© sierra college astronomy department1 pick 3 rd hour stuff! u it will first appear in the center...

© Sierra College Astronomy Department

1

Pick 3rd hour stuff! It will first appear in the center of the room

before lecture. It will then be moved to the box labeled

“3100” outside the planetarium• All 3rd hours will collect there until the end of the

semester Scores posted just outside the planetarium

(listed by 4-digit ID number) Homework now due at 11:59pm Friday! Extra Credit: see page 41 (25 pts max, 10 must be

done before midterm)

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

midterm (see midterm (see page 41 of Student of Student Handbook)Handbook)

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

Mastering Astronomy:Mastering Astronomy:masteringastronomy.sierracollege.edu

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

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

http://astronomy.sierracollege.edu/

http://masteringastronomy.sierracollege.edu/


3

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

Circ motion


4

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 2GravLaw2


5

Weight of an object away from Earth

4R

R2R

3R

1/16

1/9

1/4

GravLaw


6

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


7

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


8

• 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


9

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


10

• 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


11

• 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


12

• 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


13

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


14

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


15

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


16

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


17

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


18

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


19

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)


20

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.

© Sierra College Astronomy Department© Sierra College Astronomy Department 2121

Lecture 4: Light and the Electromagnetic SpectrumLecture 4: Light and the Electromagnetic Spectrum

The Wave Nature of LightThe Wave Nature of LightSpectrum Spectrum is the order of colors is the order of colors or or

wavelengths produced when wavelengths produced when light light is dispersed, such as by a is dispersed, such as by a prism. prism.

Wave Motion in GeneralWave Motion in GeneralWavelength (Wavelength () ) is the distance from a point is the distance from a point

on a wave to the next corresponding point.on a wave to the next corresponding point.Frequency (Frequency (ff or or )) is the number of is the number of

repetitions per unit timerepetitions per unit timeThere IS a relationship between f and There IS a relationship between f and

Wavel



The Wave Nature of LightThe Wave Nature of Light

As a water wave travels along the As a water wave travels along the surface, the wave’s motion in surface, the wave’s motion in primarily in the vertical direction primarily in the vertical direction and not along the direction of the and not along the direction of the wave.wave.

Frequency is given in Frequency is given in cycles/second or cycles/second or hertz (Hz).hertz (Hz).




Light as a WaveLight as a Wave White light is made up of light of many White light is made up of light of many

wavelengths, but all wavelengths travel wavelengths, but all wavelengths travel at 300 million meters/second (3.00 X10at 300 million meters/second (3.00 X1088 m/s).m/s).

f f = c = c = = speed of light wavespeed of light waveNanometer (nm):Nanometer (nm): unit of length = 10 unit of length = 10-9-9

m.m.Angstrom (Å):Angstrom (Å): unit of length = 10 unit of length = 10-10-10 m; m;

it is a non-SI unit. it is a non-SI unit.

wave

board

photon



The Wave Nature of LightThe Wave Nature of Light 700 nm red light has 700 nm red light has f f = 4.3 X 10= 4.3 X 101414 Hz. Hz.

400 nm violet light has 400 nm violet light has ff = 7.5 X 10 = 7.5 X 101414 Hz. Hz. Frequencies range from 10Frequencies range from 1022 Hz (low) to Hz (low) to

10102424 Hz (high). Hz (high). Wavelengths range from 10Wavelengths range from 1066 m (long) to m (long) to

1010-16-16 m (short). m (short). Based on frequency and/or wavelength, Based on frequency and/or wavelength,

the the ElectromagneticElectromagnetic (EM)(EM) spectrumspectrum is is usually broken into these regions: radio usually broken into these regions: radio (AM/FM/microwave), infrared, visible, (AM/FM/microwave), infrared, visible, ultraviolet, X-ray, gamma rayultraviolet, X-ray, gamma ray

Maxwell

EM Spec




These waves are called These waves are called “electromagnetic” because they consist “electromagnetic” because they consist of combined electric and magnetic of combined electric and magnetic waves that result when a charged waves that result when a charged particle accelerates.particle accelerates.

Astronomers refer to Astronomers refer to atomspheric atomspheric windowswindows in the Earth’s atmosphere that in the Earth’s atmosphere that allow certain wavelengths to pass.allow certain wavelengths to pass.

Electromagnetic Spectrum

EM Spec

Windows



The Colors of Planets and StarsThe Colors of Planets and Stars

Color from Reflection - Colors of Color from Reflection - Colors of PlanetsPlanets

Planets have their colors Planets have their colors because the material on their because the material on their surfaces or in their clouds surfaces or in their clouds absorbs some of the absorbs some of the wavelengths of sunlight and wavelengths of sunlight and reflects a combination of reflects a combination of wavelengths that appear, for wavelengths that appear, for example, as the rusty red of example, as the rusty red of Mars or the blue of Neptune.Mars or the blue of Neptune.




