ASTRONOMY 113 Laboratory Lab 4: the Distances to the Stars
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ASTRONOMY 113 Laboratory Lab 4: The Distances to the Stars - Parallax Introduction and Goals One of the most fundamental - and difficult - goals of astronomy is to measure the size of the Universe. At the end of the semester you will approach this goal and measure the distances to remote galaxies. However, the journey begins here with the measurement of the distances between the Sun and the very nearest stars. For all of its cosmic grandeur, the measurement of the distances to stars is founded in the most classic surveying technique - triangulation - and the most ancient astronomical observation - astrometry. Astrometry is the careful measurement of the positions in the sky of celestial objects with respect to each other. Of course, with respect to the horizon the positions of stars are constantly changing due to the rotation of the Earth. But with respect to each other the positions of stars change very little. Thus the relative positions of the stars in the bowl of the Big Dipper or of the stars in the Belt of Orion do not appear to change from year to year. In fact, though, very precise astrometric measurements reveal that stars do move with respect to each other. A change in position might be due to the tangential velocity of a star (that is, its motion across your line of sight). Alternatively, the change in position might be due to the motion of the Earth itself around the Sun. The resulting apparent motion of the star is known as the parallax effect. Parallax is the apparent change in the direction of an object resulting from the motion of the observer. Hold your pencil at arm's length. Close first one eye, and then the other. The pencil seems to move back and forth with respect to a mark on the more distant wall. This is the parallax effect. Of course the pencil has not moved; it is actually the location of the "observer" which is changing. Now move the pencil closer to your face and repeat the experiment. You will see that the pencil seems to move a greater distance than before. Thus the amount of the parallax motion depends on the distance of the pencil from your face. In fact, by measuring the amount of the parallax motion of the pencil you could derive the distance to the pencil. Surveyors use this same technique to measure the size of fields, the heights of mountains, etc. Exactly the same effect should happen due to the Earth moving in orbit about the Sun. The effect is shown in Figure 1. As seen from Earth, the target star seems to shift position with respect to the more distant reference stars over the course of one year. In fact the target star is not moving at all. It is the 1 Earth which is moving, and as a consequence the direction of the target star as seen from the Earth changes over the course of one year. This apparent motion of the target star in the sky is called its parallax motion. As can be seen in Figure 1, the change in direction to the target star is an angle. The parallax angle, called p and measured in arc seconds, is defined as half of the change in direction over 6 months. (The reason for using half the angle will be seen later.) By measuring the parallax angle p of a star and using a bit of geometry, we can measure the distance D to the star in units of the Earth-Sun distance. Thus the radius of the Earth’s orbit about the Sun becomes our yardstick for measuring the size of the Universe. The Earth-Sun distance is so fundamental that it has been given the name of Astronomical Unit or AU. Earth 1 AU Target star parallax Reference angle p stars D Sun Apparent motion of target star Figure 1: Geometry of parallax motion. (Not to scale!!) Note that measuring such motions requires the existence of a fixed reference frame, provided by celestial objects whose motions are not detectable. Usually very distant stars will do, but for the most accurate astrometry astronomers use distant galaxies or quasars as reference points. Two thousand years ago, Greek Astronomers realized that if the Earth were moving then they should be able to observe the parallax motion of the stars. As no such motions were seen, they concluded the Earth was at rest. Their logic was absolutely correct. However, the stars are vastly more distant than they realized so that their parallax motions are too small to be seen with the naked eye. In this lab, you will observe a small portion of the sky through a telescope. You will search for stars whose positions in the sky are changing with time. The goals of this lab are to: i) Use astrometry to measure the parallax angles of several stars. ii) Determine the distances to these stars. iii) Observe the tangential velocities of several stars. 2 Before You Come to Class... • Read the lab completely. Your time in the lab is best used observing the "sky", not reading this manual. • Bring to class this lab manual, your lab book, a pencil or erasable pen, a straight edge, and a scientific calculator. Schedule This lab is to be completed in two lab sessions. 3 Section 1 - Observations The computer screen will show a window with the application "Parallax". • Double click on the application "Parallax". You will see a view of the sky like that in Figure 2. Figure 2: Sample Parallax screen The display shows the image obtained from the telescope, and a console with several control buttons and readouts. The readouts show the location of the telescope in the Solar System, the direction in which the telescope is pointing, and the Earth date in years and decimal fractions of a year. This telescope can only point in certain directions: in the ecliptic plane ("Ecliptic"), toward the ecliptic poles (e.g., "North Ecliptic Pole"), and at an angle 45o above the ecliptic plane (e.g., "North Mid- Latitude"). Initially the telescope should be pointing toward the North Ecliptic Pole; if not, ask your TA for help. The buttons at the top of the console give you control over time and telescope magnification. The Forward and Back buttons move time one-step forward and backward, respectively. The time step is one tenth of a year. The Continuous button moves time forward continuously. The magnification buttons (1x, 2x, 4x, 8x) change the telescope magnification. Try them out - notice that increased magnification necessarily reduces the size of the field of view. Now that you are comfortable with the telescope, begin your observations. • Click the Reset button to set the date to the current year. • Make sure you are on Earth looking toward the North Ecliptic Pole. • Click the Continuous button to move forward in time. You will see that time is continuously (and rapidly!) passing. Just watch the stars for a while. 4 • Click the Continuous button to stop the advance of time. Q1: Tape the star chart at the end of the lab manual (Figure 4) into your lab book. Identify all of the stars whose positions are changing with time. Mark them on the star chart; you may need to do a Reset if any of the stars have moved a long way from their original positions. These will be your "target stars" for observation. Name each moving star with a name of your own choosing. • Click on magnification 8x. • Click the Continuous button to move forward in time. This allows you to see stars with smaller motions (but only at the center of the field of view). Note on the star chart and name any target stars newly discovered at this magnification. Q2: Sketch the motion of each target star on the star chart. Do any of them show parallax motion? Which ones? Why do you think the motions are due to parallax? Do any of them show motions other than parallax? Which ones? To what do you attribute their motion? Q3: Of all the stars in the field of view, which do you think is nearest the Sun? Why? • Click the Reset button. ASTROMETRY Having now observed that some stars change positions in the sky, the next step is to measure their motions. Your telescope is equipped with instrumentation designed for such astrometric measurements. In order to do astrometry, we must define a fixed reference frame against which we measure the positions of the stars. Such a reference frame can be defined by celestial objects whose tangential motions are too small to be detected. Typically astrometrists will define their reference frame with many such objects; in this lab one will suffice. • Choose a distinctive stationary star and mark it on your star chart as your "reference star". This reference star will be the fixed point from which the positions of the moving stars - or "target stars" - are measured. The reference star is your anchor point in space. Notice that your cursor turns into a cross hair when it enters the telescope field of view. • Center the cursor on your reference star, and click. A red "x" will appear where you clicked. Note that if you wish to move the red "x", double-click at the new location. • Move the cursor elsewhere in the telescope field of view. Click and hold the mouse. 5 A display will appear in the lower left-hand corner of the window showing something like X: 11.80" and Y: 23.30". These numbers show the distance of the cursor from the red "x" along the X (left- right) and Y (up-down) directions, respectively.