25 pts of Extra Credit can be done, 10 pts of these points must be done before midterm (see page 41...

25 pts of Extra Credit can be 25 pts of Extra Credit can be done, 10 pts of these points must done, 10 pts of these points must

be done before midterm (see be done before midterm (see page 41 of Student Handbook)of Student Handbook)

The Class Web Site:The Class Web Site:astronomy.sierracollege.edu

http://astronomy.sierracollege.edu/Courses/Astronomy02/ExtraCredit.htm

http://astronomy.sierracollege.edu/Courses/Astronomy02/ExtraCredit.htm

http://astronomy.sierracollege.edu/

© Sierra College Astronomy Department© Sierra College Astronomy Department 22

The Dialogue Concerning the Two Chief World The Dialogue Concerning the Two Chief World SystemsSystems (1632)(1632)Discourse between three characters (Salviati, Discourse between three characters (Salviati,

Sagredo, Simplicio) about the geocentric and Sagredo, Simplicio) about the geocentric and heliocentric theories of the universeheliocentric theories of the universe

Led to his condemnationLed to his condemnationThis wasn’t his first controversy …This wasn’t his first controversy …

Lecture 3c: GalileoLecture 3c: Galileo

Galileo Galilei’s Major WorksGalileo Galilei’s Major Works

© Sierra College Astronomy Department© Sierra College Astronomy Department 33

Lecture 3c: GalileoLecture 3c: Galileo

Galileo Galilei’s ControversyGalileo Galilei’s Controversy

SunspotsSunspots (1613) irked some Jesuits (1613) irked some Jesuits Copernicus’ book banned by Catholic ChurchCopernicus’ book banned by Catholic Church

Led to decree of 1616 about the heliocentric universeLed to decree of 1616 about the heliocentric universe Jesuit Orazio Grassi wrote book about Comets in 1619Jesuit Orazio Grassi wrote book about Comets in 1619

Had correct view of extraterrestrial nature of cometsHad correct view of extraterrestrial nature of comets Urban VIII becomes Pope in 1623Urban VIII becomes Pope in 1623

Good friend and supporter of GalileoGood friend and supporter of GalileoAssayerAssayer written in response to Jesuit bookwritten in response to Jesuit book

Dedicated to Urban VIIIDedicated to Urban VIII Dialogue Dialogue met with ire of some Jesuits and Pope Urban VIIImet with ire of some Jesuits and Pope Urban VIII

Thought to be personal attack (SimplicioThought to be personal attack (SimplicioPope’s view)Pope’s view)Book banned and led to heresy trial and conviction in 1633Book banned and led to heresy trial and conviction in 1633

© Sierra College Astronomy Department

4

Lecture 3c: Understanding Motion, Energy, and Gravity

Going Towards a Grand Synthesis Galileo Galilei

• Credited with setting the standard for studying nature through reliance on observation and experimentation to test hypotheses

• The heavens had similar features to the Earth (contrast Aristotle)• Galileo was the first to develop our modern ideas of motion –

made use of the inclined plane– Demonstrated that all objects at the Earth’s surface fall at the same rate

regardless of mass– Proposed the concept of inertia that was to overthrow Aristotle’s

notion that the natural motion of all earthly objects is to come to rest. René Descartes

• Extended Galileo’s notion of inertia along the Earth’s surface to that of straight line motion

• Proposed three laws of motion which would inspire Newton to create the now classical Three Laws of Motion

Inclinedplane


5

Lecture 4: Newton

Isaac Newton’s Grand Synthesis Robert Hooke

• Had ideas of planetary motion: a central force is required to get planet to move in a circular path

The year Galileo died - 1642 - is the year Isaac Newton was born.

Newton took the work of Galileo and Kepler and created an expansive theory of motion.

Kepler’sTheory


6

Extended school holiday 1665-1666: invent reflecting telescope invent calculus develop particle theory of optics discover laws of motion discover universal gravitation

Lucasian Prof. of Math at Cambridge University

Lecture 4: Newton

Isaac Newton’s Accomplishments


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Lecture 4: Newton

Newton’s First Two Laws of Motion

Inertia is the property of an object whereby it tends to maintain whatever velocity it has.

Newton’s First Law (Law of Inertia): Unless an object is acted upon by a net, outside force, the object will maintain a constant speed in a straight line.

Note: Speed and direction = velocityDemo

Here First:Rockaround


8

Lecture 4: Newton

Newton’s First Two Laws of Motion Acceleration is a measure of how

rapidly the speed or direction of motion of an object is changing.

An object at rest has a speed of zero. Newton’s first law says that a force is

needed to change the speed and/or direction of an object’s motion.

