Chapter 9
Gravity
The
Earth
Sucks
1. THE UNIVERSAL LAW OF GRAVITY
From Law 3 of Kepler, Newton deduced the
inverse square law of attraction.
Newton compared the fall of the moon to the
falling of an apple.
Moon's fall from straight line is (0.05 in/s).
Newton's Law of Universal
Gravitation
m1
m2
r
m1m2
F 2
r
2. The Universal Gravitational Constant, G
m1m2
F G 2
r
G  6.67 x10
11
N  m / kg
2
2
3. Gravity and Distance: The Inverse-Square Law
Gravity is the most dominant force in nature.
Yet it is the weakest.
4 units
3 units
2 units
1 unit
Let’s look at the inverse-square
nature for the force of gravity.
4. WEIGHT AND WEIGHTLESSNESS
W = mg (the gravitational force acting on m)
Weighing on an elevator and
Weighing in outer space or in orbit
We define the weight of something as the force it
exerts against the supporting floor or the
weighing scale. (Remember the elevator video.)
5. OCEAN TIDES
demo - Earth-moon system
Force of gravity decreases with distance
from moon.
Moon
Earth
Differences in gravity on different parts
of the Earth produce tidal bulges.
http://www.spacetelescope.org/videos/html/
mpeg/320px/heic0705i.html
North Pole
High Tides
Should expect two high tides, two low
tides per day.
– Moon moves in its orbit so that it returns to
the same place in your sky every 24h 50 m.
Sun has one-half the influence of the
moon
– The gravitational force is greater but tides
depend on the gravitation difference on
opposite sides of the Earth.
F3
F2
F1
m1m2
F G 2
r
Sun
Moon
f1
f2
f3
SFA
Spring Tides
First Quarter
Full Moon
Earth
New Moon
Sun
SFA
Neap Tides
First Quarter
Earth
Sun
Last Quarter
SFA
NASA Animation
MPEG
SFA
Complications
– Friction with ocean bottom
– Irregular shape of continents
Bay of Fundi
– Tides can come in very fast and exceed 15 m.
SFA
Tides in the Earth and Atmosphere
Tides in ionosphere produce electric
currents and alter the magnetic field.
– Affects penetration of cosmic rays
– Can have effects on living things
Tides in the crust mean that volcanoes
and earthquakes are more common at
new or full moon.
SFA
Tides on the Moon
Just as the earth has “land tides” the moon
has moon tides.
Because the moon always keeps the same
face toward the earth, the moon tides are
always in the same place.
Go to link
SFA
6.
GRAVITATIONAL FIELDS
Alternate view of gravitational influence
– Properties of space surrounding object are
changed so that another mass entering the
region experiences a force.
Earth
SFA
Earth
Objects accelerate in the direction of the
arrows.
Field is stronger where lines are closer
together.
SFA
The Gravitational Field Inside a Planet
Inside the Planet
a=g
a = ½g
a=0
a = ½g
a=g
SFA
Gravitational Field
Uniform Sphere
– Linear inside - like Earth outside
Hollow Sphere
– Zero inside - like Earth outside
SFA
7. EINSTEIN'S THEORY OF GRAVITATION
Warped Space
SFA
Bending of Starlight
Apparent position
of star in this
direction
Sun
Eye
Light from star bent by
the gravity of the Sun
SFA
8. BLACK HOLES
Let’s observe a star that is shrinking but whose
mass is remaining the same.
What happens to the force acting on an
indestructible mass at the surface of the star?
What effect is there on the escape velocity?
SFA
F
F
F
F
m
m
1
2
m1m2
F

G
2
G
Remember that the force between
R
2
the
two
masses
is
given
by
R
G
m1m2
G
m1m2
G
R2
R
R
R
R2
R
m1m2
R2
SFA
( 18 R ) 2 
1
64
R 2 which means the force is 64 times larger
If a massive star shrinks enough so that the
escape velocity is equal to or greater than the
speed of light, then it has become a black hole.
Particles entering it would suffer disintegration.
How are black holes detected?
SFA
Near a Black Hole
SFA
Another Look
SFA
9. UNIVERSAL GRAVITATION
Earth is a "sphere" because of gravitation.
The universal law of gravitation was a great
accomplishment.
Its accuracy is phenomenal.
Perturbations in planet's orbits
Examples:
Neptune was discovered because of Uranus's
wobble.
Pluto was discovered in a similar way.
Oscillating universe. Wow!
Chapter 9 Review Questions
If somehow the moon were moved to a
distance twice as far away from the earth as it
is now, the force that the earth has for the
moon would
(a) be twice what it is now
(b) be one half of what it is now
(c) be four times greater than it is now
(d) be one fourth as much as it is now
What must be the phase of the moon if neap
tides are occurring?
(a) first quarter
(b) full
(c) lunar eclipse
(d) new
Newton said that the path of a planet curves
because a force acts on it. Why does a
planet's path curve according to Einstein?
(a) because a force acts on it
(b) because it is spinning
(c) because it is in a geometric warp of space
and time
End of Chapter
Test 3 Questions
End of Course
Discuss final
Parting thoughts next slide