ASTR 1020

1
ASTR 1020 Introductory
Astronomy II Stars Galaxies
Week 4 Lecture 1 Special and General
Relativity atoms, nuclei, and quarks The 4 forces
of Nature
2
Announcements Observing
Wednesday, 4 Feb on SBO observing deck (700
PM) APOD (Astronomy Picture of the Day)
Google APOD .. Summary of Week 3 Where was I
last week? My 96 hour trip to Chile to visit
the construction site for the Atacama Large
Millimeter Array (ALMA) at an elevation of
16,500 ft. Plan for Week 4 Should have
read Chapter 14 (The Sun) special sections
S2, S3, and S4
3
Atacama Large Millimeter/submillimeter Array
Llano Chajnantor Northern Chile at 5000 m
elevation
Inauguration 2012 (Early Science in 2011)
gt66 12-m and 7-m telescopes
Al Wootten, ALMA/US Project Scientist
4
How can I find the ALMA Site?
Paranal
La Serena
Santiago
5
Antennas
Four Melcos
VxRSI No 2,3,4,5
VxRSI No 1
6
Summary of Week
3 Light and the EM spectrum E h x f
c f x ??????? ?visual 5 x 10-5 cm 0.5
?m
5,000 Angstroms
???????Spectra emission, absorption,
continua, spectral lines
Black-body (thermal continuum)
Peak intensity at ? 0.3 / T(K)
(cm) Atoms, molecules, and energy states
spectrum of hydrogen Doppler shift
?f / f ?????? V/c Telescopes
Cassegrain, Newtonian, refractor, .
Resolution ? ? / D in radians
2 x 105 (? / D) arc
seconds Light gathering power
Collecting area ? (D/2)2 Magnification
M f.l. Telescope / f.l. eyepiece
apparent
angle/actual angle
Diameter/diameter of exit pupil
7
Learning Points for Week
4 Review of laws of motion Gravity and
orbits Conservation of energy, momentum,
angular momentum Special relativity c
constant length contraction, time
dilation, increase of mass with V Structure of
Ordinary matter the 4 forces of nature
Gravity, electro-magnetism, weak, strong
nuclear forces photons and other
exotica (Zs, Ws, gluons, gravitons)
Electrons, protons, neutrons, neutrinos, quarks
unstable sub-atomic
particles Structure of the Sun Gravity ltgt
Pressure of hot gasses Luminosity flux
Estimating the life-time of the Sun
Gravitational, chemical, vs. nuclear energy
Energy generation in the Sun nuclear
reactions (p-p CNO)
8
Clicker question (review)

• What is wavelength of a 100 MHz ( 108 Hz)
• radio wave?
• (recall c 3 x 1010 cm/sec f x ? )
• 300 cm 3 meters
• 3 x 10-4 cm
• 100 cm
• 3 cm

9
Clicker question (review)

• What is wavelength of a 100 MHz ( 108 Hz)
• radio wave?
• (recall c 3 x 1010 cm/sec f x ? )
• 300 cm 3 meters ? 3 x 1010 / 108
  cm
• 3 x 10-4 cm
• 100 cm
• 3 cm

10
Clicker question (review)

• What is the theoretical angular resolution of a D
  10 cm
• telescope at ? 0.5 ?m (visual light)?
• recall ? ????D in radians
• 1 radian 2 x 105 arc-seconds
• 1 ?m 10-4 cm
• a) 100 arc-seconds
• b) 10 arc-seconds
• 1 arc-second
• d) 0.1 arc-seconds

11
Clicker question (review)

• What is the theoretical angular resolution of a D
  10 cm
• telescope at ? 0.5 ?m (visual light)?
• recall ? ????D in radians
• 1 radian 2 x 105 arc-seconds
• 1 ?m 10-4 cm
• a) 100 arc-seconds
• b) 10 arc-seconds
• 1 arc-second ? 2 x 105 x 5x10-5
  / 10 arc-sec
• d) 0.1 arc-seconds

12

• Evolution of
• A Star
• Birth
• Main-sequence
• life
• - fusion HgtHe
• Death
• gt 60 M
• black hole
• 8 60 M
• neutron star
• lt 8 M
• white dwarf

The Sun .
13
106
60M
Hertzsprung- Russell diagram
107 yrs
10M
108yrs
109 yrs
1M
1
1010yrs
Live Fast Die Young Lifetime 1 / mass2
1011 yrs
0.1M
10-5
14
Matter, energy, motion

• Conservation of momentum
• Momentum Mass x Velocity
  P mv
• If no force acts -
• Objects at rest stay at rest
• Objects in motion keep moving
• Conservation of Angular momentum
• Angular Momentum Mass x Velocity x
  Radius
• 
  L mvr
• Newtons Law
• Force mass x Acceleration
  F ma

