Chapter and Verse

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Chapter and Verse

• What we have so far
• Starlight ? How stars tell us about themselves
• The messenger EM radiation
• The means of collecting the message telescope
• Telescope ? flux measurements
• What we want to do now is learn how to read the
  rest of message

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The Doppler Effect

• Christian Doppler
• (1803 - 1853)
• (1842) noted an apparent change in the observed
  wavelength of a signal (sound wave) as a result
  of motion either towards or away from an observer

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• The Doppler Effect
• Applies to all wave-like phenomena
• e.g., EM waves, and sound waves

• Everyday example Sound of siren from emergency
  response vehicle
• Pitch increases as vehicle approaches and
  decreases as it moves away

Dial 911
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No relative motion case
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Wavelength
2
3
Both observers record same wavelength
Wave peaks move outward at speed c
5
Motion towards left
1
2
3
1
2
3
Records longer wavelength
Records shorter wavelength
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• So, the key idea for astronomy is
• source (star, galaxy,) emits EM radiation at
  some fixed wavelength (l)
• observer measures a wavelength of lobs
• Doppler effect says
• lobs lt l if motion of source is towards observer
• lobs gt l if motion of source is away from observer

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Dopplers formula light version

• If an object emits EM radiation at wavelength l,
  then the apparent change in wavelength (lobs -
  l), where lobs is the observed wavelength is,
• (lobs - l) / l V/c
• where V is the relative velocity in the line of
  sight (the radial velocity), c speed of light.

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• Notes
• by sign convention -V means motion is towards
  observer, and V if motion is away
• For EM radiation (e.g., light rays)
• Motion towards ? shorter wavelength
  observed (blue shifted)
• Motion away ? longer wavelength
  observed (red shifted)

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• With respect to light waves, the Doppler effect
  provides a cosmic speedometer

Applications include Planetary
rotation Stellar motion Binary stars Galactic
rotation Motion of galaxies Expansion of the
universe
Next
Ast 202
Hubbles law Lab
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Planetary rotation

• If a planet has distinctive markings - time
  transits.
• Works OK for Mars, Jupiter and Saturn

Repeat time for distinctive feature tobe in same
position spin period of planet
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• Problem planets
• Mercury small, close to Sun, no distinctive
  features
• Venus Dense atmosphere ? no surface visible (in
  optical)
• Solution for Mercury and Venus
• Use radar and exploit the Doppler effect

? UV image of Venus showing clouds in upper
atmosphere. Rotation rate of clouds is about 4
days - but is this the rotation rate of the
planet?
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Planetary rotation by radar - view from above
Limb moving away from observer
VRot
Reflected signal is red shifted
lobs
R
Radar
l
lobs
rotation
Reflected signal is blue shifted
VRot
Limb moving towards observer
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• Procedure
• we know l and c
• measure red shift (or blue shift) (lobs - l)
• use Doppler equation to find VRot
• VRot c (lobs - l) / l
• with VRot and a measure of the planets radius R,
  we can find the rotation period P
• P 2p R / VRot

? Velocity Distance / Time formula
Circumference of planet
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300 meter diameter, Arecibo radio telescope
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Rotation of Mercury

• Radar of wavelength l 0.5 m
• (lobs - l) measured to be 5.0 x 10-9 m
• Doppler equation gives
• V(Mercury) c (lobs - l) / l
• V(Mercury) 3 m/s
• Period of rotation 2 p (2440 x 1000) / 3
• 5.11 x 106 seconds 58.7 days

Radius of mercury
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Radar observations reveal

• Pspin(Mercury) 58.7 days
• 2/3 Porbit(Mercury)
• Conclusion Mercury spins three times on its axis
  for every two orbits about the Sun
• The radar results were a complete surprise-
  astronomers expected to see synchronous rotation
  for Mercury Pspin Porbit
  as in the case of our Moon

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Venus - unveiled (by radar)

• Radar obs. reveal Pspin(Venus) 243 days
• Big surprise spin motion is retrograde
• i.e., spins east to west
• Conclusion Venus is a very slow rotator, and it
  spins in the opposite sense to its orbital motion

Direction of orbital motion
Venus
Atmosphere rotates 60 times faster than
planet (ESA Venus express image)
Direction of spin