Chapter 9Chapter 9

Gravity

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

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