It takes light over four years to reach us from the nearest star, Alpha Centauri. The brightest star in the sky, Sirius is 8.6 light years away. Betelgeuse, the bright red star in Orion, is 522 l.y. away. How do astronomers measure these huge distances? Certainly not with a tape measure! Even radar -- bouncing radio waves off an object and timing the reflection -- does not work. In this activity, you will learn about parallax, the most direct and accurate method astronomers have of measuring interstellar distances.

You experience parallax every day. Look out the window. If you move your head from side to side a few inches (or cm), you will see the window frame shift slightly with respect to the distant scenery outside the window. The size of the shift -- the angle measured in degrees -- depends on how much you move your head and the distance between you and the window frame. Astronomers use this same concept to measure distances to stars.

The bottom panel of the movie at right shows the view of a particular, nearby star through a hypothetical telescope. The black disk is the field of view of the telescope, and the scale bar on the right shows that the field of view is 2 arcsec across. Within the field of view, we see our target star (the large, red dot) and several distant, background stars (small dots).

The top panel of the movie shows the view from a different perspective -- looking down from above Earth's orbit around the sun. Over the course of one year, the Earth (blue dot) completes one orbit around the sun (yellow dot). As it does so, the line of sight connecting the Earth to the nearby star (yellow arrow) moves with our changing vantage point -- the end of the arrow moves among the distant, background stars (near top of panel). Our view through the telescope also changes -- the star seems to move through the field of background stars. Notice the relationship, frame by frame, between the end of the arrow (top panel) and the position of the target star (lower panel) with respect to the fixed, background stars.

The first orbit (Jan-Dec) of the movie shows the apparent motion of the nearby star as the Earth orbits the sun. The second orbit shows the same motions but records the positions month by month. The last panel shows a green triangle which contains the geometry critical to determining the distance of the nearby star (click here for a permanent view of the triangle).

3 Movies

The movies above show the parallax motions of three different stars. Our ultimate goal is to determine the distance to each of the stars. Let us begin by drawing the Earth-sun-star triangle for each of the stars. To make the large parallax angle seen for Star A, what type of triangle must exist -- short and wide or long and thin? What type of triangle must exist for Star B? On your worksheet, sketch a triangle for each of the three stars.

Having learned about the geometry that causes the parallax effect (click for a reminder), can you tell which star is closest to the sun? Star A Star B Star C Which is farthest? Star A Star B Star C

Imagine we had a star with a very large distance from the sun. How large do you expect the parallax angle to be for this star?

Make a general statement about the relationship between the sizes of p and d. (Answer text box?).

One side of the triangle is the distance between the Earth and sun (one astronomical unit) and another is the distance from the sun to the star (d). The angle p is called the parallax angle. The diagram shows that p is half of the total shift the star makes relative to the background stars over the course of one year. Because it is a right triangle (contains one 90 degree angle), we can use basic trigonometry to solve for the sun-star distance d in a.u. provided we measure the parallax angle p. In practice, the angle p is very small -- the size of the Earth's orbit is vastly exaggerated compared to the distance between the sun and the star in the top panel of the movie. This means that we can use the Small Angle Formula (instead of trigonometry) to solve for d after we measure p. The resulting relationship is given by