Distance and Luminosity Worksheet 
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                    R
          d  =  -----------
                  tan p


   R   =  1  Astronomical Unit

       =  150 million kilometers

       =  1.5 x 10^(11) m

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   Q:  Based on Bessel's measurement, how far away was 61 Cygni?
       Express your answer in meters and in light-years.

          1 light year =  distance light travels in one year

          1 arcsecond  =  1/3600 degree






                            1.50E11 m
   dist to 61 Cygni  =   --------------    =    9.85E16 m
                         tan(0.314/3600)

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                                      26
   solar luminosity  L       =  4 x 10    Watts

   magnitude of Sun  m       =  -26.5

   magnitude of 61 Cygni A   =   +5.2



    intensity (A)              -0.4 * [ mag(A) - mag(B) ]
   -----------------      =  10
    intensity (B)


   intensity (61 Cygni A)      -0.4 * [ 5.2 - (-26.5) ]
  ----------------------- =  10
   intensity (Sun) 



                          =  2.09E-13   



This is the factor by which 61 Cygni appears fainter than the Sun.


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           Inverse Square Law  

                                                       2
   intensity (at dist d1)    [ distance (at dist d2) ]
  ----------------------  =  [ --------------------- ]
   intensity (at dist d2)    [ distance (at dist d1) ]



If we could move 61 Cygni A to the Sun's distance, it would
become brighter by a factor of

                                                              2
                                 [ actual dist to 61 Cyg A   ]
                              =  [ ------------------------  ]
                                 [      dist to Sun          ]


                                                    2
                                 [    9.85E16 m    ]
                              =  [ --------------- ]    =  4.31E11
                                 [    1.50E11 m    ]

This is the factor by which 61 Cygni A would grow in brightness,
if we moved it to the Sun's distance.

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Now, try to figure out whether 61 Cygni A would be
as bright as the Sun, if we placed it at the center
of the solar system.

                              ( brightness compared )   ( factor by which )
  brightness of 61 Cyg A   =  ( to Sun, at 61 Cyg's ) * (  61 Cyg would   )
      at dist of Sun          (  actual distance    )   (  grow brighter  )


 
                           =      2.09E-13    *   4.31E11

                           =      0.090


If this value is greater than 1, then 61 Cyg A would be brighter than
the Sun, if placed next to it.  But if the value is less than 1, then
61 Cyg A would be fainter than the Sun, if placed side-by-side.


                                  so 61 Cyg A is fainter than the Sun