chapter 9 & 10 gravity pythagoras (550 bc) n claimed that natural phenomena could be described...

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Chapter 9 & Chapter 9 & 10 10 Gravity Gravity

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Chapter 9 & 10Chapter 9 & 10

GravityGravity

Pythagoras Pythagoras (550 BC)(550 BC)

Claimed that natural Claimed that natural phenomena could be phenomena could be described by described by mathematicsmathematics

Aristotle Aristotle (350 BC)(350 BC)

Asserted that the Asserted that the universe is governed universe is governed by by physical lawsphysical laws

The ancient Greeks believed that the earth The ancient Greeks believed that the earth was at the center of a revolving sphere with was at the center of a revolving sphere with stars on it.stars on it.

The The Geocentric ModelGeocentric Model implies Earth-Centered implies Earth-Centered Universe.Universe.

CopernicusCopernicus (1500's)(1500's)

Developed a Developed a mathematical model mathematical model for a for a Sun-centered Sun-centered solar systemsolar system

Tycho Brahe Tycho Brahe (1500's)(1500's)

Made precise Made precise measurements of the measurements of the positions of the positions of the planetsplanets

KeplerKepler (1600's)(1600's)

Described the shape of Described the shape of planetary orbitsplanetary orbits as well as their orbital as well as their orbital speedsspeeds

Kepler’s First LawKepler’s First Law

The orbit of a planet The orbit of a planet about the Sun is an about the Sun is an ellipseellipse with the Sun at with the Sun at one focus.one focus.

Kepler’s Second LawKepler’s Second Law

A line joining a A line joining a planet and the Sun planet and the Sun sweeps out sweeps out equal equal areas in equal areas in equal intervals of timeintervals of time..

Kepler’s Third LawKepler’s Third Law

The square of a planet's orbital period is The square of a planet's orbital period is proportional to the cube of the length of its proportional to the cube of the length of its orbit's semimajor axis.orbit's semimajor axis.

Or simply… TOr simply… T22 = R = R33 if T is measured in if T is measured in yearsyears and R is measured in and R is measured in astronomical astronomical unitsunits..

An Astronomical Unit...An Astronomical Unit...

……is the average distance of the Earth from is the average distance of the Earth from the Sun.the Sun.

1 AU = 93,000,000 miles = 8.3 lightminutes1 AU = 93,000,000 miles = 8.3 lightminutes

Kepler’s LawsKepler’s Laws

These are three laws of physics that These are three laws of physics that relate to planetary orbits.relate to planetary orbits.

These were empirical laws. These were empirical laws.

Kepler could not explain them. Kepler could not explain them.

Kepler’s Laws...SimplyKepler’s Laws...Simply(See page 192.)(See page 192.)

Law 1: Elliptical orbits…Law 1: Elliptical orbits…

Law 2: Equal areas in equal times…Law 2: Equal areas in equal times…

Law 3: TLaw 3: T22 = R = R33

Newton’s Law of Universal Newton’s Law of Universal GravitationGravitation

From Kepler's 3rd Law, Newton deduced From Kepler's 3rd Law, Newton deduced inverse square law of attraction. inverse square law of attraction.

G=6.67 G=6.67 10-11 N m 10-11 N m22/kg/kg22

221

d

mGmF

Gravity QuestionsGravity Questions

Did the Moon exert a gravitational force on the Did the Moon exert a gravitational force on the Apollo astronauts?Apollo astronauts?

What kind of objects can exert a gravitational What kind of objects can exert a gravitational force on other objects?force on other objects?

The constant G is a rather small number. What The constant G is a rather small number. What kind of objects can exert kind of objects can exert strongstrong gravitational gravitational forces?forces?

Gravity QuestionsGravity Questions If the distance between two objects in space is If the distance between two objects in space is

doubled, then what happens to the gravitational force doubled, then what happens to the gravitational force between them?between them?

What is the distance is tripled?What is the distance is tripled? ……is quadrupled?is quadrupled?

What if the mass of one of the object is doubled?What if the mass of one of the object is doubled? ……tripled?tripled? ……quadrupled?quadrupled?

Weight and WeightlessnessWeight and Weightlessness Weight Weight

» the force due to gravity on an objectthe force due to gravity on an object» Weight = Mass Weight = Mass Acceleration of Gravity Acceleration of Gravity» W = m gW = m g

Weightlessness Weightlessness - a conditions wherein gravitational pull appears - a conditions wherein gravitational pull appears to be lackingto be lacking– Examples: Examples:

» AstronautsAstronauts» Falling in an ElevatorFalling in an Elevator» SkydivingSkydiving» UnderwaterUnderwater

Ocean TidesOcean Tides

The Moon is primarily responsible for ocean The Moon is primarily responsible for ocean tides on Earth.tides on Earth.

The Sun contributes to tides also. The Sun contributes to tides also.

What are What are spring tidesspring tides and and neap tidesneap tides??

SunEarth New MoonFull Moon

Spring Tides

SunEarth

First Quarter

Last Quarter

Neap Tides

End of Section…End of Section…

Einstein’s Theory of GravitationEinstein’s Theory of Gravitation

Einstein perceived a gravitational field as a Einstein perceived a gravitational field as a geometrical warping of 4-D space and time.geometrical warping of 4-D space and time.

BLACK HOLESBLACK HOLES

Let’s observe a star that is shrinking but Let’s observe a star that is shrinking but

whose mass is remaining the same.whose mass is remaining the same.

What happens to the force acting on an What happens to the force acting on an

indestructible mass at the surface of the star? indestructible mass at the surface of the star?

SFASFA

21mmG

R2F

21mmG

R2F

21mmG

R2F

21mmG

R2F

221

R

mmGF

R

R

R

R

Remember that the force between the two masses is given by

If a massive star shrinks enough so that the If a massive star shrinks enough so that the

escape velocity is equal to or greater than the escape velocity is equal to or greater than the

speed of light, then it has become a speed of light, then it has become a black holeblack hole..

Light cannot escape from a black hole.Light cannot escape from a black hole.

BLACK HOLESBLACK HOLES

Near a Black HoleNear a Black Hole