Download Galileo, Newton, and Einstein - Sierra College Astronomy

Pick
rd
3
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)

© Sierra College Astronomy Department
1
25 pts of Extra Credit can be done, 10
pts of these points must be done before
midterm (see page 41 of Student
Handbook)
The Class Web Site:
astronomy.sierracollege.edu
Mastering Astronomy:
masteringastronomy.sierracollege.edu
Lecture 4: Newton
Motion in a Circle
Motion of an object in a circle at constant
speed (uniform circular motion) is an example board
of acceleration by changing direction.
 Centripetal (“center-seeking”) force is the
force directed toward the center of the curve
Circ
along which the object is moving.
motion
 What happens if the centripetal force is
removed?

Demo
© Sierra College Astronomy Department
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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
Grav
and inversely proportional to the square of Law
the distance between the centers of the
objects (inverse square law).
 In equation form: F = GM1M2 / d 2
Another
where G is a constant, M and m are the form
masses, and r is the distance between
their centers.
F = GMm / r 2
© Sierra College Astronomy Department
Grav
Law2
4
Weight of an object away from Earth
1/16
Grav
Law
1/4
1/9
© Sierra College Astronomy Department
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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.
© Sierra College Astronomy Department
Cannon
Grav
Law
6
Lecture 4: Newton
The Law of Universal Gravitation
Grav
Law
Testing 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. © Sierra College Astronomy Department
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Lecture 4: Newton
Conservation Laws
Demo
• 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
© Sierra College Astronomy Department
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Lecture 4: Newton
Conservation Laws

Demo
Momentum (Along a Line) and Conservation
• The momentum of an object with mass m and velocity v is
given as
p = 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
© Sierra College Astronomy Department
Pool
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Lecture 4: Newton
Demo
Conservation of Angular Momentum
• 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:
Skater
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)
Orbit
© Sierra College Astronomy Department
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Lecture 4: Understanding Motion, Energy, and Gravity
Conservation of Angular Momentum
• 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
© Sierra College Astronomy Department
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Lecture 4: Newton
Energy is conserved too!
• Types of energy:
Demo
– 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)
Energy
cycle
– 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
© Sierra College Astronomy Department
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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




Higher
Fahrenheit scale: freezing 32°F/boiling 212°F.
Lower
Kinetic
Celsius scale: freezing 0°C/boiling 100°C.
Kelvin scale:
0 K = absolute zero (-273°C)
273 K = freezing point of water (0 °C)
Thermal
dependence
373 K = boiling point of water (100 °C)
Note that Kelvin and Celsius degrees are the “same
size.”
© Sierra College Astronomy Department
Temperature
scales
13
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?
E  mc
© Sierra College Astronomy Department
2
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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
© Sierra College Astronomy Department
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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.

2
p =
3
Ka /(M
1
+ M2)
where K=4p2/G

Objects orbit their center of mass
© Sierra College Astronomy Department
COM
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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
GM
Vc 
R
2GM
Ve 
R
• 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
Escape
• For comparisons, be careful with M and R
© Sierra College Astronomy Department
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Lecture 4: Newton
Examples of Newton’s Laws
Feather
Hammer
 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.
GM
 Acceleration due to gravity
at surface (See Mathematical g 
2
Insight 4.5):
R
• Note independence of g with respect to m
• For comparisons, be careful with M and R
2
• Notice Weight
(W)
=
mg
=
GMm/R
© Sierra College Astronomy Department
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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)
© Sierra College Astronomy Department
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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
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Lecture 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light

Spectrum is the order of colors
or wavelengths produced when
light is dispersed, such as by a
prism.
Wave Motion in General
 Wavelength (l) is the distance from a point
on a wave to the next corresponding point.
 Frequency (f or n) is the number of
repetitions per unit time
 There IS a relationship between f and l!
Wavel
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light
As a water wave travels along the
surface, the wave’s motion in primarily
in the vertical direction and not along
the direction of the wave.
 Frequency is given in cycles/second or
hertz (Hz).

© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light
Light as a Wave
wave
 White light is made up of light of many
wavelengths, but all wavelengths travel at photon
300 million meters/second (3.00 X108 m/s).



f l = c = speed of light wave
10-9
Nanometer (nm): unit of length =
m.
Angstrom (Å): unit of length = 10-10 m; it
is a non-SI unit.
© Sierra College Astronomy Department
board
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Lecture 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light




700 nm red light has f = 4.3 X 1014 Hz.
400 nm violet light has f = 7.5 X 1014 Hz.
Frequencies range from 102 Hz (low) to
1024 Hz (high).
Wavelengths range from 106 m (long) to
10-16 m (short).
Based on frequency and/or wavelength,
the Electromagnetic (EM) spectrum is
usually broken into these regions: radio
(AM/FM/microwave), infrared, visible,
ultraviolet, X-ray, gamma ray
© Sierra College Astronomy Department
EM Spec
Maxwell
24
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Wave Nature of Light
These waves are called “electromagnetic”
EM Spec
because they consist of combined electric and
magnetic waves that result when a charged
Windows
particle accelerates.
 Astronomers refer to atomspheric windows
in the Earth’s atmosphere that allow certain
wavelengths to pass.

Electromagnetic
Spectrum
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Colors of Planets and Stars
Color from Reflection - Colors of
Planets

Planets have their colors because
the material on their surfaces or
in their clouds absorbs some of
the wavelengths of sunlight and
reflects a combination of
wavelengths that appear, for
example, as the rusty red of Mars
or the blue of Neptune.
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Colors of Planets and Stars
Color as a Measure of Temperature
 An intensity/wavelength graph, a thermal spectrum,
of an object emitting electromagnetic radiation can be
used to detect its temperature.
 Therefore, the color of a star tells us about its surface
temperature.
In Cosmic Calculations 5.1:
 A quantitative derivation is given by Wien’s Law:
Wien’s
T = 2,900,000/lmax or lmax= 2,900,000/T
where T is the temperature in Kelvin and lm is the
wavelength where the thermal spectrum peaks in
intensity in nanometers (nm)
© Sierra College Astronomy Department
EM Spec
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Lecture 4: Light and the Electromagnetic Spectrum
The Colors of Planets and Stars
Intensity per square meter
 How much thermal energy is being
emitted (per square meter) from an
object with at temperature T ? (see
Cosmic Calculations 5.1)
Energy per square meter
  Stefan-Boltzmann constant
© Sierra College Astronomy Department
 T
board
4
EM Spec
29
Public Service
Anonoucement!
Please put your 4-digit ID
3rd hour assignments and
anything else you turn in
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
Spectra



By using a prism
(refraction) or grating
(diffraction) one can
take the “white” light
of a glowing object
and spread it out into
a spectrum
Can be used to study
starlight
Rainbows are formed
from light refracting in
water
© Sierra College Astronomy Department
700 nm
600 nm
500 nm
400 nm
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Lecture 4: Light and the Electromagnetic Spectrum
Spectra Examined Close Up
Continuous spectrum contains an entire
range of wavelengths rather than separate,
discrete wavelengths.
 Example of a continuous spectrum is the
heated filament of a lamp or a glowing
piece of iron in the blacksmith’s forge.

© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
Spectra Examined Close Up
Kirchhoff’s Laws
 In 1814 Fraunhofer analyzed the solar
spectrum and found a number of dark
lines across the continuous spectrum.
The dark lines are caused by absorption.
 Later it was discovered that if gases are
heated until they emit light, a spectrum
made up of bright lines appears.
© Sierra College Astronomy Department
Types
Of
Spectra
(basic)
33
Lecture 4: Light and the Electromagnetic Spectrum
Spectra Examined Close Up

Kirchhoff’s laws summarize how the three
types of spectra are produced:
Types
1. A hot, dense glowing object (a solid or Of
Spectra
dense gas) emits a continuous spectrum. (basic)
2. A hot, low-density gas emits light of only
Kirchhoff
certain wavelengths - a bright line
spectrum.
3. When light having a continuous spectrum
Demo
passes through a cool gas, dark lines
appear in the continuous spectrum.
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Atom