Color as a Measure of TemperatureColor as a Measure of Temperature An An intensity/wavelength intensity/wavelength graphgraph, , a a thermal thermal

spectrum,spectrum, of an object emitting electromagnetic of an object emitting electromagnetic radiation can be used to detect its temperature.radiation can be used to detect its temperature.

Therefore, the color of a star tells us about its Therefore, the color of a star tells us about its surfacesurface temperature. temperature.

In Cosmic Calculations 5.1:In Cosmic Calculations 5.1: A A quantitative derivation is given by Wien’s Law: quantitative derivation is given by Wien’s Law:

TT = 2,900,000/ = 2,900,000/maxmax or or maxmax= 2,900,000/= 2,900,000/TT where where TT is the temperature in is the temperature in KelvinKelvin and and m m is is

the wavelength where the thermal spectrum the wavelength where the thermal spectrum peaks in intensity in peaks in intensity in nanometers (nm)nanometers (nm)

Wien’s

EM Spec




Intensity per square meterIntensity per square meterHow much thermal energy is being How much thermal energy is being

emitted (per square meter) from an emitted (per square meter) from an object with at temperature object with at temperature TT ? (see ? (see Cosmic Calculations 5.1)Cosmic Calculations 5.1)

4Energy per square meter T

EM Spec

board

Stefan-Boltzmann constant


Public Service Public Service Anonoucement!Anonoucement!

Please put your 4-digit ID Please put your 4-digit ID 3rd hour assignments and 3rd hour assignments and anything else you turn inanything else you turn in


By using a prism By using a prism (refraction) or grating (refraction) or grating (diffraction) one can take (diffraction) one can take the “white” light of a the “white” light of a glowing object and glowing object and spread it out into a spread it out into a spectrumspectrum

Can be used to study Can be used to study starlightstarlight

Rainbows are formed Rainbows are formed from light refracting in from light refracting in waterwater

700 nm

400 nm

600 nm

500 nm

Lecture 4: Light and the Electromagnetic Lecture 4: Light and the Electromagnetic SpectrumSpectrum

SpectraSpectra



Spectra Examined Close UpSpectra Examined Close UpContinuous spectrumContinuous spectrum contains an contains an

entire range of wavelengths rather entire range of wavelengths rather than separate, discrete wavelengths.than separate, discrete wavelengths.

Example of a continuous spectrum is Example of a continuous spectrum is the heated filament of a lamp or a the heated filament of a lamp or a glowing piece of iron in the glowing piece of iron in the blacksmith’s forge.blacksmith’s forge.



Spectra Examined Close UpSpectra Examined Close Up

Kirchhoff’s LawsKirchhoff’s Laws In 1814 Fraunhofer analyzed the solar In 1814 Fraunhofer analyzed the solar

spectrum and found a number of dark spectrum and found a number of dark lines across the continuous spectrum. lines across the continuous spectrum. The dark lines are caused by The dark lines are caused by absorption.absorption.

Later it was discovered that if gases are Later it was discovered that if gases are heated until they emit light, a spectrum heated until they emit light, a spectrum made up of bright lines appears.made up of bright lines appears.

TypesOfSpectra(basic)



Spectra Examined Close UpSpectra Examined Close UpKirchhoff’s lawsKirchhoff’s laws summarize how the summarize how the

three types of spectra are produced:three types of spectra are produced:

1.1. A hot, dense glowing object (a solid or A hot, dense glowing object (a solid or dense gas) emits a dense gas) emits a continuouscontinuous spectrum.spectrum.

2.2. A hot, low-density gas emits light of A hot, low-density gas emits light of only certain wavelengths - a only certain wavelengths - a bright linebright line spectrum.spectrum.

3.3. When light having a continuous When light having a continuous spectrum passes through a cool gas, spectrum passes through a cool gas, dark dark lineslines appear in the continuous spectrum. appear in the continuous spectrum.

