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Earth – Moon
Gravity Primer
The EarthSucks
1.1. THE UNIVERSAL LAW OF GRAVITYTHE 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
221
r
mmF
r
m1 m2
2.2. The Universal Gravitational Constant, GThe Universal Gravitational Constant, G
221
r
mmGF
2211 /1067.6 kgmNxG
3.3. Gravity and Distance: The Inverse-Square LawGravity and Distance: The Inverse-Square Law
Gravity is the most dominant force in nature.
Yet it is the weakest.
1 unit2 units
3 units4 units
Let’s look at the inverse-square nature for the force of gravity.
4.4. WEIGHT AND WEIGHTLESSNESSWEIGHT 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.)
5.5. OCEAN TIDESOCEAN TIDES demo - Earth-moon systemdemo - 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
High Tides
North Pole
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.
3f2f1f
Sun
Moon
1F2F3F
221
r
mmGF
SFASFA
SunEarth
Spring Tides
SFASFA
New MoonFull Moon
First Quarter
SunEarth
First Quarter
Last Quarter
Neap Tides
SFASFA
NASA Animation
MPEG
SFASFA
Complications– Friction with ocean bottom– Irregular shape of continents
Bay of Fundi– Tides can come in very fast and exceed 15 m.
SFASFA
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.
SFASFA
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.
SFASFAGo to link
6.6. GRAVITATIONAL FIELDSGRAVITATIONAL FIELDS
Alternate view of gravitational influence– Properties of space surrounding object are
changed so that another mass entering the region experiences a force.
Earth
SFASFA
Objects accelerate in the direction of the arrows.
Field is stronger where lines are closer together.
Earth
SFASFA
The Gravitational Field Inside a Planet
Inside the Planet
a = g
a = g
a = 0
a = ½g
a = ½g
SFASFA
Gravitational Field
Uniform Sphere– Linear inside - like Earth outside
Hollow Sphere– Zero inside - like Earth outside
SFASFA
7.7. EINSTEIN'S THEORY OF GRAVITATIONEINSTEIN'S THEORY OF GRAVITATION
Warped Space
SFASFA
Bending of Starlight
Sun
Light from star bent by the gravity of the Sun
Apparent position of star in this
direction
Eye
SFASFA
8.8. BLACK HOLESBLACK 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?
SFASFA
21mmG
R2F
21mmG
R2F
21mmG
R2F
21mmG
R2F
221
R
mmGF
R
R
R
R
26412
81 )( RR which means the force is 64 times larger
Remember that the force between the two masses is given by
SFASFA
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?
SFASFA
Near a Black Hole
SFASFA
Another Look
SFASFA
9.9. UNIVERSAL GRAVITATIONUNIVERSAL 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 QuestionsChapter 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 CourseEnd of CourseEnd of ChapterEnd of Chapter Test 3 QuestionsTest 3 Questions
Discuss final Parting thoughts next slide