section
7.1
Planetary Motion and Gravitation
Kepler’s Laws
Kepler found that the
planets move faster
when they are closer
to the Sun and slower
when they are farther
away from the Sun.
Kepler’s second law
states that an
imaginary line from
the Sun to a planet
sweeps out equal
areas in equal time
intervals.
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Section
7.1
Planetary Motion and Gravitation
Kepler’s Laws
Kepler also found that there
is a mathematical
relationship between
periods of planets and their
mean distances away from
the Sun.
Kepler’s third law states
that the square of the ratio
of the periods of any two
planets revolving about the
Sun is equal to the cube of
the ratio of their average
distances from the Sun.
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Section
7.1
Planetary Motion and Gravitation
Kepler’s Laws
Thus, if the periods of the planets are TA and TB, and their
average distances from the Sun are rA and rB, Kepler’s third law
can be expressed as follows:
The squared quantity of the period of object A divided by the period
of object B, is equal to the cubed quantity of object A’s average
distance from the Sun divided by Object B’s average distance from
the Sun.
Section
7.1
Planetary Motion and Gravitation
Kepler’s Laws
The first two laws
apply to each
planet, moon, and
satellite individually.
The third law,
however, relates
the motion of
several objects
about a single
body.
Section
7.1
Planetary Motion and Gravitation
Callisto’s Distance from Jupiter
Galileo measured the orbital sizes of Jupiter’s moons using the
diameter of Jupiter as a unit of measure. He found that lo, the
closest moon to Jupiter, had a period of 1.8 days and was 4.2 units
from the center of Jupiter. Callisto, the fourth moon from Jupiter, had
a period of 16.7 days.
Using the same units that Galileo used, predict Callisto’s distance
from Jupiter.
Section
7.1
Planetary Motion and Gravitation
Callisto’s Distance from Jupiter
Label the radii.
Known:
Unknown:
TC = 16.7 days
rC = ?
TI = 1.8 days
rI = 4.2 units
Section
7.1
Planetary Motion and Gravitation
Callisto’s Distance from Jupiter
Solve Kepler’s third law for rC.
Substitute rI = 4.2 units, TC = 16.7 days, TI = 1.8 days in:
= 19 units
7.1The Gravitational
Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on
every
other particle.
A particle is a piece of matter, small enough in size to be
regarded as a mathematical point.
The force that each exerts on the other is directed along the
line
joining the particles.
7.1 The Gravitational
Force
For two particles that have masses m1 and m2 and are
separated by a distance r, the force has a magnitude
given by
F G
m1m 2
r
G  6 . 673  10
2
 11
N m
2
kg
2
7.1 The Gravitational Force
What is the magnitude of the gravitational force
for two particles that have masses m1 =12kg
and m2 =25kg and are separated by a distance r
= 1.2m?
7.1 The Gravitational
Force
F G
m1m 2
r
2

 6 . 67  10
 1 . 4  10
8
 11
N
N m
2
kg
2

12
kg  25 kg 
1.2
m
2
7.1 The Gravitational
Force
7.1 The Gravitational
Force
Definition of Weight
The weight of an object on or above the earth is the
gravitational force that the earth exerts on the object.
The weight always acts downwards, toward the center
of the earth.
On or above another astronomical body, the weight is the
gravitational force exerted on the object by that body.
SI Unit of Weight: newton (N)
7.1 The Gravitational
Force
Relation Between Mass and Weight
W G
M Em
r
W  mg
g G
M
r
E
2
2
7.1 The Gravitational
Force
On the earth’s surface:
g G
M
R
E
2
E

 6 . 67  10
 9 . 80 m s
 11
2
N m
2
kg
2

5 . 98  10

6.38  10
24
6
kg
m


2