Kirchhoff

Demo

TypesOfSpectra(basic)



The AtomThe AtomThe atom is made of three partsThe atom is made of three parts::

Proton, electron, neutronProton, electron, neutronThe type of atom is determined by the The type of atom is determined by the

number of protonsnumber of protonsAn isotope of a given atom differs in the An isotope of a given atom differs in the

number of neutronsnumber of neutrons# of proton + neutrons = # of proton + neutrons = atomic mass atomic mass

numbernumber

atoms

PeriodicTable

AtomStructure



The Bohr AtomThe Bohr Atom Three postulates of the Three postulates of the Bohr atom:Bohr atom:

1.1. Electrons in orbit around a Electrons in orbit around a nucleus can have only certain nucleus can have only certain specific energies.specific energies.2.2. An electron can move from one An electron can move from one energy level to another – changing energy level to another – changing the energy of the atom.the energy of the atom.3.3. The energy of a photon The energy of a photon determines the frequency (or determines the frequency (or wavelength) of light that is wavelength) of light that is associated with the photon,associated with the photon,

Atom

TalkingAtom

Levels

FlatLevels



The Bohr AtomThe Bohr Atom““StatesStates” of an electron” of an electron

An electron at it minimum energy level An electron at it minimum energy level is said to be in its is said to be in its ground stateground state

If a photon with just the right amount If a photon with just the right amount interacts with the atom, the electron interacts with the atom, the electron may be raised to a new level, the may be raised to a new level, the electron is said to be in an electron is said to be in an excited excited statestate

While in an excited state, the electron While in an excited state, the electron can “relax” and fall down to a lower can “relax” and fall down to a lower energy state releasing a photonenergy state releasing a photon

FlatLevels



The Doppler EffectThe Doppler Effect

•Doppler effectDoppler effect is the observed is the observed change in wavelength from a source change in wavelength from a source moving toward or away from the moving toward or away from the observer.observer.

• It is most well known as the change in It is most well known as the change in pitch of sound waves when a speeding pitch of sound waves when a speeding car or train blowing its horn passes by.car or train blowing its horn passes by.

• In front of the moving source one In front of the moving source one hears higher frequency (shorter hears higher frequency (shorter wavelength) sound.wavelength) sound.

•Behind the source one hears lower Behind the source one hears lower frequency (longer wavelength) sound.frequency (longer wavelength) sound.

Doppler

EM Spec




RedshiftRedshift is the change in wavelength is the change in wavelength toward toward longerlonger wavelengths. wavelengths.

BlueshiftBlueshift is the change in wavelength is the change in wavelength toward toward shortershorter wavelengths. wavelengths.

Except for very distant galaxies, most Except for very distant galaxies, most redshifts or blueshifts caused by the redshifts or blueshifts caused by the Doppler effect are very small.Doppler effect are very small.

It is spectral lines in stellar spectra that It is spectral lines in stellar spectra that make the Doppler effect a powerful tool.make the Doppler effect a powerful tool.

Doppler II

DopplerInSpectra




Doppler Effect as a Measurement TechniqueDoppler Effect as a Measurement TechniqueMeasuring the amount of the shifting of stellar Measuring the amount of the shifting of stellar

spectral lines can determine the spectral lines can determine the radial radial velocityvelocity of the star relative to the Earth. of the star relative to the Earth.

Radial velocityRadial velocity is velocity along the is velocity along the line of sight, toward or away from the line of sight, toward or away from the observer.observer.

Tangential velocityTangential velocity is velocity perpendicular is velocity perpendicular to the line of sight.to the line of sight. vvrad

vt

To Earth

DopplerFormula

In cosmicCalculations 5.2




Other Doppler Effect MeasurementsOther Doppler Effect MeasurementsThe rotation rate of the SunThe rotation rate of the SunRotation rates of the planets and the Rotation rates of the planets and the

rings of Saturnrings of SaturnThe motion of some binary starsThe motion of some binary starsThe motion of other stars with planets The motion of other stars with planets

around themaround themSpeeding cars by police radarSpeeding cars by police radar

Doppler

DopplerFormula




Speed measured by the Doppler effect Speed measured by the Doppler effect is the speed of the object is the speed of the object relativerelative to the to the speed of the Earth.speed of the Earth.

All speeds are relative to something. All All speeds are relative to something. All motion (or non-motion) is relative, too.motion (or non-motion) is relative, too.

The understanding of the relativity of The understanding of the relativity of motion is called motion is called Galilean relativityGalilean relativity or or Newtonian relativityNewtonian relativity..


44

Other Slides



The Inverse Square LawThe Inverse Square Law

Inverse square lawInverse square law of radiation of radiation states that radiation spreading states that radiation spreading from a small source decreases in from a small source decreases in intensity as the inverse square of intensity as the inverse square of the distance from the source.the distance from the source.

Force of gravity also follows an Force of gravity also follows an inverse square relationship with inverse square relationship with distance.distance.

InverseSquareLaw


46

Lecture 3b: Galileo, Newton, and Einstein

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.


47

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 3b: Galileo, Newton, and Einstein

Beyond Newton to Einstein

D-14

D-13

Astronomy Club

Meets every Wednesday at 9:30AM

in S-202(Planetarium)Fall 2005

© sierra college astronomy department1 pick 3 rd hour stuff! u it will first appear in the center...

Documents