15
Matter, energy, motion

• Kinetic energy
• Energy 1/2 Mass x Velocity 2
  E 1/2 mv2
• Meter-Kilogram-second (mks) Units are
  called joules
• Centimeter-gram-second (cgs) Units are
  called ergs
• 1 joule 107
  erg
• Power
• Power rate at which energy is used
• Energy / time
  P E / t
• Meter-Kilogram-second (mks) Units are
  called Watts
• 
  

16
Luminosity Flux

• Luminosity
• Rate at which energy is given off in all
  directions
• Luminosity of the Sun
• Lo 4 x 1033 erg/sec 4 x
  1026 Watts
• Flux
• Rate at energy flows through a unit
  area
• Flux of Sunlight at Earth
• F Lo / 4 ? D2 where D 1.5
  x 1013 cm
• 
  1 Astronomical Unit
• 1.4 x 106 erg / sec per cm2
  
• 1.4 x 1010 erg / sec meter2
  (104 cm2 in 1 m2)
• 1.4 x 103 Watts / meter2
  (107 erg/s in 1 Watt)
• 1.4 kilo-Watts
  (1 kW 103 Watts)

17
Energy scales

• Energy of a photon of light 10-12
  erg
• A typical light bulb (or a human) 100
  Watts 109 erg/sec
• Sunlight at Earths surface 103
  Watts / square meter
• 
  106 erg sec-1 cm-2
• The luminosity of the Sun 1033
  erg/sec
• Energy released by a supernova 1051 ergs
  (in a few hrs)
• Total energy given off by the Sun in
• 10 billion (1010) years
  1051 ergs
• (1 erg the energy required by an ant to do a
  push-up)

18
Figure 4.8 Unannotated
Conservation of angular momentum
19
Figure 4.9 Unannotated
Conservation of angular momentum
20
Gravity (the weakest force)
21
Figure 4.17 Unannotated
Gravity angular momentum gt orbits
22
Figure 4.21
Orbits in the Solar System
23
Figure 4.18 Unannotated
Objects orbit the Center of mass
24
ASTR 1020 Introductory
Astronomy II Stars Galaxies
Week 4 Lecture 2 Special Relativity General
Relativity Gravity Quantum Mechanics and the 4
Forces of Nature The Sun as a Star
25
Chapter S2Space and Time
26
Special Relativity (S2)Laws of motion for
speed near c speed of light

• Laws of physics same for all observers
  regardless of state of motion
• Speed of light 3 x 1010 cm/sec for all
  observers regardless of state of motion
• Consequences
• No information can travel faster than light
• Time slows for objects moving with respect to you
• Lengths shrink
  
• Simultaneous events are NOT simultaneous in an
  other frame
• Mass grows with V approaches infinity as V gt c
  
• m mrest / 1 -
  (V/c)21/2
• At V 0.9999 x speed of light
• 1 gram has mass 70.7 grams
• 1 second gt 0.014 seconds as you see it
  in moving frame
• 1 cm gt 0.014 cm

27
The Time Dilation Formula
t trest x 1 - (V/c)21/2

• Time will appear to pass more slowly in a moving
  object by an amount depending on its speed
• Time almost halts for objects nearing the speed
  of light

28
Special Relativity (S2)Addition of velocities

• Jack
  Jill
• gt you
  lt
• V1
  V2
• What does Jack measure for Jills Velocity?
• o lt
  lt
• Expect
• V V1 V2
  Only correct when V ltlt c !
• Special Relativity
• V1 V2
  V1 0.9 c V2 0.8c
• V ----------------------------
  
• ( 1 V1 V2 / c2 )
  gt V 0.988c

29
Formulas of Special Relativity
30
Deriving E mc2
Mass-Energy of object at rest
Kinetic Energy
31
Chapter S3Spacetime and Gravity
32
The Equivalence Principle

• Einstein preserved the idea that all motion is
  relative by pointing out that the effects of
  acceleration are exactly equivalent to those of
  gravity

33
General Relativity (S3)Einsteins view of
Gravity

• Generalize motion at constant speed to
  Accelerated motion
• Principle of equivalence
• force on astronaut in accelerating ship
• ltgt indistinguishable from force of gravity
  on a surface
• free fall (in falling elevator) ltgt free
  fall in space
• Mass Energy Curve (warp) space slow time
• Curved space Determines motion of mass and
  energy

34
Spacetime Diagram of a Car
distance between two different events in
spacetime d2 x2 y2
z2 (ct)2

• A spacetime diagram plots an objects position in
  space at different moments in time

35
What is curved spacetime?
36
Rules of Saddle-Shaped Geometry

• Piece of hyperbola is shortest distance between
  two points
• Parallel lines diverge
• Angles of a triangle sum to lt 180
• Circumference of circle is gt 2pr

37
What is gravity?
38
Gravitational Lensing

• Gravitational lensing can distort the images of
  objects
• Lensing can even make one object appear to be at
  two or more points in the sky

