## Parallax

Here are some hints for tackling the parallax problems.

First, recall that parallax measures the apparent shift in position of a star when viewed from Earth at times 6 months apart (that is, from opposite sides of the Earth's orbit.) So begin by drawing a picture showing this situation. The parallax angle is one half of the total shift, that is, it is the angle between lines from the sun to the star and from the earth to the star.

Now to help with the calculations, draw a circle with the star at its center and both the Sun and the Earth on its circumference. The two lines that define the parallax angle now slice out a wedge of the circle. Calculate what fraction of the circle the wedge is in 2 ways.

1. Compare the angle of the wedge (the parallax angle) with the angle of a complete circle (360°).
2. Compare the distance along the end of the wedge ("the pie crust") with the circumference of the complete circle. Notice that the radius of the circle is the distance to the star.
Now set the two calculations of the fraction equal to each other. You will have an equation relating the parallax angle to the distance to the star. Notice that the angle is inversely proportional to the distance.

You can use the relation in both problems 1a and 1b of set 3.