The atom is made of three parts:

Atom
Structure
Proton, electron, neutron
The type of atom is determined by the number
of protons
atoms
 An isotope of a given atom differs in the
number of neutrons


# of proton + neutrons = atomic mass number
Periodic
Table
© Sierra College Astronomy Department
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Lecture 4: Light and the Electromagnetic Spectrum
The Bohr Atom

Three postulates of the Bohr atom:
1. Electrons in orbit around a nucleus
can have only certain specific
energies.
2. An electron can move from one
energy level to another – changing
the energy of the atom.
3. The energy of a photon determines
the frequency (or wavelength) of light
that is associated with the photon,
© Sierra College Astronomy Department
Atom
Talking
Atom
Levels
Flat
Levels
37
Lecture 4: Light and the Electromagnetic Spectrum
The Bohr Atom

“States” of an electron
 An
electron at it minimum energy level is
said to be in its ground state
 If a photon with just the right amount
interacts with the atom, the electron may be
raised to a new level, the electron is said to
be in an excited state
 While in an excited state, the electron can
“relax” and fall down to a lower energy state
releasing a photon
© Sierra College Astronomy Department
Flat
Levels
38
Lecture 4: Light and the Electromagnetic Spectrum
The Doppler Effect
• Doppler effect is the observed change
in wavelength from a source moving
toward or away from the observer.
• It is most well known as the change in
pitch of sound waves when a speeding
car or train blowing its horn passes by.
• In front of the moving source one hears
higher frequency (shorter wavelength)
sound.
• Behind the source one hears lower
frequency (longer wavelength) sound.
© Sierra College Astronomy Department
EM Spec
Doppler
39
Lecture 4: Light and the Electromagnetic Spectrum
The Doppler Effect




Redshift is the change in wavelength
toward longer wavelengths.
Blueshift is the change in wavelength
toward shorter wavelengths.
Except for very distant galaxies, most
redshifts or blueshifts caused by the
Doppler effect are very small.
It is spectral lines in stellar spectra that
make the Doppler effect a powerful tool.
© Sierra College Astronomy Department
Doppler II
Doppler
In
Spectra
40
Lecture 4: Light and the Electromagnetic Spectrum
The Doppler Effect
In cosmic
Calculations 5.2
Doppler Effect as a Measurement
Doppler
Technique
Formula
 Measuring the amount of the shifting of
stellar spectral lines can determine the radial
velocity of the star relative to the Earth.
 Radial velocity is velocity along
vt
the line of sight, toward or away
vrad
v
from the observer.
 Tangential velocity is velocity
To Earth
perpendicular to the line of sight.
© Sierra College Astronomy Department
41
Lecture 4: Light and the Electromagnetic Spectrum
The Doppler Effect
Other Doppler Effect Measurements
 The rotation rate of the Sun
 Rotation rates of the planets and the rings of
Saturn
 The motion of some binary stars
Doppler
 The motion of other stars with planets
around them
Doppler
 Speeding cars by police radar
Formula
© Sierra College Astronomy Department
42
Lecture 4: Light and the Electromagnetic Spectrum
The Doppler Effect



Speed measured by the Doppler effect is the
speed of the object relative to the speed of
the Earth.
All speeds are relative to something. All
motion (or non-motion) is relative, too.
The understanding of the relativity of motion
is called Galilean relativity or Newtonian
relativity.
© Sierra College Astronomy Department
43
Other Slides
© Sierra College Astronomy Department
44
Lecture 4: Light and the Electromagnetic Spectrum
The Inverse Square Law
 Inverse
square law of radiation states
that radiation spreading from a small Inverse
Square
source decreases in intensity as the
Law
inverse square of the distance from the
source.
 Force of gravity also follows an inverse
square relationship with distance.
© Sierra College Astronomy Department
45
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.
© Sierra College Astronomy Department
46
Lecture 3b: Galileo, Newton, and Einstein
Beyond Newton to Einstein
 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.
© Sierra College Astronomy Department
D-13
D-14
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Astronomy Club
Meets every Wednesday
at 9:30AM in S-202
(Planetarium)
Fall 2005