Demo


9

Lecture 4: Newton


Some more definitions: Mass (M or m): quantity of inertia

• An intrinsic property of an object• Not volume or weight• SI unit of measurement is a kilogram (kg)

Weight (W): gravitational force between some object and a planetary body on which the object rests• On the Earth: 1 kilogram has an equivalent weight

of 2.2 lbs. Density: Mass divided by Volume


10

Lecture 4: Newton


Some more definitions: Momentum: mass times velocity p=mv Angular momentum (or circular

momentum) : mass times velocity times distance from center or axis of motion mvr

Torque: a “twisting” force which changes the angular momentum


11

Lecture 4: Newton

Newton’s First Two Laws of MotionNewton’s Second Law Acceleration is inversely proportional to the mass

being accelerated. Acceleration = net force / mass Force = mass × acceleration, or F = ma When the net force is zero, there is no acceleration. Another way of stating the 2nd law: “When a net

force acts on and object, it produces a change of momentum of in the direction in which the force acts”

2nd law

Demo


12

Lecture 4: Newton

Newton’s Third LawNewton’s Third Law: When object X exerts a force on object Y,

object Y exerts and equal and opposite force back on X.

The Third Law is sometimes stated as “For every action there is an opposite and equal reaction,” but the first statement is more precise in terms of physical forces.

This law does not “feel” right – be careful not to confuse force with acceleration Demo

3rd Law


13

Lecture 4: Newton

Motion in a Circle

Motion of an object in a circle at constant speed (uniform circular motion) is an example of acceleration by changing direction.

Centripetal (“center-seeking”) force is the force directed toward the center of the curve along which the object is moving.

What happens if the centripetal force is removed?

board

Demo


14

Lecture 4: Newton

The Law of Universal Gravitation This law states that between every two

objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects (inverse square law).

In equation form: F = GM1M2 / d 2

where G is a constant, M and m are the masses, and r is the distance between their centers.

Another form

GravLaw

F = GMm / r 2

Weight of an object away from Earth

4R

R2R

3R

1/16

1/9

1/4GravLaw


16

Lecture 4: Newton

The Law of Universal Gravitation

According to Newton, gravity not only makes objects fall to Earth but keeps the Moon in orbit around the Earth and keeps the planets in orbit around the Sun. He could therefore explain the planets’ motions and why Kepler’s laws worked.

Cannon

GravLaw


17

Lecture 4: Newton

The Law of Universal GravitationTesting the Law of Universal Gravitation Because the distance from the center of the Earth

to the Moon is about 60 times the distance from the center of the Earth to its surface, the centripetal acceleration of the Moon should be (1/60²) or 1/3600 of the acceleration of gravity on Earth. Newton’s calculations showed this to be the case and confirmed the validity of his theory of gravitation.

GravLaw


18

• Under certain conditions, certain physical quantities will not change in time

• These unchanging quantities are said to be conserved

• Three important conservation laws for astronomy

• (linear) momentum

• angular momentum

• energy

Demo

Lecture 4: Newton

Conservation Laws


19

Momentum (Along a Line) and Conservation• The momentum of an object with mass m and velocity v is

given asp = mv

• The momentum of a system of objects is

P = p1 + p2 + … = m1v1 + m2v2 + …• If the absence of external forces acting on the system, P

remains constant for all time - this is the Conservation of Momentum

• Examples: Rockets and billiard balls• For more than one direction, conservation of momentum

is applied in each direction separately

Demo

Lecture 4: Newton

Conservation Laws

Pool


20

• Angular Momentum and Conservation– Spinning objects and objects in orbit are said to possess angular

momentum– In the absence of a “twisting force” or torque, a spinning object will

maintain its angular momentum - this is the Conservation of Angular Momentum

– Orbital angular momentum• The orbital angular momentum, J, of an object is the product of that

object’s mass m, speed of rotation v, and distance from the center of rotation r:

J = mvr• The conservation of J means that (in the absence of an outside

torque) as the distance to the spin axis decreases (contraction), the speed increases

• This is what Kepler really observed as his 2nd Law of Planetary Motions (the Law of Equal Areas)

DemoLecture 4: Newton

Conservation of Angular Momentum

Skater

Orbit


21

• Angular Momentum and Conservation (continued)

– Rotational angular momentum• An object (like the Earth) will continue to spin at the

same rate as long as there is no net torque on it– Precession is the result of an external torque

(observed for the Earth)• In a system of objects, the total angular momentum can

be conserved (no outside torque), but the objects may transfer rotational angular energy between themselves

– The slowing of the Earth’s day is due to the transfer of rotational angular momentum of the Earth to orbital angular momentum of the Moon

Lecture 4: Understanding Motion, Energy, and Gravity

Conservation of Angular Momentum


22

• Types of energy:– Kinetic: the energy of moving objects (½ mv2)

• Ex: cars in motion, planets going around the sun, molecules jostling in the air

• Thermal energy is a important subcategory (next slide)

– Radiative: energy carried by light (photons)– Potential: stored energy which may be converted later

into kinetic or radiative energy• Ex: A rock perched on a ledge, chemical (or nuclear)

bonds in an atom (or nucleus) (more later).

• MKS unit for energy: Joule– 4,184 joules are in one food calorie– Typical adult eats 2500 calories = 10 million joules

Demo

Lecture 4: Newton

Energy is conserved too!

