Let's work out another example. There is a star called 70 Herculis, which
really is a near-clone of the Sun. It has an apparent magnitude of 6.39.
Question: Is it closer than 10 parsecs or more distant?
Let's work out the numbers. The absolute magnitude of the Sun = +4.85. Therefore
the Distance Modulus m - M = 6.39 - 4.85 = 1.54 magnitudes.
For logarithmphobes: Let's look up the Table from the last
lecture. From this we see that a distance modulus of 1.54 means the star is between
15 and 25 parsecs away.
With the handy-dandy equation
so 
, so 
.
Thus 
so d = 20.3 parsecs.
This distance = 66.2 light years. (1 parsec = 3.26 light years).