1. The north star, Polaris, is located 208 parsecs from the Earth.

a. Calculate the distance to Polaris in light-years.

d = 208 parsecs x 3.26 light-years/1 parsec

d = 678 light-years

b. What is the parallax of this star?

parallax = 1 / # of parsecs = 1 / 208 parsecs

= 0.0048 seconds of arc

This angle is so small that we must actually find some other method of determining the distance to Polaris. Parallax measurements can only be used to find the distance to a few hundred of the nearest stars in our own Milky Way Galaxy.

The brightnesses of stars are also of great importance to astronomers. The ratio of the absolute brightnesses of two stars can be used to find the relative distances to these stars.


2. How much brighter is a star of absolute magnitude -1 than a star of absolute magnitude +4?

First, we must find the difference in absolute magnitude.

(+4) - (-1) = 5 magnitudes of difference

This means that, since there is an increase in brightness of 2.5 for each magnitude of change, the brightness increase in this case is:

2.5 x 2.5 x 2.5 x 2.5 x 2.5 = (2.5)⁵ = 100 times

The -1 magnitude star is therefore 100 times brighter than the +4 magnitude star.

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