39
Gravitational lensingby a cluster of galaxies
40

• How do we test the predictions of the general
  theory of relativity?
• Precession of Mercury
• Gravitational Lensing
• Gravitational Time Dilation
• What are gravitational waves?
• Movements of massive objects produce wavelike
  disturbances in spacetime called gravitational
  waves

41

• Gravitational Waves
• - Binary neutron stars, merging black holes
• - Laser Interferometer Gravitational-wave
• Observatory (LIGO). Washington Louisiana

42
Chapter S4Building Blocks of the Universe
43
Particle Accelerators

• Much of our knowledge about the quantum realm
  comes particle accelerators
• Smashing together high-energy particles produces
  showers of new particles

44
Properties of Particles

• Mass
• Charge (proton 1, electron -1)
• Spin
• Each type of subatomic particle has a certain
  amount of angular momentum, as if it were
  spinning on its axis

45
Fermions and Bosons

• Physicists classify particles into two types,
  depending on their spin (measured in units of
  h/2p)
• Fermions have half-integer spin (1/2, 3/2, 5/2,)
• Electrons, protons, neutrons
• Bosons have integer spin (0,1,2,)
• Photons

46
Fundamental Particles
47
Quarks
Proton
Neutron
10-13 cm

• Protons and neutrons are made of quarks
• Up quark (u) has charge 2/3
• Down quark (d) has charge -1/3

48
Quarks and Leptons

• Six types of
• quarks up, down,
• strange, charmed,
• top, and bottom
• Six types of
• leptons
• electron, muon, tauon
• electron neutrino, mu neutrino, tau
  neutrino
• Neutrinos are very light and
  uncharged

49
Matter and Antimatter
Insert TCP 5e Figure S4.5b

• Energy of two photons can combine to create a
  particle and its antimatter counterpart (pair
  production)

50
Four Forces

• Strong Force (holds nuclei together)
• Exchange particle gluons
• Electromagnetic Force (holds electrons in atoms)
• Exchange particle photons
• Weak force (mediates nuclear reactions)
• Exchange particle weak bosons
• Gravity (holds large-scale structures together)
• Exchange particle gravitons

51
Strength of Forces

• Inside nucleus
• strong force is 100 times electromagnetic
• weak force is 10-5 times electromagnetic force
• gravity is 10-43 times electromagnetic
• Outside nucleus
• Strong and weak forces are unimportant

52
Forces in Nature
Strong Nuclear force
Grand Unified Theories
Electromagnetic force
?
Electroweak force
Weak nuclear force
Gravity
energy
53
Electron Waves
Insert TCP 5e Figure S4.8

• On atomic scales, an electron behaves more like a
  wave with a well-defined momentum but a poorly
  defined position

54
Uncertainty Principle

• The more we know about where a particle is
  located, the less we can know about its momentum,
  and conversely, the more we know about its
  momentum, the less we can know about its location

Uncertainty in energy
Uncertainty in time
Plancks Constant (h)

X
Uncertainty in energy
Uncertainty in time
Plancks Constant (h)

X
55
Virtual Particles

• Uncertainty principle (in energy time) allows
  production of matter-antimatter particle pairs
• But particles must annihilate in an undetectably
  short period of time

56
Vacuum Energy

• According to quantum mechanics, empty space (a
  vacuum) is actually full of virtual particle
  pairs popping in and out of existence
• The combined energy of these pairs is called the
  vacuum energy

57
The Universe
General relativity
nearest star
planets
molecules
people
galaxies
quarks
atoms
nuclei
Universe
superstrings
stars
EM
weak
GUTS
gravity
strong
58

• Understanding matter, energy, and the Universe
  ..
• The Engine that Drives Our Economy
• Galileo, Newton, (1600s)
• - Gravity, mechanics, calculus
• gt Industrial Revolution
• Maxwell, Lorentz, Hertz, Tesla, (1800s) the
  ether
• - Electricity, magnetism, electrons, atoms
• gt Electrification, broadcasting,
  communications,
• Einstein, Lorentz, Planck, Bohr, Dirac, Fermi,
  (1900 - 1950s)
• - Electricity, magnetism, electrons, atoms,
  quantum mechanics
• fundamental forces
• gt Electronics, sensors, transistors,
  lasers, computers,
• Cosmic evolution ( 1960s 2000 beyond)
• - Nature of ordinary matter / energy, dark
  matter / energy

59
Clicker Question

• Molecules are held together by which force ?
• Gravity
• Electro-magnetism
• Weak nuclear force
• Strong nuclear force

60
Clicker Question

• Molecules are held together by which force ?
• Gravity
• Electro-magnetism
• Weak nuclear force
• Strong nuclear force

61
Clicker Question

• Radioactive decay is caused by which force?
• Gravity
• Electro-magnetism
• Weak nuclear force
• Strong nuclear force

62
Clicker Question

• Radioactive decay is caused by which force?
• Gravity
• Electro-magnetism
• Weak nuclear force
• Strong nuclear force