Doppler Shift

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Doppler Shift
Consider a stationary point source emitting light
waves
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Doppler Shift
If source moves away, light appears redder than
it is. If source moves towards us, light appears
bluer.
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Visible light
The shift in the light waves is proportional to
the relative speeds of the source and observer
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Doppler Shift
Wavelength is shorter when approaching
Stationary waves
Wavelength is longer when receding
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Comparison of laboratory to blue-shifted object
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Comparison of laboratory to red-shifted object
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Wavelength shift
Assume radial speed, v, of glowing object is
small compared to speed of light, c v ltlt c.
l0 is reference wavelength of medium at rest.


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Frequency shift
Df


f
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Example calculation

• The star Vega has a hydrogen line of
  656.255nm, which is shifted from the reference
  value of 656.285 nm.
• Is it moving towards us or away?
• Calculate its speed

Red shifted to LONGER wavelength so moving away.
Speed is 13.7 km/s.
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Rotation Rate from Doppler Shift
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Spectroscopic Binary Stars
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Discovery of Planets Around Remote Stars
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Rotation speed of galaxy from 21-cm spectral line
of Atomic hydrogen
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Historical Note

• Using the Doppler shift, Edwin Hubble observed
• that the Universe is expanding!

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What Hubble Found
The Hubble constant Ho 558 km s -1 Mpc -1 is
the slope of these graphs
Compared to modern measurements, Hubbles
results were off by a factor of ten!
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Hubbles Law

• v Ho d
• Ho is called the Hubble constant. It is
  generally
• believed to be around 65 km/sec/Mpc
• plus or minus about 10 km/sec/Mpc.
• Note The further away you are,
• the faster you are moving!

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Implications of Hubbles Law
Distance velocity/(Hubble constant)

• To get a rough idea of how far away a very
  distant object is from Earth, all we need to know
  is the object's velocity.
• The velocity is relatively easy for us to measure
  using the Doppler effect, or Doppler shift.

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Caveat!
Space between the galaxies expands while
galaxies stay the same size
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The Tools of All Astronomy

• Light Curves examining how bright something is
  
• as a function of time

• Images examining what something
• looks like spatially

• Spectra examining how much energy an object
• emits as a function of energy

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Kinds of Spectra
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Another Way to Look at a Spectrum
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The Atoms Family

• Bohr atom
• Electrons in fixed orbits around
• Protons and neutrons in the nucleus
• Only certain electron orbits are allowed
• Electrons jump between orbits to make photons of
  specific energies

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Periodic Table
Electrons fill shells labeled s, p, d, f, etc. ?
New shells are added ?
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The Atoms Family

• Quantum atom
• Electrons are clouds of probability density
• No two electrons can have identical quantum
  numbers ? Pauli exclusion principle
• Heisenberg Uncertainty principle limits knowledge
  our simultaneous knowledge of
• position momentum
• energy time

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Gravitational Force
The gravitational force is weak, but very long
ranged. Furthermore, it is always attractive, and
acts between any two pieces of matter in the
Universe since mass is its source.
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Remember the Tortoise and the Hare?
Gravity has basic properties that set it apart
from the other forces (1) it is long-ranged and
thus can act over cosmological distances (2) it
always supplies an attractive force between any
two pieces of matter in the Universe. Thus,
although extremely weak, it always wins over
cosmological distances and is the most important
force for the understanding of the large scale
structure and evolution of the Universe.
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So, let us deal with GRAVITY

• Well need a bit of a history lesson
• Brahe
• Kepler
• Newton
• Einstein

Pay close attention, gravity has many
implications!
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Tycho Brahe
1546 - 1601
A wild Dane, but he made and recorded large
quantities of accurate measurements of the
motions of the planets around the Sun.
Began working with Johannes Kepler in 1600.
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• Keplers Three Laws of Planetary Motion
• Landmarks in the history for astronomy
  and mathematics, for in the effort to justify
  them Isaac Newton was led to create modern
  celestial mechanics. The three laws are
• 1) The planets move abort the sun in elliptical
  orbits with the sun at one focus.
• The radius vector joining a planet
• to the sun sweeps over equal areas
• in equal intervals of time.

• The square of the time of one compete
• revolution of a planet about its orbit is
  proportional
• to the cube of the orbit's semi-major axis

T12/ T22 R13/ R23 or T2k.R3
The empirical discovery of these laws from Tycho
Brahe's mass of data constitutes one of the most
remarkable inductions ever made in science.
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Isaac Newton

• Born 1642, the year Galileo died
• Loner, tinkerer, paranoid
• 1665-1666 Plague was very good for him
• Suffered mental breakdown 1675
• Math, Chemistry, Theology, Parliament
• Died 1727
• Has his picture on the British pound note

He put the physics and mathematics to Keplers
Laws!
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Was there really an apple?

• We know he was on a farm
• We dont know anything else

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Newtons Laws of Motion

• First Law
• - A body remains in its state of motion unless
  acted upon by an outside force
• Second Law
• - A body acted upon by an external force will
  change its momentum in the direction of the force
  such that the greater the force the greater the
  change in momentum (F ma)
• Third Law
• - Forces always occur in pairs, i.e. for every
  action there is an equal and opposite reaction

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Universal Law of Gravitation

• All objects in the Universe attract each other
  with a force that varies directly as the product
  of their masses and inversely as the square of
  their separation from each other.
• F G m m
• r

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2
gravity
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Albert Einstein
Besides having great hair, he taught us a few
fundamentally important things
E m c2

• Energy can be neither created nor destroyed. It
  can just
• change from one form to another. Light, heat,
  kinetic, potential,
• etc. etc. etc.

• No object can move faster than the speed of
  light.

• Space and time are linked together.