Nataliya Ohorilko

1
Magnitude System

• Historical Background
• Apparent vs. Absolute Magnitude
• The Distance Module
• Interpreting For Our Observations

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Historical Background
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Historical Background cont.

• The idea of apparent magnitude was discovered
  about 2000 years ago by a Greek astronomer
  Hipparchus. He looked at the night sky and
  decided to classify the stars by how bright they
  appear.
• The brightest stars he saw, he labeled magnitude
  1", the next brightest - magnitude 2", and so on
  all the way to the faintest stars, which he could
  barely see, which he labeled magnitude 6".

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Historical Background cont.

• We still use Hipparchus' apparent magnitude scale
  today, but we evolved it a little.
• The "zero point" of the apparent magnitude system
  today is a star Vega in the constellation of
  Lyra. Any star that is brighter than Vega is
  labeled with a negative number for its apparent
  magnitude.

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Apparent vs. Absolute Magnitude

• Apparent magnitude - measures how bright
  objects appear to us (which depends on how close
  they are to us), not how bright they actually
  are.
• Absolute magnitude - measures the actual
  brightness of the object, and it is also defined
  as the apparent magnitude an object would have
  if it were 10 parsecs away from us.
• Which magnitude do we observe at night?
• Right! The apparent magnitude )

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The Distance Modulus

• The Distance Modulus is a difference between an
  apparent magnitude and absolute magnitude.
• To find the Distance Modulus (µ) we need to know
  both the apparent and absolute magnitudes of a
  star.
• µ m-M5 log d -5

M absolute magnitude m apparent magnitude D
distance in parsecs
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Interpreting For Our Observations

• Betelgeuse
• We found that the apparent magnitude of
  Betelgeuse is 0.43 and that its distance is 429
  light years (131.53 parsec) away. With those
  numbers we can find its absolute magnitude.

M absolute magnitude m apparent magnitude D
distance in parsec
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Finding the Absolute Magnitude of Betelgeuse

• M m - 5 log(d/10)
• M 0.43-5 log (131.53/10)
• M 0.43-5 log (13.153)
• M -5.165
• The absolute magnitude of Betelgeuse is -5.165

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Proxima CentauriThe closest star to Earth

• Apparent Magnitude 11
• Absolute magnitude 15.5
• Distance 4.3 light-years

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• How close would Proxima Centauri have to be to
  have an apparent magnitude of -1.0?
• M 15.5
• m -1.0
•  
• 5 log (d/10) m - M
• 5 log (d/10) -1.0 - 15.5
• 5 log (d/10) -16.5
• log (d/10) -16.5 /5
• log (d/10) -3.3
• d/10 10(-3.3)
• d/10 0.0005
• d 0.005 parsec
•  
• 1 parsec 206 264.806 AU
• 0.005 parsec 1,031.324 AU