Notes
Slide Show
Outline
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Astro 1050 Sep. 5, 2003

  • A Little More about Scientific Notation, Units, and the Scale of the Universe
  • How we name and start to classify stars
    • *Constellations*, Magnitudes
  • How the stars move across the sky
    • The celestial sphere
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Scientific Notation
  • 101 =       10
  • 102 =       100
  • 103 =     1,000  (one thousand)
  • 106 = 1,000,000  (one million )


  • You can think of this as raising 10 to some power –
    or just think of it as moving decimal place over some given number of steps.  Think of computer speeds and disk space.


  • 100 =         1
  • 10-1 =         0.1 = 1 /        10
  • 10-2 =         0.01 = 1 /       100
  • 10-3 =         0.001 = 1 /     1,000
  • 10-6 =         0.000001 = 1 / 1,000,000


  • How to write numbers which are not powers of 10:
    1 A.U. = 149,597,900 km = 1.496 ´ 108  km
                            = mantissa     ´ 10exponent
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Arithmetic and Scientific Notation
  • Multiplication:  Multiply the mantissa
          Add the exponents


  • 20 AU = (2 ´ 101 ) ´ (1.496 ´108 km)
     
          = (2     ´ 1.496) ´  (101 x 108) km
          =   2.9992        ´      109       km


  • Division:        Divide the mantissa
          Subtract the exponents
  • 1 AU / 500 = (1.496 ´108 km) / (5 ´ 102)
               = (1.496 / 5 )     ´  (108 / 102) km

  •            =  0.2992      ´      106     km
               =  2.992           ´      105     km


  • Be careful when adding or subtracting:
  •   (2.0´106) + (2.0´103) = 2,002,000 = 2.002´106
                                  not 4.       ´106
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Scientific notation and the metric system
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A light-year: Distance Not Time!
  • speed of light = c = 3.0 ´ 108 m/s


  • distance =   speed      ´   time
  • d =      c                     ´     t
  • light-second =  3.0 ´ 108   m/s     ´    1 s
    =  3.0     ´ 108   m
  • light-minute =  3.0 ´ 108   m/s      ´   60 s
    = 180     ´ 108   m
    =  1.8     ´ 1010  m


  • light-year      =  3.0 ´ 108   m/s      ´  3.14 ´ 107 s (i.e. 31.4 million s) =  9.4 ´ 1015  m
    =  9.5     ´ 1012  km
    =  9.5 trillion km
    =  9,500,000,000,000 km
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Example of using Units as a check
  • If someone says: 
    “The time it took me to walk to class today was 10 minutes.”

    the number could possibly be wrong, but the statement at least makes sense.


  • If someone says:
    “The time it took me to walk to class today was 10 kilograms.”

    something is obviously wrong.


  • When you use a formula to calculate some answer – you can treat units just like numbers – multiplying and canceling them.
  • The units you are left with MUST be those which match the ones expected – or you have made some mistake.
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Another example of Units, with conversions
  • 1 light-year  =     c ´ t    (where c is the speed of light and t is one year)

    = 3.0     ´ 108 m/s    ´   365 days
    = 1.1     ´ 1011    (m ´ days /s)
  • but we know light-years is a distance and must have “dimensions” of distance.  We should have units of just meters.  The fact that we have this extra (days/s) means we have left something out.
  • If we multiply by  (24 hr/day ´ 60 min/hr ´  60 sec/min) the units will work out right and so will the numerical answer

  •        = 1.1 ´ 1011 ´ 24 ´ 60 ´ 60  m
           = 9.5     ´ 1015    m
           = 9.5     ´ 1012 km
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"Chapter 2:"
  • Chapter 2: The Sky


  • Constellations:
  • -Originally vague
  • -Mostly Greek
  • -Now well defined
  • -Total of 88


  • Asterisms:
  • -Less Formal Groups
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Big Dipper
  • The stars in a constellation or asterism like the Big Dipper are NOT necessarily at the same distances.


  • These are just chance arrangements as seen from Earth.
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Names of stars
  • Proper names mostly from Arabic
  • Astronomers use
    (a, b, d, e, ... )  + Constellation
    in approximate order of brightness
      • Alpha Orionis = Betelgeuse
      • Beta   Orionis = Rigel
      • Alpha Tauri    = Aldebaran
  • Numbers and other schemes for fainter stars.  (About 6000 stars are visible to naked eye.)
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Magnitudes (m) to denote brightness
  • Ancient system created by Hipparchus
    • 1st magnitude = brightest stars in sky
    • 6th magnitude = faintest visible to naked eye
    • Confusing because smaller number implies brighter
      • (Think of first magnitude as “first in class”)


  • Astronomers want a numerical measure of
     Intensity (I)  which is proportional to energy per unit time received from the star.


  • Relationship between I and m turns out to be “logarithmic”  (result of properties of human eye)
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Numerical Relationship between m and I
  • Every increase in m by 1 is a drop in brightness by a factor of 2.512
    • We receive 2.512 times less power from a 2nd magnitude star than from a 1st magnitude one.
    • We receive 2.512 ´2.512 = 6.310 times less from a 3rd magnitude than a 1st magnitude
    • We receive (2.512)5 times less from a 6th magnitude star than a 1st magnitude.  The 5 comes from 6-1.
    • Because (2.512)5 = 100 (not by accident) the faintest stars we can see are 100 times fainter than the brightest.
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Apparent Visual Magnitude Scale
  • From our Text, Horizons by Seeds
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Formula for Intensity vs. m:
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Examples:
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Examples:
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Examples:
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Examples:
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For Next Time…