Energycycle


23

Lecture 4: Newton

Temperatures Temperature is the measure of the average kinetic

energy of a system of particles• Thermal energy depends on temperature and density

Fahrenheit scale: freezing 32°F/boiling 212°F. Celsius scale: freezing 0°C/boiling 100°C. Kelvin scale:

0 K = absolute zero (-273°C)273 K = freezing point of water (0 °C)373 K = boiling point of water (100 °C)

Note that Kelvin and Celsius degrees are the “same size.”

HigherLowerKinetic

Temperaturescales

Thermal dependence


24

Lecture 4: Newton

Potential Energy in Astronomy

Of the many types of potential energy, two are of particular importance in astronomy

Gravitational potential energy: How much energy would one get from motions due to gravity? This energy get converted in kinetic energy.

Mass-energy: How much energy is stored in the atom or nucleus?

2E mc


25

Lecture 4: Newton

Conservation of Energy Conservation of Energy states that in an isolated

system, although energy may change from one form to another, the total amount of energy must remain constant

Energy cannot be created nor destroyed, but can be transferred between different types• Ex: As a ball is dropped, its potential energy gets converted

to kinetic energy such that the sum of the kinetic and potential energies remains constant

The ultimate source of all the energy in the Universe is the Big Bang


26

Lecture 4: Newton

Newton’s Laws and Kepler’s Laws Newton showed mathematically (using calculus) that

Kepler’s laws derive from the inverse square law for gravitation and the equation of motion (F = ma).

Newton modified Kepler’s third law, showing that the masses are an important factor.

p2 = Ka3/(M1 + M2)where K=42/G

Objects orbit their center of mass COM


27

Lecture 4: Newton

Examples of Newton’s Laws Orbits: Circular and Escape Speed

• Just how much speed does take to orbit the Earth? To leave the Earth? See Mathematical Insight 4.4

• Notice that it requires only √2 times the circular velocity to escape from the planet

• For the Earth Vc = 8 km/s and Ve = 11 km/s

• For comparisons, be careful with M and R

c

GMV

R e

2GMV

R

Escape


28

Lecture 4: Newton

Examples of Newton’s Laws Surface Gravity is the gravitational attraction at

the surface of a planet or star. It is the acceleration on a mass created by the local gravitational force.

Acceleration due to gravity at surface (See Mathematical Insight 4.5):

• Note independence of g with respect to m• For comparisons, be careful with M and R• Notice Weight (W) = mg = GMm/R2

2R

GMg

FeatherHammer


29

Lecture 4: Newton

Examples of Newton’s Laws Weightlessness

• Weight is the force that counters gravity creating a zero net force

• Weightlessness is the absence of the countering force• People in orbit around the Earth feel weightless

because gravity is not countered by a surface connected to the Earth

Changing Orbits• Objects in orbit around each other do not spontaneously change

into other orbital configurations.• The orbital energy of the system must change through:

– Gravitational encounters (encounters with a third object)– Atmospheric drag (friction that diverts kinetic energy into other forms)


30

Lecture 4: Newton

The Importance of Newton’s Laws Kepler’s laws can be derived from them. They explain tides and precession. Their use predicted the existence of the

planet Neptune. They provide a way to measure things

quantitatively and predict the motion of things.

Newton laid the foundation for our notion of the Universe.


31

Lecture 4: Newton

Tides Moon and Sun pull on Earth causing the water to

rise producing tides• The Moon provides 2/3 of the tidal force, the Sun 1/3

Earth’s rotation provides daily rise and fall of tides Moon’s revolution about Earth cause half-monthly

rise and fall of tides• Spring tide: Moon and Sun on same or opposite side of the

Earth• Neap tide: Moon and Sun at perpendicular angles to the Earth

tides

SpringNeap

Leadingbulge


32

Lecture 4: Newton

Tides Effects of Tides on Earth-Moon System

Causes Moon’s synchronous rotation Tidal forces make Moon recede

• Moon steals energy from Earth

Tidal forces slow Earth’s rotation• Moon steals energy from Earth

Tidal forces create Roche Limit• How close can something large be to planet/star until it

breaks apart?


33

Other slides


34

Lecture 4: Newton

Beyond Newton to Einstein Newton assumed time was absolute.

Einstein’s Special Theory of Relativity showed this was not true.

Newton proposed that inertial mass was equivalent to gravitational mass. Subsequent measurements confirmed this coincidence.

Einstein in his General Theory of Relativity showed mathematically that the two types of masses are indeed equivalent.


35

Principle of equivalence states that the effects of the force of gravity are indistinguishable from those of acceleration.

The general theory predicts that light will curve in the presence of a massive object. This prediction, made in 1907, was first confirmed during a solar eclipse in 1919.

Lecture 4: Newton

Beyond Newton to Einstein

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25 pts of Extra Credit can be done, 10 pts of these points must be done before midterm (see page 41...

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