Astronomy 101Introduction to AstronomyWinter 2010Part 2: Labs 8-11(Excluding Galaxy Classification Images for Lab 9)Credits:Cover image of M51 from NASA’s Hubble Heritage Project - Labs: Gravity:Oliver Fraser, Julianne Dalcanton - Atoms: Apocryphal, Julianne Dalcanton -Thermal Radiation: Julianne Dalcanton - Atoms & Light: Apocryphal, Julianne Dalcan-ton - Spectral Classification of Stars: Stacey Palen, Richard Plotkin, Julianne DalcantonColors: Julianne Dalcanton - Color-Magnitude Diagrams: Marcel Agueros, Nate Mc-Crady, Ana Larson, Julianne Dalcanton - Measuring Distance: Todd Grinsteiner, JulianneDalcanton - Galaxy Classification: Andrew West, Julianne Dalcanton - Dark Matter:Greg Stinson, Julianne Dalcanton - Hubble Law: Luis Mendoza, Toby Smith, Ana Lar-son, Julianne Dalcantonc° 2010 Julianne Dalcanton - unless otherwise credited the images are copyrighted byNASA, the Sloan Digital Sky Survey, or by the author. Permission is given to make anddistribute copies of this document for educational purposes.Lab #8 Measuring Astronomical DistancesDetermining the distances to stars and galaxies is one of the most vexing problems in astron-omy. There are four basic methods that are used to determine distances: radar, parallax,standard rods or candles, and the Hubble Law. Each of these methods is most useful atcertain distances. Radar methods are only useful within the Solar System, while the HubbleLaw is useful only on the most distant scales (> 40 Mpc). In this exercise, we investigatethe use of parallax and standard rods to determine distances.ParallaxAlthough we may be able to derive many of a star’s properties through the spectrum of thelight it emits, in most cases we cannot immediately figure out its luminosity or its distance.Instead, for nearby stars we rely on a method with which you are actually already familiar:parallax.You can see the parallax effect by holding your thumb out at arm’s length. As you alternateopening and closing each eye, you should be able so see the position of your thumb jumpback and forth relative to objects in the background. This is because the centers of youreyes are a few centimeters apart, so that each eye has a slightly different point of view.In this lab, you will experiment with using parallaxes to determine distances. You will alsouse the standard rod method to measure distances to objects that are too far away to havemeasurable parallaxes.ProcedureFor this lab you will need a meterstick and a partner. It may also be helpful to use somemasking tape to mark out intervals of one meter on the floor before beginning this exercise.1. Take the meter stick and hold it in front of you, horizontally to the floor. Orient themeter stick so that one end touches your nose, and the other end points forward awayfrom your body, like Pinocchio.2. When your partner is done mocking you, he or she should hold a pencil halfway downthe meter stick at the 50 cm mark.3. Alternately open and close each eye, noting how the pencil moves against specificbackground objects. You will need to remember how large the parallax shift is, so thatlater you can compare it to the angular shift with the pencil in a different position.Astronomy 101 8 – 1 Introduction to Astronomy4. Have your partner move the pencil to half of the original distance (to 25 cm). Whenyou alternate opening and closing each eye, does the pencil appear to move more orless than before? Try to quantify how much more or less (twice as much? half asmuch? four times as much? etc.), and record your answer in the table below.5. Now, have your lab partner move the pencil to twice the original distance to you, atthe end of the meterstick. When you alternate opening and closing each eye does thepen appear to move more than or less than before? Try to quantify how much more orless (twice as much? half as much? four times as much? etc.) and record your answerin the table below.25 cm 100 cmAngular Parallax ShiftCompared to 50 cmDistance6. Based on your results above, parallax is [more/less] effective at measuringdistances to distant objects.There is a limiting distance beyond which parallax becomes ineffective. This occurswhen the parallax angle becomes so small that you cannot detect an angular shift fromone eye to the other. The angle at which that occurs depends on the “resolution”of your eye. For people with bad eyesight, this may happen at nearer distances thanpeople with excellent vision. You and your partner can find your personal limit bytaking the pencil farther and farther away from the observer until the parallax becomesundetectable.7. Have your partner walk away from you holding out the pencil. Your partner shouldstop every meter or so, so that you can alternately open and close each eye to check thesize of the parallax shift. Measure how far away the pencil is when it stops appearingto move relative to even more distant objects, and record your answer in the spaceprovided belowFor my eyes, parallax becomes ineffective beyondmeters.Astronomy 101 8 – 2 Introduction to Astronomy8. The angular shift produced by parallax depends not just on the distance to the object,but on the distance between the two observations. For your eyes, the “distance betweenthe two observations” is the separation between your two eyes. Do you think that theangular shift you observed would be larger or smaller if your eyes were further apart?[larger/smaller]It may help you to draw a small diagram below:9. Test your assumption by having your partner hold out the pencil while you comparethe angular shift by first opening and closing each eye and by then stepping from leftto right, keeping one eye closed at both positions.Parallax Questions1. Based on your results above, circle which of the following equations you think betterdescribes the relationship between the angular shift θparallaxof an object and its distanceD? [Hint: the relative shift between 25cm and 100cm should give you the best idea of theanswer.] The symbol ∝ means “is proportional to”.θparallax∝1Dθparallax∝1D2As you discovered above, the parallax method has its limitations. In your experiment above,there was a maximum distance that produced observable shifts1. The maximum distance waslimited by your eyesight and the separation between your eyes. In astronomical circumstanceswe can do a bit better. By using telescopes in space rather than telescopes on the ground, wecan decrease the minimum angular shift we can measure by a factor of ten,
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