Question 450140
The apparent magnitude, M of a celestial body can be approximated by the formula
M=6-2.5 log I/Io
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Note: I could not tell from your post if the fraction was I/Io or Io/I
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Where I is the intensity of light as measured from earth, and Io is the approximate intensity light of light from the faintest star, visible by the naked eye. Find M if I and Io=1
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M = 6-2.5*log[1/1]
M = 6-2.5*0
M = 6
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What apparent magnitude of a star whose light as measured from earth is 1,000,000 times as intense as the faintest stars visible to the naked eye.
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M = 6-2.5log[1,000,000Io/Io]
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M = 6-2.5*log[10^6]
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M = 6-2.5*6 = 6-15 = -9
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Note: If the fraction is really Io/I the answer would be 
as follows: 
M = 6-2.5*log[10^-6] 
= 6-2.5*(-6) = 6+15 = 21
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Cheers,
Stan H.