Student Manual PAGE 8 The Principles of Parallax Measurement of precise positions are key to one of the most powerful methods astronomers have of measuring the distances to objects in the sky, a method known as parallax.  Parallax is the most direct way astronomers have of measur- ing the distances to stars. The parallax of an object is its apparent shift in position when you view the object from two different vantage points.  It’s commonly used on the earth to measure the distance across a wide river (see Figure 5 below).  You view a tree from two vantage points on the opposite shore.  You carefully measure the distance between the two vantage points, called the baseline, B, and the angle between the two lines of sight to the tree, parallax angle designated as Q.  Using trigonom- etry, you can find the perpendicular distance across the river.  Since the distance, D, is one side of a right triangle, the opposite angle of which is Q/2, and the adjacent side of which is B/2, the distance across the river can be repre- sented  as In general, if you can measure the parallax, Q, of an object as measured from two points separated by a baseline, B, you can measure its distance. In astronomy, a commonly used baseline is the diameter of the earth’s orbit and the parallax we measure is due to the shift in vantage point as the earth orbits the sun.  If we view a nearby star from opposite sides of the earth’s orbit, and measure its position against a background of distant stars, we will see that it appears to move.  For example, its equatorial coordi- nates measured in June, when the earth is at one side of the sun, will be different from its position in January when the earth is at the other side of the sun (see Figure 5).  The further the star, the smaller the parallax.  Even the nearest stars have parallax shifts of less than a second of an arc, hard to see and hard to measure.  However, astronomers have been able to measure the parallaxes of over a hundred thousand stars using sophisticated techniques and a special satellite called Hipparchos. It is also possible to measure the distance to asteroids using parallax too.  Because asteroids are closer, their parallax is larger, and we can even use a short baseline - like the diameter of the earth.  Viewed from two points on the earth, aster- oids show a very noticeable parallax, as you will see in Part IV of this exercise.  Measuring the parallax of asteroids using astrometry is a useful exercise for showing us how the much smaller parallax of stars is measured in practice. ( ) D B = 2 2 tan  q Figure  5 Parallax  of  an  Object