Download M = 5 log d - Astro @ UChicago

Logarithms and The Distance
Modulus
Logarithms and Exponents
• 102 = 100
• 103= 1000
• Question asked: If you
multiply a number by
itself a number of times
what is the answer?
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Log10 100 = 2
Log 100 = 2
Log10 1000 = 3
Log 1000 = 3
Question asked: If you
know two numbers what
exponent will I have to
raise the first number to
get the second number?
Rewriting Exponential Expressions
as Logarithmic Expressions
• Base exponent = result
• Logbase result = exponent
• Discuss writing the following exponential
equations as logarithmic equations
• 2 3= 8
• 104 = 10,000
Distance Modulus
• Apparent magnitude (brightness) is a
function of the distance to the star and the
absolute magnitude (luminosity).
• We can use this relationship to determine
star distances or absolute magnitude after
we determine the apparent magnitude
Distance Modulus Continued
• If we know the apparent magnitude and
the distance we can determine the
absolute magnitude of the star.
• If we know the apparent magnitude and
the absolute magnitude we can determine
the distance to the star
Distance Modulus Continued
• Absolute magnitude is a way of comparing
the magnitude of stars. It is a measure of
how stars would appear if they were all
32.5 light years (10 parsecs from Earth)
Distance Modulus Continued
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m – M = 5 log d – 5
m = apparent magnitude
M = Absolute magnitude
d = distance to the star in parsecs
Determining Distance
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Proxima Centauri
m = 11.09
M = 15.53
m – M = 5 log d – 5
11.09 – 15.53 = 5 log d – 5
-4.44 = 5 log d – 5
.56 = 5 log d
.56/5 = log d
.112 = log d
10 .112 = d
d = 1.29 parsecs
Determining Absolute Magnitude
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Wolf 359
m = +13.44
d = 2.39 parsecs
m – M = 5 log d - 5
+13.44 – M = 5 log d – 5
- M = 5 log 2.39 – 18.44
- M = 5(.378398) – 18.44
- M = 1.89199 – 18.44
-M = -16.54
M = 16.54