Section   18.2The Celestial Sphere

1. (Exercises 1 and 2) Calculate the distance, in parsecs and light-years, to the star Vega if the parallax of this star has been measured to be 0.125 seconds of arc.

The distance in parsecs is the reciprocal of the parallax as measured in seconds of arc so:

d = 1 / 0.125 s = 8 parsecs

In distance units of light-years this result would be:

d = 8 parsecs x 3.26 light-years/1 parsec = 26.1 light-years

Section 18.3Classifying Stars

2. (Exercises 7 and 8) How much brighter is a star of magnitude 0 than a star of magnitude +3?

First, find the difference in magnitude, which is (+3) - (0), or 3. Because there is an increase in brightness of 2.51 for each magnitude of difference, the brightness increase in this case is: 2.51 x 2.51 x 2.51, or 15.8. The magnitude 0 star is therefore 15.8 times brighter than the magnitude +3 star.


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