1. Logarithms and The Distance Modulus

2. Logarithms and Exponents 10 2 = 100 10 3 = 1000 Question asked: If you multiply a number by itself a number of times what is the answer? Log 10 100 = 2 Log 100 = 2 Log 10 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?

3. Rewriting Exponential Expressions as Logarithmic Expressions Base exponent = result Log base result = exponent Discuss writing the following exponential equations as logarithmic equations 2 3 = 8 10 4 = 10,000

4. 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

5. 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

6. 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)

7. Distance Modulus Continued m – M = 5 log d – 5 m = apparent magnitude M = Absolute magnitude d = distance to the star in parsecs

8. Determining Distance 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

9. Determining Absolute Magnitude 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