'-""'-.'vvvvvvvvv FARAWAY STARS Parallax and Stellar Distances Introduction How are astronomers able to say that a star was a certain distance away from Earth when they've never been able to travel to the star to measure the distance? Astronomers and mathematicians are clever people that work well in solving challenging problems together. Stellar distances can be determined using proven principles, relationships and mathematical equations that have proven accurate on smaller scales. here on planet Earth. Background Helpful denitions and conversions I kilometer (km) I meter (in) I centimeter (cm) I millimeter (mm) Parallax Galaxies Clusters Superclusters Light Year Parsec = m = cm = mm =_____m The measurement of the apparent shift of a star against the more distant background stars. Regions of space where there are hundreds of billions of stars spaced relatively close together (distances between individual stars are best measured in light years). Regions of space where there are tens of thousands of galaxies spaced relatively close to one another (distances between individ- ual galaxies are best measured in parsecs). Regions of space where there are vast numbers of clusters spaced '77 we\") -, ~ -relatively close to one another (distances between clusters are best measured in parsecs). The distance that light travels in one Earth year. It's used to measure distances between stars. One light year is equal to 10 trillion kilo- meters (1 x 1013 km). This unit is used to measure even larger distances like those between galaxies. It is also used to measure distances between stars. One parsec is equal to 3.26 light years. One parsec is deter- mined to be the distance to an object that measures 1 arcSECond of PARallax. One parsec of distance is equal to = l stellar parallax Our star, Sol, appears much larger than all other stars in the night sky because it is so much closer to us than all the others. Sol is an average of 93,000,000 miles from Earth. As dis- tance between objects decreases, the apparent size of objects will increase. As if the large dis- tance of 93,000,000 miles isn't bad enough, distances to other stars are much greater. Astronomers have developed units just to make the distances manageable to calculate and use. Astronomy Activity Lab Manual 43 FARAWAY STARS Parallax and Stellar Distances Activity Overview In this activity, Parallax and Stellar Distances will be further investigated. Materials Masking tape Pencil Meter stick Pin Pen Rubber stopper Activity 1 A. How do we measure distances to stars . . . Practicing Parallax Parallax. . . is the distance of apparent shift of an object against a background. Hold your thumb up at arm's length and toward an object such as a clock on the wall. Close your right eye. Then open your right and close your left eye. The clock (or other object) did. not move, but it did appear to move. Half the amount that the clock appeared to move is called parallax. Figure A. .' , Astronomers don't use their thumb #1 width to determine parallax of stars. :"l l T @ = 3" focus They have to use something much big- . = Mathmatical ger . . . the entire orbit of Earth! Note the Pomt- locus " . line on the diagram at the left that repre- sents the angle of parallax to this star. @ = Earth ; I Parallax ' Ang |e'-" edite June 21 December 21 When astronomers observe stars in the night sky using powerful telescopes, they can take photographs to carefully measure the stellar parallax of that star. Then using basic trigo nometry (and some other mathematics) they can calculate its distance from Earth. 44 Astronomy Activity Lab Manual illIII!!!'11||1|IIIIIIIIIllllllllllll[111111 FARAWAY STARS Parallax and Stellar Distances Activity 2 Procedure 46 . Cut off a 60 cm-long strip of masking tape. . Center it on your desk so that it runs down the length of the desk lengthwise. . Use a meter stick or ruler to measure sections of the tape and label them as follows: from 0 cm at the edge closest to you. to 50 cm at the far end. Mark off and label 5 cm intervals. . At the 50-cm line, rest a meter stick on edge perpendicular to the tape (horizontally across the desk) on the tape (the SOcm line on the tape and the SOcm line of the meter stick should be aligned). The meter stick should stand on its edge so the num- bers can be read at eye level (See step 7.) . Stick a pin into a rubber stopper. The head of the pin will be used to represent a \"star." and the distance of the pin from your eyes is used to represent the distance of a star from Earth. . Place the stopper with the straight pin on the 5-cm line of the tape. Place your nose at the table edge, close your left eye. and use the pin as a sight line. . Determine the value on the meter stick that the pin line up with. Record this value in the appropriate location on Table l (Parallax Data Table). . Now close your right eye and record this value on Table 1. Continue this procedure to complete the table. Round data to the nearest tenth of a cm. . Graph the data in Table 2. Label the Xaxis \"Distance (in cm).\" Label the Yaxis \"Parallax (in cm)" Astronomy A ctiuily Lab Manual V a IIIQIQIIIIIIIIIIIIIIIIII ' .. H I"! IIIIIIIIIIIllii FARAWAY STARS Parallax and Stellar Distances Student Data Tables Table 1. Parallax Data Table Difference (= Parallax) (cm) Astronomy Activity Lab Manual 47 FARAWAY STARS Parallax and Stellar Distances Questions to Master 1. State the relationship between distance to a star and its parallax. X=1farc second (pc) 2. Why have astronomers developed the units of parsecs to measure distances to stars and galaxies when we have a perfectly good unit, kilometers? 3. The following are real stars in the night sky of the Northern Hemisphere. Their paral- lax values are presented below. Complete the table by calculating their distances from Earth in light years, just as astronomers do. Finally, calculate what these values equal in km. Write these values in scientific notation. Parallax Light Years Km from Earth Star name (\" of arc) from Earth (scientic notation) Alpha Centauri 0.760 Vega 0.123 Sirius 0.375 Polaris 0.005 Aldebaran 0.048 4. The diagrams below represent photographs that astronomers work with to deter mine parallax. These two views of the night sky are taken of the same night sky, but 6 months apart. if you observe these photographs carefully, you'll notice that one star does not appear in the same position against the background stars in each photo- graph. Complete the following based upon these photographs A and B. Photo A. Taken on June 21Photo B. Taken on December 21 48 Scale 1 mm = 0.01 arc second a. On both photographs, circle the star showing a parallax shift. b. Draw the star from photograph B onto photograph A (be accurate!) 27.5 c. Measure the distance between the two stars on photograph A in mm. Astronomy Activity Lab Manual IallnllillltlIllOllilllilliiiIIIIIIl' ' "\" _.'t-~vv'vwvvvvvvvvvvvvvvvvvvvv FARAWAY STARS Parallax and Stellar Distances d. Use this distance to convert the measurement into parallax angle. (use the scale provided). 2. Stellar parallax is half the measured parallax angle of the apparent motion of a star against its background stars. What is the stellar parallax for this star? f. Calculate the distance in parsecs to this star. g. Calculate the number of km to this star. 5. Circle all correct choices within the parentheses. Parsecs are measurements of (time/distance/age/speed). They' are used for distances between (stars/cities/planets/galaxies/clusters/superclusters). Light Years are mea- surements of (time/distance/age/speed). They are used for distances between (stars/ cities/planets/galaxies/clusters/superclusters). Stellar parallax is the method used to measure (distances between galaxies/distances between stars/distances in space). Astronomy Activity Lab Manual 49